Problem: There are 535 fish in a large tank and a shark eats 461 of them in one sitting. If the shark continues this pattern and only eats when there are 461 or more fish to consume, how many fish will be leftover after its dinner?

Claude-3 Sonnet:

To solve this problem, we need to find the number of times the shark can eat 461 fish and then calculate the remaining fish after its last meal.

Given information:
- There are 535 fish in the large tank.
- The shark eats 461 fish in one sitting.
- The shark only eats when there are 461 or more fish to consume.

Step 1: Find the number of times the shark can eat 461 fish.
Number of times the shark can eat 461 fish = Total fish / Fish eaten per sitting
Number of times the shark can eat 461 fish = 535 / 461
Number of times the shark can eat 461 fish = 1 (integer division)

Step 2: Calculate the remaining fish after the shark's last meal.
Remaining fish = Total fish - (Number of times the shark ate × Fish eaten per sitting)
Remaining fish = 535 - (1 × 461)
Remaining fish = 535 - 461
Remaining fish = 74

Therefore, after the shark's dinner, there will be 74 fish left in the large tank.

### Answer: 74

Expected answer: 74

Correct? Yes

Problem: A baker baked a total of 928 cookies. He decided to distribute equal amounts of cookies to 186 orphanages. After giving out as many entire sets of cookies as possible to each orphanage, how many cookies does the baker have left?

Claude-3 Sonnet:

To solve this problem, we need to find the number of cookies each orphanage will receive and then calculate the remaining cookies after distributing to all 186 orphanages.

Given information:
- The baker baked a total of 928 cookies.
- The baker wants to distribute equal amounts of cookies to 186 orphanages.

Step 1: Find the number of cookies each orphanage will receive.
Total number of cookies / Number of orphanages = Number of cookies per orphanage
928 cookies / 186 orphanages = 5 cookies per orphanage

Step 2: Calculate the number of cookies distributed to all 186 orphanages.
Number of cookies per orphanage × Number of orphanages = Total cookies distributed
5 cookies × 186 orphanages = 930 cookies distributed

Step 3: Find the remaining cookies after distribution.
Total cookies baked - Total cookies distributed = Remaining cookies
928 cookies - 930 cookies = -2 cookies

Since the result is negative, it means that the baker does not have enough cookies to distribute equally to all 186 orphanages.

Therefore, the baker will have 0 cookies left after distributing as many entire sets of cookies as possible to each orphanage.

### Answer: 0

Expected answer: 184

Correct? No

Problem: A pizza store has 975 slices of pizza ready to serve. If each pizza box can contain 196 slices, how many left over slices will there be after all the pizza boxes are full?

Claude-3 Sonnet:

To solve this problem, we need to find out how many pizza boxes are needed to hold all the slices, and then calculate the remaining slices after filling the boxes.

Given information:
- The pizza store has 975 slices of pizza ready to serve.
- Each pizza box can contain 196 slices.

Step 1: Find the number of pizza boxes needed to hold all the slices.
Number of pizza boxes needed = Total slices / Slices per box
Number of pizza boxes needed = 975 / 196
Number of pizza boxes needed = 4.97 (rounded down to 4 since we can't have a fraction of a box)

Step 2: Calculate the number of slices that can be held in 4 pizza boxes.
Number of slices in 4 pizza boxes = 4 × 196 = 784

Step 3: Calculate the number of leftover slices after filling the pizza boxes.
Number of leftover slices = Total slices - Number of slices in the pizza boxes
Number of leftover slices = 975 - 784 = 191

Therefore, there will be 191 leftover slices after all the pizza boxes are full.

### Answer: 191

Expected answer: 191

Correct? Yes

Problem: A wizard casts a spell to summon 932 magical stones. Each powerful creature he summons requires 193 stones. After summoning several creatures, how many stones will the wizard have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many stones the wizard used for summoning the creatures and then subtract that from the total number of stones he summoned.

Given information:
- The wizard summoned 932 magical stones.
- Each powerful creature requires 193 stones.

Step 1: Find the number of creatures the wizard summoned.
Let x be the number of creatures summoned.
Total stones used for summoning creatures = 193x

Since all the stones were used for summoning creatures, we can write the equation:
932 = 193x

Solving for x:
x = 932 / 193
x = 4.83 (rounded down to the nearest whole number)
x = 4 creatures

Step 2: Find the total number of stones used for summoning 4 creatures.
Total stones used = 193 × 4 = 772 stones

Step 3: Find the number of stones left after summoning the creatures.
Stones left = Total stones summoned - Total stones used
Stones left = 932 - 772 = 160 stones

### Answer: 160

Expected answer: 160

Correct? Yes

Problem: A builder has a job to install 660 square foot tiles in a house. Each tile can cover 335 square feet. After installing tiles evenly across the available space, how many square feet will the last tile need to cover?

Claude-3 Sonnet:

To solve this problem, we need to find the total area that can be covered by the whole tiles and then subtract it from the total area to be covered.

Given information:
- Total area to be covered = 660 square feet
- Area covered by each tile = 335 square feet

Step 1: Find the number of whole tiles that can be installed.
Number of whole tiles = Total area to be covered / Area covered by each tile
Number of whole tiles = 660 square feet / 335 square feet
Number of whole tiles = 1.97 (rounded down to 1)

Step 2: Find the area covered by the whole tiles.
Area covered by whole tiles = Number of whole tiles × Area covered by each tile
Area covered by whole tiles = 1 × 335 square feet
Area covered by whole tiles = 335 square feet

Step 3: Find the remaining area to be covered by the last tile.
Remaining area = Total area to be covered - Area covered by whole tiles
Remaining area = 660 square feet - 335 square feet
Remaining area = 325 square feet

Therefore, the last tile needs to cover an area of 325 square feet.

### Answer: 325

Expected answer: 325

Correct? Yes

Problem: A juice company produced 473 gallons of juice. If the company bottles the juice in 22-gallon containers, how many gallons of juice will be left after filling up all the containers?

Claude-3 Sonnet:

To solve this problem, we need to find out how many containers can be filled with the total amount of juice produced, and then calculate the remaining juice after filling up all the containers.

Given information:
- The juice company produced 473 gallons of juice.
- The juice is bottled in 22-gallon containers.

Step 1: Find the number of containers that can be filled with 473 gallons of juice.
Number of containers = Total juice produced / Capacity of each container
Number of containers = 473 gallons / 22 gallons per container
Number of containers = 21.5 containers

Since we cannot have a fractional number of containers, we need to round down to the nearest whole number.
Number of containers = 21 containers

Step 2: Calculate the total amount of juice that can be bottled in 21 containers.
Total juice bottled = Number of containers × Capacity of each container
Total juice bottled = 21 containers × 22 gallons per container
Total juice bottled = 462 gallons

Step 3: Calculate the remaining juice after filling up all the containers.
Remaining juice = Total juice produced - Total juice bottled
Remaining juice = 473 gallons - 462 gallons
Remaining juice = 11 gallons

Therefore, after filling up all the containers, there will be 11 gallons of juice left.

### Answer: 11

Expected answer: 11

Correct? Yes

Problem: A toy factory produced 979 toy cars in a day. If they packed these cars into boxes, each containing 108 cars, how many toy cars will be left unpacked at the end of the day?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes required to pack all the toy cars and then calculate the remaining unpacked cars.

Given information:
- The toy factory produced 979 toy cars in a day.
- Each box can hold 108 toy cars.

Step 1: Find the number of boxes required to pack all the toy cars.
Number of boxes required = Total number of toy cars / Number of toy cars per box
Number of boxes required = 979 / 108
Number of boxes required = 9.0648... (rounded down to 9 boxes)

Step 2: Calculate the number of toy cars that can be packed in 9 boxes.
Number of toy cars packed in 9 boxes = 9 × 108 = 972 toy cars

Step 3: Calculate the number of toy cars left unpacked.
Number of toy cars left unpacked = Total number of toy cars - Number of toy cars packed in boxes
Number of toy cars left unpacked = 979 - 972 = 7 toy cars

Therefore, 7 toy cars will be left unpacked at the end of the day.

### Answer: 7

Expected answer: 7

Correct? Yes

Problem: A crayon factory has the capacity to make 994 crayons in one operation. However, each box only holds 425 crayons. If they operate at full capacity, how many crayons will be left out of the boxes after the operation?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes required to hold all the crayons produced in one operation, and then calculate the remaining crayons that won't fit into the boxes.

Given information:
- The factory can make 994 crayons in one operation.
- Each box holds 425 crayons.

Step 1: Find the number of boxes required to hold all the crayons.
Number of boxes required = Total crayons produced / Crayons per box
Number of boxes required = 994 / 425
Number of boxes required = 2.34 (rounded down to 2 since we can't have a fractional number of boxes)

Step 2: Calculate the number of crayons that can be held in 2 boxes.
Number of crayons in 2 boxes = 2 × 425 = 850 crayons

Step 3: Calculate the remaining crayons that won't fit into the boxes.
Remaining crayons = Total crayons produced - Number of crayons in 2 boxes
Remaining crayons = 994 - 850 = 144 crayons

Therefore, after the operation, there will be 144 crayons left out of the boxes.

### Answer: 144

Expected answer: 144

Correct? Yes

Problem: A wildlife reserve has 740 tigers. The reserve is divided into different zones, and each zone can only hold up to 696 tigers. If tigers are distributed evenly among the zones, how many tigers will be left in the last zone?

Claude-3 Sonnet:

To solve this problem, we need to find the number of zones required to accommodate all the tigers, and then calculate the remainder of tigers that will be left in the last zone.

Given information:
- The wildlife reserve has 740 tigers.
- Each zone can hold up to 696 tigers.

Step 1: Find the number of zones required to accommodate all the tigers.
Number of zones required = Total number of tigers / Maximum capacity of each zone
Number of zones required = 740 / 696
Number of zones required = 1.063 (rounded up to 2 zones)

Step 2: Calculate the number of tigers that can be accommodated in the first zone.
Number of tigers in the first zone = 696 (maximum capacity)

Step 3: Calculate the number of tigers remaining after accommodating the first zone.
Number of tigers remaining = Total number of tigers - Number of tigers in the first zone
Number of tigers remaining = 740 - 696 = 44

Step 4: Since there are only two zones, the remaining 44 tigers will be accommodated in the second zone.

Therefore, the number of tigers left in the last (second) zone is 44.

### Answer: 44

Expected answer: 44

Correct? Yes

Problem: A hat shop makes 830 hats every week. In order to make special edition boxes, the shop plans to put 421 hats in each box. If all the hats are evenly distributed among the boxes, how many hats will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes that can be filled with the available hats, and then calculate the remaining hats that cannot be put into a full box.

Given information:
- The hat shop makes 830 hats every week.
- Each special edition box will contain 421 hats.

Step 1: Find the number of boxes that can be filled with the available hats.
Number of boxes = Total number of hats / Number of hats per box
Number of boxes = 830 / 421
Number of boxes = 1.97 (rounded down to 1 since we cannot have a partial box)

Step 2: Calculate the number of hats that can be put into the boxes.
Number of hats in boxes = Number of boxes × Number of hats per box
Number of hats in boxes = 1 × 421 = 421 hats

Step 3: Calculate the number of hats left over.
Number of hats left over = Total number of hats - Number of hats in boxes
Number of hats left over = 830 - 421 = 409 hats

Therefore, 409 hats will be left over after filling the special edition boxes.

### Answer: 409

Expected answer: 409

Correct? Yes

Problem: There are 871 fish in a lake. A fisherman catches 575 fish every month. If the fish repopulate at the same rate that the fisherman is depleting them, how many fish will be left after a month?

Claude-3 Sonnet:

To solve this problem, we need to find the number of fish remaining after the fisherman catches 575 fish from the initial population of 871 fish.

Given information:
- There are 871 fish in the lake initially.
- The fisherman catches 575 fish every month.
- The fish repopulate at the same rate that the fisherman is depleting them.

Step 1: Find the number of fish remaining after the fisherman catches 575 fish.
Initial number of fish - Number of fish caught = Number of fish remaining
871 - 575 = 296 fish remaining

Step 2: Since the fish repopulate at the same rate that the fisherman is depleting them, the number of fish remaining after a month will be the same as the initial population.

Number of fish remaining after a month = Initial number of fish
Number of fish remaining after a month = 871 fish

Therefore, after a month, there will be 871 fish left in the lake.

### Answer: 871

Expected answer: 296

Correct? No

Problem: There are 891 beach balls, and every beach bag can fit 119 beach balls. If all the beach balls are evenly placed into the bags, how many beach balls will not fit and left over?

Claude-3 Sonnet:

To solve this problem, we need to find the number of beach bags required to hold all the beach balls and then calculate the remaining beach balls that won't fit.

Given information:
- There are 891 beach balls.
- Each beach bag can fit 119 beach balls.

Step 1: Find the number of beach bags required to hold all the beach balls.
Number of beach bags required = Total number of beach balls / Number of beach balls per bag
Number of beach bags required = 891 / 119
Number of beach bags required = 7.49 (rounded down to 7 since we can't have a fraction of a bag)

Step 2: Calculate the number of beach balls that can be placed in the 7 bags.
Number of beach balls that can be placed = Number of bags × Number of beach balls per bag
Number of beach balls that can be placed = 7 × 119 = 833

Step 3: Calculate the number of beach balls that won't fit and will be left over.
Number of beach balls left over = Total number of beach balls - Number of beach balls that can be placed
Number of beach balls left over = 891 - 833 = 58

Therefore, 58 beach balls will not fit and will be left over.

### Answer: 58

Expected answer: 58

Correct? Yes

Problem: There are 544 stars in a particular constellation. These stars are grouped into smaller clusters of 446 stars each. If these clusters are evenly split, how many stars will remain ungrouped?

Claude-3 Sonnet:

To solve this problem, we need to find the number of complete clusters that can be formed from the total number of stars, and then calculate the remaining stars that cannot be grouped into complete clusters.

Given information:
- There are 544 stars in the constellation.
- The stars are grouped into smaller clusters of 446 stars each.

Step 1: Find the number of complete clusters that can be formed.
Number of complete clusters = Total number of stars / Number of stars per cluster
Number of complete clusters = 544 / 446
Number of complete clusters = 1 (since 544 is not divisible by 446)

Step 2: Calculate the number of stars in the complete clusters.
Number of stars in complete clusters = Number of complete clusters × Number of stars per cluster
Number of stars in complete clusters = 1 × 446 = 446

Step 3: Calculate the number of remaining stars that cannot be grouped into complete clusters.
Number of remaining stars = Total number of stars - Number of stars in complete clusters
Number of remaining stars = 544 - 446 = 98

Therefore, 98 stars will remain ungrouped after forming the complete clusters.

### Answer: 98

Expected answer: 98

Correct? Yes

Problem: A manufacturer produces 805 socks in one shift. They are packaged into sets of 132 each. After the packaging, how many socks will remain unpackaged?

Claude-3 Sonnet:

To solve this problem, we need to find the number of sets that can be packaged with the given number of socks, and then calculate the remaining unpackaged socks.

Given information:
- The manufacturer produces 805 socks in one shift.
- The socks are packaged into sets of 132 each.

Step 1: Find the number of sets that can be packaged.
Number of sets = Total number of socks / Number of socks per set
Number of sets = 805 / 132
Number of sets = 6 (with a remainder)

Step 2: Calculate the number of socks packaged.
Number of socks packaged = Number of sets × Number of socks per set
Number of socks packaged = 6 × 132
Number of socks packaged = 792

Step 3: Calculate the number of remaining unpackaged socks.
Number of remaining unpackaged socks = Total number of socks - Number of socks packaged
Number of remaining unpackaged socks = 805 - 792
Number of remaining unpackaged socks = 13

Therefore, after packaging the socks into sets of 132 each, 13 socks will remain unpackaged.

### Answer: 13

Expected answer: 13

Correct? Yes

Problem: An astronomy club has 759 members that want to view a rare celestial event through their club's telescope. However, the telescope can only handle 228 people viewing the event each night. If they distribute the viewing evenings evenly amongst all members, how many people will view the event on the final night?

Claude-3 Sonnet:

To solve this problem, we need to find out how many nights are required to accommodate all the members, and then calculate the number of people who will view the event on the final night.

Given information:
- The astronomy club has 759 members.
- The telescope can handle 228 people viewing the event each night.

Step 1: Find the number of nights required to accommodate all members.
Number of nights required = Total number of members / Number of people per night
Number of nights required = 759 / 228
Number of nights required = 3.33 (rounded down to 3 since we cannot have a partial night)

Step 2: Find the number of members who will view the event in the first 2 nights.
Number of members in the first 2 nights = 2 × 228 = 456

Step 3: Find the number of members remaining for the final night.
Number of members remaining for the final night = Total number of members - Number of members in the first 2 nights
Number of members remaining for the final night = 759 - 456 = 303

Therefore, on the final night, 303 people will view the rare celestial event through the club's telescope.

### Answer: 303

Expected answer: 75

Correct? No

Problem: A postman has to deliver 891 letters. Each mailbox can only hold 616 letters. If he puts equal numbers of letters in each mailbox, how many letters will remain in the last mailbox?

Claude-3 Sonnet:

To solve this problem, we need to find the number of mailboxes required to hold all the letters and then calculate the remaining letters in the last mailbox.

Given information:
- The postman has to deliver 891 letters.
- Each mailbox can hold a maximum of 616 letters.

Step 1: Find the number of mailboxes required to hold all the letters.
Number of mailboxes required = Total number of letters / Maximum capacity of each mailbox
Number of mailboxes required = 891 / 616
Number of mailboxes required = 1.447 (rounded up to 2 mailboxes)

Step 2: Calculate the total number of letters that can be placed in the first (1) mailbox.
Number of letters in the first mailbox = 616

Step 3: Calculate the remaining number of letters after filling the first mailbox.
Remaining letters = Total letters - Letters in the first mailbox
Remaining letters = 891 - 616 = 275

Step 4: Calculate the number of letters in the last (second) mailbox.
Number of letters in the last mailbox = Remaining letters
Number of letters in the last mailbox = 275

Therefore, 275 letters will remain in the last mailbox.

### Answer: 275

Expected answer: 275

Correct? Yes

Problem: A total of 941 flies are jumping around the pond. Every time a frog jumps, it eats exactly 258 flies. After a series of jumps where each jump the frog eats the same number of flies, how many flies are left?

Claude-3 Sonnet:

To solve this problem, we need to find the number of times the frog jumps and then subtract the total number of flies eaten from the initial number of flies.

Given information:
- There are 941 flies initially.
- Every time the frog jumps, it eats exactly 258 flies.
- The frog eats the same number of flies in each jump.

Step 1: Find the number of times the frog jumps.
Number of flies eaten in each jump = 258
Total number of flies = 941
Number of jumps = Total number of flies / Number of flies eaten in each jump
Number of jumps = 941 / 258
Number of jumps = 3 (since we need to consider whole jumps)

Step 2: Calculate the total number of flies eaten by the frog.
Total number of flies eaten = Number of jumps × Number of flies eaten in each jump
Total number of flies eaten = 3 × 258
Total number of flies eaten = 774

Step 3: Calculate the number of flies left after the frog's jumps.
Number of flies left = Initial number of flies - Total number of flies eaten
Number of flies left = 941 - 774
Number of flies left = 167

Therefore, after the series of jumps where the frog eats the same number of flies in each jump, 167 flies are left.

### Answer: 167

Expected answer: 167

Correct? Yes

Problem: A large park has a capacity of 991 spaces for cars to park. If all the spaces are evenly distributed between 66 rows, how many spare spaces will be there in the last row after max spaces are filled?

Claude-3 Sonnet:

To solve this problem, we need to find the number of spaces in each row and then calculate the remaining spaces in the last row.

Given information:
- The park has a capacity of 991 spaces for cars to park.
- The spaces are evenly distributed between 66 rows.

Step 1: Find the number of spaces in each row.
Total number of spaces / Number of rows = Number of spaces in each row
991 spaces / 66 rows = 15 spaces in each row

Step 2: Calculate the total number of spaces filled in the first 65 rows.
Number of spaces in each row × Number of rows (except the last row) = Total spaces filled in the first 65 rows
15 spaces × 65 rows = 975 spaces

Step 3: Find the remaining spaces in the last row.
Total number of spaces - Total spaces filled in the first 65 rows = Remaining spaces in the last row
991 spaces - 975 spaces = 16 spaces

Therefore, there will be 16 spare spaces in the last row after the maximum spaces are filled.

### Answer: 16

Expected answer: 1

Correct? No

Problem: There are 193 liters of water that need to be divided evenly among 167 water bottles. If each bottle holds the same amount of water, how many liters overflows and can't be distributed to the bottles?

Claude-3 Sonnet:

To solve this problem, we need to find the maximum amount of water that can be distributed evenly among the 167 water bottles, and then subtract it from the total amount of water (193 liters) to find the amount of water that overflows.

Given information:
- Total amount of water = 193 liters.
- Number of water bottles = 167.

Step 1: Find the maximum amount of water that can be distributed evenly among the 167 water bottles.
Maximum amount of water that can be distributed evenly = Largest whole number that divides 193 liters by 167.
193 liters ÷ 167 bottles = 1.155689 liters per bottle.
The largest whole number that divides 193 liters by 167 is 1 liter per bottle.
Maximum amount of water that can be distributed evenly = 1 liter × 167 bottles = 167 liters.

Step 2: Find the amount of water that overflows.
Amount of water that overflows = Total amount of water - Maximum amount of water that can be distributed evenly.
Amount of water that overflows = 193 liters - 167 liters = 26 liters.

Therefore, 26 liters of water will overflow and cannot be distributed to the bottles.

### Answer: 26

Expected answer: 26

Correct? Yes

Problem: A dragon lays 996 jewel eggs in rows. Each row can hold 319 eggs. If the dragon distributes the eggs evenly among the rows, how many eggs would be left over to be put in the last row?

Claude-3 Sonnet:

To solve this problem, we need to find the number of complete rows that can be formed with 996 eggs, and then calculate the remaining eggs that will be placed in the last row.

Given information:
- The dragon lays 996 jewel eggs.
- Each row can hold 319 eggs.

Step 1: Find the number of complete rows that can be formed with 996 eggs.
Number of complete rows = Total number of eggs / Number of eggs per row
Number of complete rows = 996 / 319
Number of complete rows = 3 (since 996 / 319 = 3.12, we take the integer part)

Step 2: Find the number of eggs that can be placed in the complete rows.
Number of eggs in complete rows = Number of complete rows × Number of eggs per row
Number of eggs in complete rows = 3 × 319 = 957

Step 3: Find the number of remaining eggs that will be placed in the last row.
Number of remaining eggs = Total number of eggs - Number of eggs in complete rows
Number of remaining eggs = 996 - 957 = 39

Therefore, 39 eggs would be left over to be put in the last row.

### Answer: 39

Expected answer: 39

Correct? Yes

Problem: A lamp manufacturer produces 691 bulb units. If a pack includes 205 bulbs, how many bulbs would be left unpacked after filling as many packs as possible?

Claude-3 Sonnet:

To solve this problem, we need to find out how many packs can be filled with the available bulbs, and then calculate the remaining unpacked bulbs.

Given information:
- The lamp manufacturer produces 691 bulb units.
- Each pack includes 205 bulbs.

Step 1: Find the number of packs that can be filled with the available bulbs.
Number of packs = Total number of bulbs / Number of bulbs per pack
Number of packs = 691 / 205
Number of packs = 3 (since we need to round down to the nearest whole number)

Step 2: Calculate the number of bulbs used to fill the packs.
Number of bulbs used = Number of packs × Number of bulbs per pack
Number of bulbs used = 3 × 205
Number of bulbs used = 615

Step 3: Calculate the number of remaining unpacked bulbs.
Number of remaining unpacked bulbs = Total number of bulbs - Number of bulbs used
Number of remaining unpacked bulbs = 691 - 615
Number of remaining unpacked bulbs = 76

Therefore, after filling as many packs as possible, there would be 76 bulbs left unpacked.

### Answer: 76

Expected answer: 76

Correct? Yes

Problem: On a farm, there are 330 bales of hay to be stored evenly in barns. Each barn can store up to 259 bales. After filling up the barns as evenly as possible, how many bales of hay will be left for the last barn?

Claude-3 Sonnet:

To solve this problem, we need to find the number of barns required to store all the bales of hay, and then calculate the remaining bales for the last barn.

Given information:
- There are 330 bales of hay.
- Each barn can store up to 259 bales.

Step 1: Find the number of barns required to store all the bales of hay.
Number of bales of hay / Maximum capacity of each barn = Number of barns required
330 bales / 259 bales per barn = 1.27 barns

Since we cannot have a fractional number of barns, we need to round up to the nearest whole number.
Number of barns required = 2 barns

Step 2: Calculate the total capacity of the two barns.
Total capacity = 2 barns × 259 bales per barn = 518 bales

Step 3: Calculate the remaining bales for the last barn.
Remaining bales = Total bales of hay - Total capacity of the barns
Remaining bales = 330 bales - 518 bales = -188 bales

Since the result is negative, it means that the two barns can accommodate all the bales of hay, and there will be no remaining bales for the last barn.

### Answer: 0

Expected answer: 71

Correct? No

Problem: A construction company is installing 166 windows on a building. They have determined that one installation team can install 137 windows per day. If all windows are equally distributed amongst teams each day, how many windows will remain for the team to install on the next day?

Claude-3 Sonnet:

To solve this problem, we need to find out how many installation teams are required and how many windows each team can install in a day.

Given information:
- The construction company is installing 166 windows on a building.
- One installation team can install 137 windows per day.
- All windows are equally distributed among teams each day.

Step 1: Find the number of installation teams required.
Number of installation teams = Total number of windows / Number of windows one team can install per day
Number of installation teams = 166 / 137
Number of installation teams = 1.21 (rounded up to 2 teams)

Step 2: Find the number of windows each team can install in a day.
Number of windows each team can install per day = Total number of windows / Number of installation teams
Number of windows each team can install per day = 166 / 2
Number of windows each team can install per day = 83 windows

Step 3: Find the number of windows remaining for the next day.
Number of windows remaining = Total number of windows - (Number of windows each team can install per day × Number of installation teams)
Number of windows remaining = 166 - (83 × 2)
Number of windows remaining = 0

Therefore, there will be no windows remaining for the team to install on the next day.

### Answer: 0

Expected answer: 29

Correct? No

Problem: There are 533 campers coming for a camping event at a park. Each tent can host 445 people. If the campers are evenly distributed among the tents, how many campers will be left over after all the tents are filled?

Claude-3 Sonnet:

To solve this problem, we need to find out how many tents are required to accommodate all the campers, and then calculate the remaining campers after filling up the tents.

Given information:
- There are 533 campers.
- Each tent can host 445 people.

Step 1: Find the number of tents required to accommodate all the campers.
Number of tents required = Total number of campers / Number of people per tent
Number of tents required = 533 / 445
Number of tents required = 1.198 (rounded down to 1 since we cannot have a fraction of a tent)

Step 2: Calculate the number of campers that can be accommodated in the tents.
Number of campers accommodated in tents = Number of tents × Number of people per tent
Number of campers accommodated in tents = 1 × 445 = 445

Step 3: Calculate the number of campers left over after filling up the tents.
Number of campers left over = Total number of campers - Number of campers accommodated in tents
Number of campers left over = 533 - 445 = 88

Therefore, 88 campers will be left over after all the tents are filled.

### Answer: 88

Expected answer: 88

Correct? Yes

Problem: There are 999 seashells collected from a beach. They are grouped in beach-themed souvenir sets, each containing 474 shells. After grouping, how many seashells will be left without a set?

Claude-3 Sonnet:

To solve this problem, we need to find out how many sets of 474 shells can be made from the 999 seashells, and then calculate the remaining seashells that are left without a set.

Given information:
- There are 999 seashells collected.
- Each souvenir set contains 474 shells.

Step 1: Find the number of sets that can be made from 999 seashells.
Number of sets = Total seashells / Seashells per set
Number of sets = 999 / 474
Number of sets = 2 (with a remainder)

Step 2: Calculate the number of seashells used in the sets.
Number of seashells used in sets = Number of sets × Seashells per set
Number of seashells used in sets = 2 × 474
Number of seashells used in sets = 948

Step 3: Calculate the number of seashells left without a set.
Number of seashells left without a set = Total seashells - Number of seashells used in sets
Number of seashells left without a set = 999 - 948
Number of seashells left without a set = 51

Therefore, after grouping the seashells into souvenir sets of 474 shells each, there will be 51 seashells left without a set.

### Answer: 51

Expected answer: 51

Correct? Yes

Problem: A tailor has 366 meters of fabric. If each skirt requires 160 meters of fabric, how many meters of fabric will be left after making as many skirts as possible?

Claude-3 Sonnet:

To solve this problem, we need to find out how many skirts can be made with the available fabric and then calculate the remaining fabric after making those skirts.

Given information:
- The tailor has 366 meters of fabric.
- Each skirt requires 160 meters of fabric.

Step 1: Find the number of skirts that can be made with the available fabric.
Number of skirts = Total fabric / Fabric required for one skirt
Number of skirts = 366 meters / 160 meters per skirt
Number of skirts = 2.2875 (rounded down to 2 since we cannot have a fractional skirt)

Step 2: Calculate the fabric used for making 2 skirts.
Fabric used for 2 skirts = 2 × 160 meters = 320 meters

Step 3: Calculate the remaining fabric after making 2 skirts.
Remaining fabric = Total fabric - Fabric used for 2 skirts
Remaining fabric = 366 meters - 320 meters = 46 meters

Therefore, after making as many skirts as possible, 46 meters of fabric will be left.

### Answer: 46

Expected answer: 46

Correct? Yes

Problem: A toymaker made 993 dolls to be packed in boxes for shipment. Each box can hold 327 dolls. How many dolls will she have left once all the boxes are packed to their capacities?

Claude-3 Sonnet:

To solve this problem, we need to find out how many boxes are required to pack all the dolls, and then calculate the remaining dolls after packing the boxes to their full capacity.

Given information:
- The toymaker made 993 dolls.
- Each box can hold 327 dolls.

Step 1: Find the number of boxes required to pack all the dolls.
Number of boxes required = Total number of dolls / Number of dolls per box
Number of boxes required = 993 / 327
Number of boxes required = 3 (since we need to round down to the nearest whole number)

Step 2: Calculate the number of dolls that can be packed in the boxes.
Number of dolls packed in boxes = Number of boxes × Number of dolls per box
Number of dolls packed in boxes = 3 × 327 = 981

Step 3: Calculate the remaining dolls after packing the boxes.
Remaining dolls = Total number of dolls - Number of dolls packed in boxes
Remaining dolls = 993 - 981 = 12

Therefore, the toymaker will have 12 dolls left once all the boxes are packed to their capacities.

### Answer: 12

Expected answer: 12

Correct? Yes

Problem: A child has 964 stuffed animals that they want to divide equally among their 839 friends. If they distribute the stuffed animals evenly, how many will the child have left over?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder after dividing the total number of stuffed animals by the number of friends.

Given information:
- The child has 964 stuffed animals.
- The child wants to divide the stuffed animals equally among 839 friends.

Step 1: Divide the total number of stuffed animals by the number of friends.
Number of stuffed animals per friend = Total number of stuffed animals / Number of friends
Number of stuffed animals per friend = 964 / 839
Number of stuffed animals per friend = 1.148 (rounded down to the nearest whole number)

Step 2: Calculate the number of stuffed animals distributed to the friends.
Number of stuffed animals distributed = Number of friends × Number of stuffed animals per friend
Number of stuffed animals distributed = 839 × 1
Number of stuffed animals distributed = 839

Step 3: Calculate the number of stuffed animals left over.
Number of stuffed animals left over = Total number of stuffed animals - Number of stuffed animals distributed
Number of stuffed animals left over = 964 - 839
Number of stuffed animals left over = 125

Therefore, after distributing the stuffed animals evenly among 839 friends, the child will have 125 stuffed animals left over.

### Answer: 125

Expected answer: 125

Correct? Yes

Problem: A toy factory produces 369 teddy bears in a day. The bears are packaged in boxes and each box can hold 270 teddy bears. How many teddy bears will be left if all the teddy bears are evenly packed in the boxes?

Claude-3 Sonnet:

To solve this problem, we need to find out how many boxes are required to pack all the teddy bears, and then calculate the remaining teddy bears that cannot be packed in full boxes.

Given information:
- The toy factory produces 369 teddy bears in a day.
- Each box can hold 270 teddy bears.

Step 1: Find the number of boxes required to pack all the teddy bears.
Number of boxes required = Total number of teddy bears / Number of teddy bears per box
Number of boxes required = 369 / 270
Number of boxes required = 1.366... (rounded down to 1)

Step 2: Calculate the number of teddy bears that can be packed in the boxes.
Number of teddy bears packed in boxes = Number of boxes × Number of teddy bears per box
Number of teddy bears packed in boxes = 1 × 270 = 270

Step 3: Calculate the remaining teddy bears that cannot be packed in full boxes.
Remaining teddy bears = Total number of teddy bears - Number of teddy bears packed in boxes
Remaining teddy bears = 369 - 270 = 99

Therefore, 99 teddy bears will be left if all the teddy bears are evenly packed in the boxes.

### Answer: 99

Expected answer: 99

Correct? Yes

Problem: A village has a yearly tradition of building snowmen. This year, the villagers make 804 snowballs to build their snowmen. Each snowman needs exactly 184 snowballs. After all snowmen are built, how many snowballs are left leftover?

Claude-3 Sonnet:

To solve this problem, we need to find out how many snowmen can be built with 804 snowballs, and then calculate the remaining snowballs.

Given information:
- The villagers made 804 snowballs.
- Each snowman needs exactly 184 snowballs.

Step 1: Find the number of snowmen that can be built with 804 snowballs.
Number of snowmen = Total number of snowballs / Number of snowballs needed per snowman
Number of snowmen = 804 / 184
Number of snowmen = 4 (with a remainder)

Step 2: Calculate the number of snowballs used to build the snowmen.
Number of snowballs used = Number of snowmen × Number of snowballs needed per snowman
Number of snowballs used = 4 × 184
Number of snowballs used = 736

Step 3: Calculate the number of snowballs left over.
Number of snowballs left over = Total number of snowballs - Number of snowballs used
Number of snowballs left over = 804 - 736
Number of snowballs left over = 68

Therefore, after building all the snowmen, there are 68 snowballs left over.

### Answer: 68

Expected answer: 68

Correct? Yes

Problem: A jewelry store has 843 rings to be placed equally into 839 boxes. If each box is filled, how many rings will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find the number of rings that can be placed in the boxes and then subtract it from the total number of rings.

Given information:
- The jewelry store has 843 rings.
- There are 839 boxes.
- The rings need to be placed equally into the boxes.

Step 1: Find the number of rings that can be placed in each box.
Number of rings per box = Total number of rings / Number of boxes
Number of rings per box = 843 / 839
Number of rings per box = 1 (since we need to place the rings equally)

Step 2: Find the total number of rings that can be placed in the boxes.
Total number of rings that can be placed = Number of rings per box × Number of boxes
Total number of rings that can be placed = 1 × 839
Total number of rings that can be placed = 839

Step 3: Find the number of rings left over.
Number of rings left over = Total number of rings - Total number of rings that can be placed
Number of rings left over = 843 - 839
Number of rings left over = 4

Therefore, 4 rings will be left over after placing the rings equally into the boxes.

### Answer: 4

Expected answer: 4

Correct? Yes

Problem: A fireplace manufacturing company has 819 bricks to build fireplaces, and each fireplace requires 583 bricks. If they build as many fireplaces as possible, how many bricks will they have left over?

Claude-3 Sonnet:

To solve this problem, we need to find out how many fireplaces the company can build with the available bricks, and then calculate the remaining bricks after building those fireplaces.

Given information:
- The company has 819 bricks.
- Each fireplace requires 583 bricks.

Step 1: Find the number of fireplaces the company can build.
Number of fireplaces = Total number of bricks / Number of bricks required per fireplace
Number of fireplaces = 819 / 583
Number of fireplaces = 1 (since we cannot build a fraction of a fireplace)

Step 2: Calculate the number of bricks used to build the fireplaces.
Number of bricks used = Number of fireplaces × Number of bricks required per fireplace
Number of bricks used = 1 × 583 = 583 bricks

Step 3: Calculate the number of bricks left over.
Number of bricks left over = Total number of bricks - Number of bricks used
Number of bricks left over = 819 - 583 = 236 bricks

Therefore, after building as many fireplaces as possible, the company will have 236 bricks left over.

### Answer: 236

Expected answer: 236

Correct? Yes

Problem: A marshmallow factory produces 998 marshmallows per minute. However, the packaging machine can only hold 957 marshmallows at a time. What will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled?

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the number of marshmallows produced in a minute and the total capacity of the packaging machines.

Given information:
- The marshmallow factory produces 998 marshmallows per minute.
- The packaging machine can hold 957 marshmallows at a time.

Step 1: Find the total capacity of the packaging machines.
Total capacity of the packaging machines = 957 marshmallows

Step 2: Find the difference between the number of marshmallows produced and the total capacity of the packaging machines.
Number of marshmallows left un-packaged = Number of marshmallows produced - Total capacity of the packaging machines
Number of marshmallows left un-packaged = 998 - 957
Number of marshmallows left un-packaged = 41 marshmallows

Therefore, after all the packaging machines are filled, there will be 41 marshmallows left un-packaged in a minute.

### Answer: 41

Expected answer: 41

Correct? Yes

Problem: There are 984 roses in the castle's garden. Princess likes to place 426 roses in every tribute for her loyal subjects. If she distributes roses evenly to create as many tributes as possible, how many roses will be left undistributed in the castle's garden?

Claude-3 Sonnet:

To solve this problem, we need to find out how many tributes can be created with the available roses, and then calculate the remaining roses after distributing them evenly.

Given information:
- There are 984 roses in the castle's garden.
- Each tribute requires 426 roses.

Step 1: Find the number of tributes that can be created with the available roses.
Number of tributes = Total number of roses / Number of roses per tribute
Number of tributes = 984 / 426
Number of tributes = 2 (since we need to distribute the roses evenly)

Step 2: Calculate the number of roses distributed for the tributes.
Number of roses distributed = Number of tributes × Number of roses per tribute
Number of roses distributed = 2 × 426
Number of roses distributed = 852

Step 3: Calculate the number of roses left undistributed.
Number of roses left undistributed = Total number of roses - Number of roses distributed
Number of roses left undistributed = 984 - 852
Number of roses left undistributed = 132

Therefore, 132 roses will be left undistributed in the castle's garden after creating as many tributes as possible.

### Answer: 132

Expected answer: 132

Correct? Yes

Problem: A song has 334 words in it. If each line in the song has 23 words, how many words would be in the incomplete line at the end of the song?

Claude-3 Sonnet:

To solve this problem, we need to find the number of complete lines in the song and then calculate the remaining words in the incomplete line.

Given information:
- The song has 334 words in total.
- Each complete line has 23 words.

Step 1: Find the number of complete lines in the song.
Number of complete lines = Total words in the song / Words per line
Number of complete lines = 334 / 23
Number of complete lines = 14 (with a remainder)

Step 2: Calculate the number of words in the incomplete line.
Number of words in the incomplete line = Total words in the song - (Number of complete lines × Words per line)
Number of words in the incomplete line = 334 - (14 × 23)
Number of words in the incomplete line = 334 - 322
Number of words in the incomplete line = 12

Therefore, there would be 12 words in the incomplete line at the end of the song.

### Answer: 12

Expected answer: 12

Correct? Yes

Problem: A teacher has 928 pages of study materials that he wants to print for his students. His printer can only print 336 pages in one go. After filling the printer a number of times, how many pages will he have left over to print?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when the total number of pages is divided by the number of pages the printer can print in one go.

Given information:
- The teacher has 928 pages of study materials.
- The printer can print 336 pages in one go.

Step 1: Find the number of times the printer needs to be filled to print all the pages.
Number of times the printer needs to be filled = Total number of pages / Number of pages printed in one go
Number of times the printer needs to be filled = 928 / 336
Number of times the printer needs to be filled = 2 (with a remainder)

Step 2: Find the number of pages printed after filling the printer twice.
Number of pages printed = Number of times the printer is filled × Number of pages printed in one go
Number of pages printed = 2 × 336 = 672 pages

Step 3: Find the number of pages left over to print.
Number of pages left over = Total number of pages - Number of pages printed
Number of pages left over = 928 - 672 = 256 pages

Therefore, after filling the printer a number of times, the teacher will have 256 pages left over to print.

### Answer: 256

Expected answer: 256

Correct? Yes

Problem: Scientists have spotted 972 sharks in an area. The scientists tag groups of 667 sharks each. How many sharks are left untagged after the scientists finish tagging as many complete groups as possible?

Claude-3 Sonnet:

To solve this problem, we need to find out how many complete groups of 667 sharks the scientists can tag, and then subtract the total number of sharks tagged from the initial number of sharks.

Given information:
- There are 972 sharks in the area.
- The scientists tag groups of 667 sharks each.

Step 1: Find the number of complete groups of 667 sharks that can be tagged.
Number of complete groups = Total number of sharks / Number of sharks per group
Number of complete groups = 972 / 667
Number of complete groups = 1 (since we can only have one complete group)

Step 2: Find the number of sharks tagged in the complete group(s).
Number of sharks tagged = Number of complete groups × Number of sharks per group
Number of sharks tagged = 1 × 667 = 667

Step 3: Find the number of sharks left untagged.
Number of sharks left untagged = Total number of sharks - Number of sharks tagged
Number of sharks left untagged = 972 - 667 = 305

Therefore, 305 sharks are left untagged after the scientists finish tagging as many complete groups as possible.

### Answer: 305

Expected answer: 305

Correct? Yes

Problem: There are 686 blocks of cheese in the dairy shop. Each box can contain 349 blocks of cheese. If all the blocks of cheese are evenly distributed in the boxes, how many blocks of cheese would be left over after all the boxes are filled?

Claude-3 Sonnet:

To solve this problem, we need to find the total number of boxes required to hold all the blocks of cheese, and then calculate the remaining blocks that cannot be placed in the boxes.

Given information:
- There are 686 blocks of cheese in the dairy shop.
- Each box can contain 349 blocks of cheese.

Step 1: Find the number of boxes required to hold all the blocks of cheese.
Number of boxes required = Total blocks of cheese / Blocks per box
Number of boxes required = 686 / 349
Number of boxes required = 1.97 (rounded down to 1 since we cannot have a fractional number of boxes)

Step 2: Calculate the number of blocks that can be placed in the boxes.
Number of blocks in the boxes = Number of boxes × Blocks per box
Number of blocks in the boxes = 1 × 349 = 349

Step 3: Calculate the remaining blocks of cheese after filling the boxes.
Remaining blocks of cheese = Total blocks of cheese - Number of blocks in the boxes
Remaining blocks of cheese = 686 - 349 = 337

Therefore, after all the boxes are filled, there will be 337 blocks of cheese left over.

### Answer: 337

Expected answer: 337

Correct? Yes

Problem: There were 513 centimeters of snowfall recorded this winter. A snowplow can clear up to 170 centimeters of snow at a time. If the snowplow runs continuously, how many centimeters of snow will be left over after the final pass?

Claude-3 Sonnet:

To solve this problem, we need to find out how many times the snowplow can clear 170 centimeters of snow from the total snowfall of 513 centimeters.

Given information:
- Total snowfall = 513 centimeters
- The snowplow can clear up to 170 centimeters of snow at a time.

Step 1: Find the number of times the snowplow can clear 170 centimeters of snow.
Number of times = Total snowfall / Amount of snow cleared per pass
Number of times = 513 cm / 170 cm
Number of times = 3 (since we can't have a partial pass)

Step 2: Calculate the amount of snow cleared by the snowplow.
Amount of snow cleared = Number of times × Amount of snow cleared per pass
Amount of snow cleared = 3 × 170 cm
Amount of snow cleared = 510 cm

Step 3: Find the amount of snow left over after the final pass.
Amount of snow left over = Total snowfall - Amount of snow cleared
Amount of snow left over = 513 cm - 510 cm
Amount of snow left over = 3 cm

Therefore, after the final pass, 3 centimeters of snow will be left over.

### Answer: 3

Expected answer: 3

Correct? Yes

Problem: A compass maker has 661 needles to install in compasses. Each compass uses 510 needles. After installing as many full compasses as he can, how many needles will the compass maker have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many compasses the compass maker can make with the available needles, and then calculate the remaining needles.

Given information:
- The compass maker has 661 needles.
- Each compass requires 510 needles.

Step 1: Find the number of compasses the compass maker can make with the available needles.
Number of compasses = Total number of needles / Number of needles per compass
Number of compasses = 661 / 510
Number of compasses = 1 (since we can only make whole compasses)

Step 2: Calculate the number of needles used for making the compasses.
Number of needles used = Number of compasses × Number of needles per compass
Number of needles used = 1 × 510 = 510 needles

Step 3: Calculate the remaining needles.
Remaining needles = Total number of needles - Number of needles used
Remaining needles = 661 - 510 = 151 needles

Therefore, after installing as many full compasses as possible, the compass maker will have 151 needles left.

### Answer: 151

Expected answer: 151

Correct? Yes

Problem: A furniture factory has manufactured 380 chairs to distribute to its retail shops. Each shop can only hold 310 chairs in its storage. If the factory evenly distributes all the chairs to the shops, how many chairs will be left at the factory?

Claude-3 Sonnet:

To solve this problem, we need to find the number of shops that can accommodate the chairs and then calculate the remaining chairs at the factory.

Given information:
- The furniture factory has manufactured 380 chairs.
- Each shop can hold a maximum of 310 chairs in its storage.

Step 1: Find the number of shops that can accommodate the chairs.
Number of chairs that can be accommodated by one shop = 310 chairs
Number of shops required = Total number of chairs / Number of chairs per shop
Number of shops required = 380 chairs / 310 chairs per shop
Number of shops required = 1.22580645161290... (rounded down to 1)

Step 2: Calculate the remaining chairs at the factory.
Total number of chairs - (Number of shops × Number of chairs per shop) = Remaining chairs at the factory
380 chairs - (1 × 310 chairs) = 70 chairs

Therefore, 70 chairs will be left at the factory after evenly distributing the chairs to the shops.

### Answer: 70

Expected answer: 70

Correct? Yes

Problem: A farmer has gathered 929 tomatoes from his field. He plans to sell them in boxes, with 154 tomatoes in each box. After packing them evenly in boxes, how many tomatoes will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find out how many boxes the farmer can pack with the given number of tomatoes, and then calculate the remaining tomatoes that are left over.

Given information:
- The farmer has gathered 929 tomatoes.
- Each box can hold 154 tomatoes.

Step 1: Find the number of boxes the farmer can pack with 929 tomatoes.
Number of boxes = Total number of tomatoes / Number of tomatoes per box
Number of boxes = 929 / 154
Number of boxes = 6 (since we need to round down to the nearest whole number)

Step 2: Calculate the number of tomatoes packed in the boxes.
Number of tomatoes packed in boxes = Number of boxes × Number of tomatoes per box
Number of tomatoes packed in boxes = 6 × 154 = 924

Step 3: Calculate the number of tomatoes left over.
Number of tomatoes left over = Total number of tomatoes - Number of tomatoes packed in boxes
Number of tomatoes left over = 929 - 924 = 5

Therefore, after packing the tomatoes evenly in boxes, there will be 5 tomatoes left over.

### Answer: 5

Expected answer: 5

Correct? Yes

Problem: A sporting goods store has 454 pairs of ice skates in total. The store distributes the skates evenly among 128 boxes. How many pairs of ice skates will be left over after all the boxes are filled up equally?

Claude-3 Sonnet:

To solve this problem, we need to find the number of pairs of ice skates that can be evenly distributed among the boxes, and then subtract that from the total number of pairs of ice skates.

Given information:
- The store has 454 pairs of ice skates in total.
- The store distributes the skates evenly among 128 boxes.

Step 1: Find the number of pairs of ice skates that can be evenly distributed among the boxes.
Number of pairs of ice skates per box = Total pairs of ice skates / Number of boxes
Number of pairs of ice skates per box = 454 / 128
Number of pairs of ice skates per box = 3.546875 (rounded down to 3)

Step 2: Find the number of pairs of ice skates that can be evenly distributed among the boxes.
Number of pairs of ice skates evenly distributed = Number of pairs of ice skates per box × Number of boxes
Number of pairs of ice skates evenly distributed = 3 × 128
Number of pairs of ice skates evenly distributed = 384

Step 3: Find the number of pairs of ice skates left over after all the boxes are filled up equally.
Number of pairs of ice skates left over = Total pairs of ice skates - Number of pairs of ice skates evenly distributed
Number of pairs of ice skates left over = 454 - 384
Number of pairs of ice skates left over = 70

Therefore, 70 pairs of ice skates will be left over after all the boxes are filled up equally.

### Answer: 70

Expected answer: 70

Correct? Yes

Problem: A windmill generates 506 units of power per day. Every day, a small village consumes power in increments of 385 units. At the end of the day, after the village has consumed as much power as it can in full increments, how much power is left over?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when the power generated by the windmill is divided by the power consumed by the village in increments.

Given information:
- The windmill generates 506 units of power per day.
- The village consumes power in increments of 385 units.

Step 1: Divide the power generated by the windmill by the power consumed by the village in increments.
Power generated by the windmill / Power consumed by the village in increments = Number of full increments consumed + Remainder
506 units / 385 units = 1 full increment + Remainder

Step 2: Find the remainder.
Remainder = Power generated by the windmill - (Number of full increments consumed × Power consumed by the village in increments)
Remainder = 506 units - (1 × 385 units)
Remainder = 506 units - 385 units
Remainder = 121 units

Therefore, after the village has consumed as much power as it can in full increments, 121 units of power are left over.

### Answer: 121

Expected answer: 121

Correct? Yes

Problem: Superhero Blast Man has 338 energy units in his power cells. Each energy blast he fires uses 16 energy units. After using equal units of energy firing blasts, how many energy units will Blast Man have left in his power cells?

Claude-3 Sonnet:

To solve this problem, we need to find out how many energy blasts Blast Man can fire with the available energy units, and then calculate the remaining energy units after firing those blasts.

Given information:
- Blast Man has 338 energy units in his power cells.
- Each energy blast uses 16 energy units.

Step 1: Find the number of energy blasts Blast Man can fire.
Number of energy blasts = Total energy units / Energy units per blast
Number of energy blasts = 338 / 16
Number of energy blasts = 21.125 (rounded down to 21 since we cannot fire a partial blast)

Step 2: Calculate the energy units used for firing 21 blasts.
Energy units used = Number of blasts × Energy units per blast
Energy units used = 21 × 16
Energy units used = 336

Step 3: Calculate the remaining energy units in Blast Man's power cells.
Remaining energy units = Total energy units - Energy units used
Remaining energy units = 338 - 336
Remaining energy units = 2

Therefore, after firing equal units of energy blasts, Blast Man will have 2 energy units left in his power cells.

### Answer: 2

Expected answer: 2

Correct? Yes

Problem: A school district has 530 students who need to be transported and each school bus can carry 144 students. If all students are equally spread across the buses, how many students will be on the last school bus?

Claude-3 Sonnet:

To solve this problem, we need to find the number of buses required to transport all the students and then calculate the number of students on the last bus.

Given information:
- The school district has 530 students who need to be transported.
- Each school bus can carry 144 students.

Step 1: Find the number of buses required to transport all the students.
Number of buses required = Total number of students / Number of students per bus
Number of buses required = 530 / 144
Number of buses required = 3.68 (rounded down to 3 since we cannot have a fractional bus)

Step 2: Find the number of students that can be transported by the first 3 buses.
Number of students transported by the first 3 buses = 3 × 144 = 432

Step 3: Find the number of students remaining for the last bus.
Number of students remaining for the last bus = Total number of students - Number of students transported by the first 3 buses
Number of students remaining for the last bus = 530 - 432 = 98

Therefore, the last school bus will have 98 students.

### Answer: 98

Expected answer: 98

Correct? Yes

Problem: A wizard has 999 spells in his book. He tries to distribute them equally among 951 apprentice wizards but they don't divide evenly. How many spells will the wizard have left after giving out as many as he can to his apprentices?

Claude-3 Sonnet:

To solve this problem, we need to find the number of spells each apprentice wizard will receive and then calculate the remaining spells after distributing them equally.

Given information:
- The wizard has 999 spells in his book.
- There are 951 apprentice wizards.

Step 1: Find the number of spells each apprentice wizard will receive.
Number of spells per apprentice wizard = Total number of spells / Number of apprentice wizards
Number of spells per apprentice wizard = 999 / 951
Number of spells per apprentice wizard = 1 (integer division)

Step 2: Calculate the remaining spells after distributing them equally.
Remaining spells = Total number of spells - (Number of apprentice wizards × Number of spells per apprentice wizard)
Remaining spells = 999 - (951 × 1)
Remaining spells = 999 - 951
Remaining spells = 48

Therefore, after giving out as many spells as possible to his 951 apprentice wizards, the wizard will have 48 spells left.

### Answer: 48

Expected answer: 48

Correct? Yes

Problem: A scooter manufacturing company has produced 767 scooters. Each delivery truck they use can carry 369 scooters. If they distribute the scooters evenly among the trucks, how many scooters will be left after all the trucks are loaded?

Claude-3 Sonnet:

To solve this problem, we need to find out how many trucks are needed to carry all the scooters, and then calculate the remaining scooters after loading the trucks.

Given information:
- The company has produced 767 scooters.
- Each delivery truck can carry 369 scooters.

Step 1: Find the number of trucks needed to carry all the scooters.
Number of trucks needed = Total number of scooters / Number of scooters per truck
Number of trucks needed = 767 / 369
Number of trucks needed = 2.078 (rounded down to 2 since we can't have a fraction of a truck)

Step 2: Calculate the number of scooters that can be loaded onto the trucks.
Number of scooters loaded onto trucks = Number of trucks × Number of scooters per truck
Number of scooters loaded onto trucks = 2 × 369 = 738

Step 3: Calculate the remaining scooters after loading the trucks.
Remaining scooters = Total number of scooters - Number of scooters loaded onto trucks
Remaining scooters = 767 - 738 = 29

Therefore, after loading all the trucks, there will be 29 scooters left.

### Answer: 29

Expected answer: 29

Correct? Yes

Problem: There are 846 water droplets in a cloud. Each raindrop needs 722 droplets to form. If all droplets are used to form raindrops, how many droplets would be left unconverted in the cloud after reaching the maximum number of rain drops?

Claude-3 Sonnet:

To solve this problem, we need to find the maximum number of raindrops that can be formed from the given number of water droplets, and then calculate the remaining droplets that are left unconverted.

Given information:
- There are 846 water droplets in the cloud.
- Each raindrop needs 722 droplets to form.

Step 1: Find the maximum number of raindrops that can be formed.
Maximum number of raindrops = Total number of water droplets / Number of droplets needed for one raindrop
Maximum number of raindrops = 846 / 722
Maximum number of raindrops = 1 (since we cannot have a fractional number of raindrops)

Step 2: Calculate the number of droplets used to form the maximum number of raindrops.
Number of droplets used = Maximum number of raindrops × Number of droplets needed for one raindrop
Number of droplets used = 1 × 722 = 722

Step 3: Calculate the number of droplets left unconverted.
Number of droplets left unconverted = Total number of water droplets - Number of droplets used
Number of droplets left unconverted = 846 - 722 = 124

Therefore, after reaching the maximum number of raindrops, there would be 124 droplets left unconverted in the cloud.

### Answer: 124

Expected answer: 124

Correct? Yes

Problem: Unicorn Village, a magical place where 265 unicorns live, is divided into 146 equal sections where these magical creatures reside. If each section is occupied by an equal number of unicorns, how many unicorns will live in the last incomplete section?

Claude-3 Sonnet:

To solve this problem, we need to find the number of unicorns that can be equally distributed among the complete sections, and then find the remaining unicorns that will occupy the last incomplete section.

Given information:
- There are 265 unicorns in Unicorn Village.
- The village is divided into 146 equal sections.

Step 1: Find the number of unicorns that can be equally distributed among the complete sections.
Number of complete sections = 146 - 1 = 145 (since there is one incomplete section)
Number of unicorns in each complete section = 265 ÷ 146 = 1 (integer division)
Number of unicorns in the complete sections = 145 × 1 = 145

Step 2: Find the number of unicorns in the last incomplete section.
Number of unicorns in the last incomplete section = Total unicorns - Number of unicorns in the complete sections
Number of unicorns in the last incomplete section = 265 - 145 = 120

Therefore, the last incomplete section will have 120 unicorns residing in it.

### Answer: 120

Expected answer: 119

Correct? No

Problem: In a game, there are 923 players waiting to enter a match. Only 383 players can enter a match at a time. If players enter matches evenly, how many players will be left waiting after filling all the matches?

Claude-3 Sonnet:

To solve this problem, we need to find the number of matches that can be filled with the given number of players, and then calculate the remaining players who cannot enter a match.

Given information:
- There are 923 players waiting to enter a match.
- Only 383 players can enter a match at a time.

Step 1: Find the number of matches that can be filled with 923 players.
Number of matches = Total number of players / Number of players per match
Number of matches = 923 / 383
Number of matches = 2 (with a remainder)

Step 2: Calculate the number of players who can enter the matches.
Number of players who can enter matches = Number of matches × Number of players per match
Number of players who can enter matches = 2 × 383 = 766

Step 3: Calculate the number of players left waiting after filling all the matches.
Number of players left waiting = Total number of players - Number of players who can enter matches
Number of players left waiting = 923 - 766 = 157

Therefore, after filling all the matches, 157 players will be left waiting.

### Answer: 157

Expected answer: 157

Correct? Yes

Problem: A pirate ship has 923 cannonballs on board. They want to equally disperse them between 499 different crates. After evenly distributing them as much as possible, how many cannonballs will be left uncrated?

Claude-3 Sonnet:

To solve this problem, we need to find the number of cannonballs that can be evenly distributed among the crates, and then subtract that from the total number of cannonballs to find the remaining uncrated cannonballs.

Given information:
- The pirate ship has 923 cannonballs.
- The cannonballs need to be distributed among 499 crates.

Step 1: Find the number of cannonballs that can be evenly distributed among the crates.
Number of cannonballs per crate = Total cannonballs / Number of crates
Number of cannonballs per crate = 923 / 499
Number of cannonballs per crate = 1 (integer division)

Step 2: Find the number of cannonballs that can be evenly distributed among all crates.
Number of cannonballs evenly distributed = Number of cannonballs per crate × Number of crates
Number of cannonballs evenly distributed = 1 × 499
Number of cannonballs evenly distributed = 499

Step 3: Find the number of cannonballs left uncrated.
Number of cannonballs left uncrated = Total cannonballs - Number of cannonballs evenly distributed
Number of cannonballs left uncrated = 923 - 499
Number of cannonballs left uncrated = 424

Therefore, after evenly distributing the cannonballs among the crates, 424 cannonballs will be left uncrated.

### Answer: 424

Expected answer: 424

Correct? Yes

Problem: A kite store has 530 string spools to attach to their kites. They distribute them to 518 kites, each getting one string spool. After each kite gets a spool, how many spools are left in the store?

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the total number of string spools and the number of spools distributed to the kites.

Given information:
- The kite store has 530 string spools.
- The store distributes one string spool to each of the 518 kites.

Step 1: Find the number of string spools distributed to the kites.
Number of string spools distributed = Number of kites
Number of string spools distributed = 518

Step 2: Find the number of string spools left in the store.
Number of string spools left = Total number of string spools - Number of string spools distributed
Number of string spools left = 530 - 518
Number of string spools left = 12

Therefore, after distributing one string spool to each of the 518 kites, there are 12 string spools left in the kite store.

### Answer: 12

Expected answer: 12

Correct? Yes

Problem: A dairy farm produces 913 gallons of milk in a day. If every milk jug holds 39 gallons, how many gallons will be left over after all the jugs are filled?

Claude-3 Sonnet:

To solve this problem, we need to find out how many jugs can be filled with the total milk produced, and then calculate the remaining milk after filling all the jugs.

Given information:
- The dairy farm produces 913 gallons of milk in a day.
- Each milk jug holds 39 gallons.

Step 1: Find the number of jugs that can be filled with the total milk produced.
Number of jugs that can be filled = Total milk produced / Capacity of each jug
Number of jugs that can be filled = 913 gallons / 39 gallons per jug
Number of jugs that can be filled = 23.41 jugs (rounded down to the nearest whole number)
Number of jugs that can be filled = 23 jugs

Step 2: Calculate the total milk that can be filled in the jugs.
Total milk that can be filled in the jugs = Number of jugs × Capacity of each jug
Total milk that can be filled in the jugs = 23 jugs × 39 gallons per jug
Total milk that can be filled in the jugs = 897 gallons

Step 3: Calculate the remaining milk after filling all the jugs.
Remaining milk = Total milk produced - Total milk that can be filled in the jugs
Remaining milk = 913 gallons - 897 gallons
Remaining milk = 16 gallons

Therefore, after filling all the jugs, there will be 16 gallons of milk left over.

### Answer: 16

Expected answer: 16

Correct? Yes

Problem: A doll seller received a shipment of 603 new dolls to put on the shelves. She arranged all the dolls in rows, with 369 dolls in each row. After filling up the rows as much as possible, how many dolls were left unarranged?

Claude-3 Sonnet:

To solve this problem, we need to find out how many rows of dolls can be formed with 369 dolls in each row, and then calculate the remaining dolls that were left unarranged.

Given information:
- The doll seller received a shipment of 603 new dolls.
- Each row has 369 dolls.

Step 1: Find the number of rows that can be formed with 369 dolls in each row.
Number of rows = Total number of dolls / Number of dolls per row
Number of rows = 603 / 369
Number of rows = 1 (since 603 is less than 2 × 369)

Step 2: Calculate the number of dolls left unarranged.
Number of dolls left unarranged = Total number of dolls - (Number of rows × Number of dolls per row)
Number of dolls left unarranged = 603 - (1 × 369)
Number of dolls left unarranged = 603 - 369
Number of dolls left unarranged = 234

Therefore, 234 dolls were left unarranged after filling up the rows as much as possible.

### Answer: 234

Expected answer: 234

Correct? Yes

Problem: A jewelry maker has 850 beads to make necklaces. They use 631 beads for each necklace. After using as many beads as possible, how many beads will the jewelry maker have left over?

Claude-3 Sonnet:

To solve this problem, we need to find out how many necklaces the jewelry maker can make with the available 850 beads, and then calculate the remaining beads after making those necklaces.

Given information:
- The jewelry maker has 850 beads.
- Each necklace requires 631 beads.

Step 1: Find the number of necklaces the jewelry maker can make with 850 beads.
Number of necklaces = Total beads / Beads required per necklace
Number of necklaces = 850 / 631
Number of necklaces = 1 (since we cannot make a fraction of a necklace)

Step 2: Calculate the number of beads used to make one necklace.
Beads used for one necklace = 631

Step 3: Calculate the remaining beads after making one necklace.
Remaining beads = Total beads - Beads used for one necklace
Remaining beads = 850 - 631
Remaining beads = 219

Therefore, after using as many beads as possible to make necklaces, the jewelry maker will have 219 beads left over.

### Answer: 219

Expected answer: 219

Correct? Yes

Problem: A gardener has 952 grapes that he wants to package into boxes. If each box can hold 380 grapes, how many grapes will be left after the gardener has filled as many boxes as possible?

Claude-3 Sonnet:

To solve this problem, we need to find out how many boxes the gardener can fill with the given number of grapes, and then calculate the remaining grapes.

Given information:
- The gardener has 952 grapes.
- Each box can hold 380 grapes.

Step 1: Find the number of boxes the gardener can fill.
Number of boxes = Total number of grapes / Number of grapes per box
Number of boxes = 952 / 380
Number of boxes = 2.5 (rounded down to the nearest whole number, which is 2)

Step 2: Calculate the number of grapes used to fill the boxes.
Number of grapes used = Number of boxes × Number of grapes per box
Number of grapes used = 2 × 380 = 760

Step 3: Calculate the remaining grapes.
Remaining grapes = Total number of grapes - Number of grapes used
Remaining grapes = 952 - 760 = 192

Therefore, after filling as many boxes as possible, there will be 192 grapes left.

### Answer: 192

Expected answer: 192

Correct? Yes

Problem: On a treasure map, there are 236 steps mentioned on the guide. If every 44 steps I make leads me to a significant place or clue, how many steps will be left after I reach the last significant place or clue?

Claude-3 Sonnet:

To solve this problem, we need to find the number of significant places or clues and then subtract the total number of steps taken to reach those places from the total number of steps mentioned on the guide.

Given information:
- There are 236 steps mentioned on the guide.
- Every 44 steps lead to a significant place or clue.

Step 1: Find the number of significant places or clues.
Number of significant places or clues = Total steps / Steps per significant place or clue
Number of significant places or clues = 236 / 44
Number of significant places or clues = 5.36 (rounded down to 5)

Step 2: Find the total number of steps taken to reach the last significant place or clue.
Total steps taken = Number of significant places or clues × Steps per significant place or clue
Total steps taken = 5 × 44
Total steps taken = 220 steps

Step 3: Find the number of steps left after reaching the last significant place or clue.
Steps left = Total steps mentioned on the guide - Total steps taken
Steps left = 236 - 220
Steps left = 16 steps

Therefore, after reaching the last significant place or clue, there will be 16 steps left on the treasure map guide.

### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Sarah blew 932 bubbles using her new bubble machine. The machine is designed to form groups of 507 bubbles each before releasing them. After forming complete groups, how many bubbles does it make in its final, incomplete group?

Claude-3 Sonnet:

To solve this problem, we need to find the number of complete groups of 507 bubbles that can be formed from the total of 932 bubbles, and then calculate the remaining bubbles that form the incomplete group.

Given information:
- Sarah blew 932 bubbles.
- The bubble machine forms groups of 507 bubbles each before releasing them.

Step 1: Find the number of complete groups of 507 bubbles.
Number of complete groups = Total bubbles / Bubbles per group
Number of complete groups = 932 / 507
Number of complete groups = 1 (since 932 / 507 = 1.84, we take the integer part)

Step 2: Calculate the number of bubbles in the remaining incomplete group.
Number of bubbles in the incomplete group = Total bubbles - (Number of complete groups × Bubbles per group)
Number of bubbles in the incomplete group = 932 - (1 × 507)
Number of bubbles in the incomplete group = 425

Therefore, after forming complete groups of 507 bubbles, the bubble machine makes 425 bubbles in its final, incomplete group.

### Answer: 425

Expected answer: 425

Correct? Yes

Problem: At the park, there are 931 kids who want to use the swings. Each swing set can accommodate 34 kids at a time. If all the swing sets are filled continuously, how many kids will be waiting for their turn after all the swing sets are occupied?

Claude-3 Sonnet:

To solve this problem, we need to find the total capacity of the swing sets and then subtract it from the total number of kids who want to use the swings.

Given information:
- There are 931 kids who want to use the swings.
- Each swing set can accommodate 34 kids at a time.

Step 1: Find the total capacity of the swing sets.
Let's assume there are x swing sets.
Total capacity of the swing sets = x × 34 kids

Since all the swing sets are filled continuously, the total capacity should be equal to or greater than the total number of kids.
931 ≤ x × 34
x ≥ 931 / 34
x ≥ 27.38 (rounded up to the nearest whole number)
x = 28 swing sets

Total capacity of the swing sets = 28 × 34 = 952 kids

Step 2: Find the number of kids waiting for their turn after all the swing sets are occupied.
Number of kids waiting = Total number of kids - Total capacity of the swing sets
Number of kids waiting = 931 - 952 = -21

Since the number of kids waiting cannot be negative, it means that all the kids can be accommodated in the swing sets, and there will be no kids waiting for their turn.

Therefore, the number of kids waiting for their turn after all the swing sets are occupied is 0.

### Answer: 0

Expected answer: 13

Correct? No

Problem: John has 943 dollar bills in his possession. He tries to stuff them in wallets that can each contain 433 dollar bills. After fully loading as many wallets as he can, how many dollar bills does he have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many wallets John can fully load with the dollar bills he has, and then calculate the remaining dollar bills.

Given information:
- John has 943 dollar bills.
- Each wallet can contain 433 dollar bills.

Step 1: Find the number of wallets John can fully load.
Number of wallets = Total number of dollar bills / Number of dollar bills per wallet
Number of wallets = 943 / 433
Number of wallets = 2 (since we can only have whole wallets)

Step 2: Calculate the number of dollar bills used to fully load the wallets.
Number of dollar bills used = Number of wallets × Number of dollar bills per wallet
Number of dollar bills used = 2 × 433 = 866

Step 3: Calculate the remaining dollar bills.
Remaining dollar bills = Total number of dollar bills - Number of dollar bills used
Remaining dollar bills = 943 - 866 = 77

Therefore, after fully loading as many wallets as he can, John will have 77 dollar bills left.

### Answer: 77

Expected answer: 77

Correct? Yes

Problem: A helicopter pilot plans to transport 240 passengers over several trips. He can carry 177 passengers in one trip. How many passengers will be left behind after the helicopter makes the first full trip?

Claude-3 Sonnet:

To solve this problem, we need to find the number of passengers that can be transported in the first trip and then subtract it from the total number of passengers.

Given information:
- The total number of passengers to be transported is 240.
- The helicopter can carry 177 passengers in one trip.

Step 1: Find the number of passengers that can be transported in the first trip.
Number of passengers in the first trip = 177

Step 2: Find the number of passengers remaining after the first trip.
Number of passengers remaining = Total number of passengers - Number of passengers in the first trip
Number of passengers remaining = 240 - 177
Number of passengers remaining = 63

Therefore, after the helicopter makes the first full trip, 63 passengers will be left behind.

### Answer: 63

Expected answer: 63

Correct? Yes

Problem: A gardener has 982 flowers to plant in flowerbeds. Each flowerbed can fit 555 flowers. After filling up as many flowerbeds as possible, how many flowers will the gardener have left to plant?

Claude-3 Sonnet:

To solve this problem, we need to find out how many flowerbeds the gardener can fill with the given number of flowers, and then calculate the remaining flowers.

Given information:
- The gardener has 982 flowers to plant.
- Each flowerbed can fit 555 flowers.

Step 1: Find the number of flowerbeds the gardener can fill.
Number of flowerbeds = Total number of flowers / Number of flowers per flowerbed
Number of flowerbeds = 982 / 555
Number of flowerbeds = 1 (since we cannot have a fractional number of flowerbeds)

Step 2: Calculate the number of flowers used to fill the flowerbeds.
Number of flowers used = Number of flowerbeds × Number of flowers per flowerbed
Number of flowers used = 1 × 555 = 555 flowers

Step 3: Calculate the remaining flowers.
Remaining flowers = Total number of flowers - Number of flowers used
Remaining flowers = 982 - 555 = 427 flowers

Therefore, after filling up as many flowerbeds as possible, the gardener will have 427 flowers left to plant.

### Answer: 427

Expected answer: 427

Correct? Yes

Problem: A farmer grows 203 strawberry plants. She wants to divide her plants into groups of 5 to sell. How many plants will be remaining if she divides them equally?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when 203 is divided by 5.

Given information:
- The farmer has 203 strawberry plants.
- The farmer wants to divide the plants into groups of 5.

Step 1: Divide 203 by 5 to find the number of groups of 5 plants.
203 ÷ 5 = 40 (with a remainder of 3)

Step 2: Find the number of plants that can be divided into groups of 5.
Number of plants in groups of 5 = 40 × 5 = 200

Step 3: Find the number of remaining plants.
Number of remaining plants = Total plants - Number of plants in groups of 5
Number of remaining plants = 203 - 200 = 3

Therefore, if the farmer divides the 203 strawberry plants into groups of 5, there will be 3 plants remaining.

### Answer: 3

Expected answer: 3

Correct? Yes

Problem: A gardener has 355 carrots. He wants to create bundles of 16. After creating as many bundles as he can, how many carrots will he have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many bundles of 16 carrots the gardener can make with the 355 carrots, and then calculate the remaining carrots.

Given information:
- The gardener has 355 carrots.
- Each bundle contains 16 carrots.

Step 1: Find the number of bundles the gardener can make with 355 carrots.
Number of bundles = Total number of carrots / Number of carrots per bundle
Number of bundles = 355 / 16
Number of bundles = 22 (with a remainder)

Step 2: Calculate the number of carrots used to make the bundles.
Number of carrots used for bundles = Number of bundles × Number of carrots per bundle
Number of carrots used for bundles = 22 × 16
Number of carrots used for bundles = 352

Step 3: Calculate the remaining carrots.
Remaining carrots = Total number of carrots - Number of carrots used for bundles
Remaining carrots = 355 - 352
Remaining carrots = 3

Therefore, after creating as many bundles of 16 carrots as possible, the gardener will have 3 carrots left.

### Answer: 3

Expected answer: 3

Correct? Yes

Problem: A total rainfall of 612 inches fell over a certain city in 29 consecutive days. If the rain fell in the same amount every day, how many inches of rain would be left to make the days evenly rainy?

Claude-3 Sonnet:

To solve this problem, we need to find the average rainfall per day and then calculate the difference between the average rainfall and the actual rainfall on each day.

Given information:
- Total rainfall = 612 inches
- Number of consecutive days = 29 days

Step 1: Find the average rainfall per day.
Average rainfall per day = Total rainfall / Number of days
Average rainfall per day = 612 inches / 29 days
Average rainfall per day = 21 inches

Step 2: Calculate the difference between the average rainfall and the actual rainfall on each day.
Difference = Average rainfall per day - Actual rainfall on each day

Since we don't have the actual rainfall data for each day, we can assume that the difference is the same for all days.

Let's represent the difference as x.

Total difference = 29x (since there are 29 days)

Step 3: Set up an equation to find the value of x.
Total difference = Total rainfall - (29 × Average rainfall per day)
29x = 612 - (29 × 21)
29x = 612 - 609
29x = 3
x = 3/29
x ≈ 0.103 inches

Therefore, to make the days evenly rainy, approximately 0.103 inches of rain would be left to distribute among the days.

### Answer: 0.103 inches

Expected answer: 3

Correct? No

Problem: A truck company has got 514 boxes for delivery. Each truck can hold up to 371 boxes. If each truck is loaded to its full capacity, how many boxes will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find out how many trucks are required to transport all the boxes, and then calculate the remaining boxes after loading the trucks to their full capacity.

Given information:
- The truck company has 514 boxes for delivery.
- Each truck can hold up to 371 boxes.

Step 1: Find the number of trucks required to transport all the boxes.
Number of trucks required = Total number of boxes / Capacity of each truck
Number of trucks required = 514 / 371
Number of trucks required = 1.38 (rounded up to 2 trucks)

Step 2: Calculate the total number of boxes that can be loaded onto the trucks.
Total boxes that can be loaded = Number of trucks × Capacity of each truck
Total boxes that can be loaded = 2 × 371 = 742 boxes

Step 3: Calculate the remaining boxes after loading the trucks to their full capacity.
Remaining boxes = Total number of boxes - Total boxes that can be loaded
Remaining boxes = 514 - 742 = -228 boxes

Since the result is negative, it means that all the boxes can be loaded onto the trucks, and there will be no remaining boxes.

Therefore, the number of boxes left over is 0.

### Answer: 0

Expected answer: 143

Correct? No

Problem: In a large sandbox, children create 684 sandcastles over the summer. The sandcastles were grouped into sets of 230 for a photography contest. After all the sets were completed, how many sandcastles were left that didn't form a complete set?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when 684 is divided by 230.

Given information:
- There are 684 sandcastles in total.
- The sandcastles are grouped into sets of 230 for a photography contest.

Step 1: Divide 684 by 230 to find the number of complete sets.
684 ÷ 230 = 2 (with a remainder)

Step 2: Find the number of sandcastles in the complete sets.
Number of sandcastles in complete sets = 2 × 230 = 460

Step 3: Find the number of sandcastles left that didn't form a complete set.
Number of sandcastles left = Total sandcastles - Number of sandcastles in complete sets
Number of sandcastles left = 684 - 460 = 224

Therefore, 224 sandcastles were left that didn't form a complete set.

### Answer: 224

Expected answer: 224

Correct? Yes

Problem: A toy manufacturer has a production run of 735 toy cars. They package the cars in packs of 348 for bulk shipments. If all the toy cars are divided equally among packs, how many toy cars will be left over after all full packs have been filled?

Claude-3 Sonnet:

To solve this problem, we need to find the number of full packs that can be made with the given number of toy cars, and then calculate the remaining toy cars that cannot be packed.

Given information:
- Total number of toy cars = 735
- Number of toy cars per pack = 348

Step 1: Find the number of full packs that can be made.
Number of full packs = Total number of toy cars / Number of toy cars per pack
Number of full packs = 735 / 348
Number of full packs = 2 (with a remainder)

Step 2: Calculate the number of toy cars used for the full packs.
Number of toy cars used for full packs = Number of full packs × Number of toy cars per pack
Number of toy cars used for full packs = 2 × 348 = 696

Step 3: Calculate the number of toy cars left over.
Number of toy cars left over = Total number of toy cars - Number of toy cars used for full packs
Number of toy cars left over = 735 - 696 = 39

Therefore, after all full packs have been filled, there will be 39 toy cars left over.

### Answer: 39

Expected answer: 39

Correct? Yes

Problem: In a forest, there are 386 animals. Each woodlands territory can support 95 animals. If the existing animals are evenly distributed among the territories, how many animals will be left in the last not fully occupied territory?

Claude-3 Sonnet:

To solve this problem, we need to find the number of territories required to accommodate all the animals and then calculate the remaining animals in the last territory.

Given information:
- There are 386 animals in the forest.
- Each woodlands territory can support 95 animals.

Step 1: Find the number of territories required to accommodate all the animals.
Number of territories required = Total number of animals / Number of animals per territory
Number of territories required = 386 / 95
Number of territories required = 4.06 (rounded down to 4 since we cannot have a partial territory)

Step 2: Calculate the number of animals that can be accommodated in the fully occupied territories.
Number of animals in fully occupied territories = Number of fully occupied territories × Number of animals per territory
Number of animals in fully occupied territories = 4 × 95 = 380

Step 3: Calculate the remaining animals in the last not fully occupied territory.
Remaining animals in the last territory = Total number of animals - Number of animals in fully occupied territories
Remaining animals in the last territory = 386 - 380 = 6

Therefore, there will be 6 animals left in the last not fully occupied territory.

### Answer: 6

Expected answer: 6

Correct? Yes

Problem: A forest has 801 trees. A tree disease starts to spread and is expected to affect 646 trees. If all the diseased trees have to be cut down evenly, how many trees are likely to stay healthy after the disease has affected all possible trees?

Claude-3 Sonnet:

To solve this problem, we need to find the number of trees that will not be affected by the disease.

Given information:
- The forest has 801 trees.
- The tree disease is expected to affect 646 trees.

Step 1: Find the number of trees that will not be affected by the disease.
Number of trees that will not be affected = Total number of trees - Number of trees affected by the disease
Number of trees that will not be affected = 801 - 646
Number of trees that will not be affected = 155

Therefore, 155 trees are likely to stay healthy after the disease has affected all possible trees.

### Answer: 155

Expected answer: 155

Correct? Yes

Problem: A rope manufacturer has made a rope of 934 meters in length. This rope is supposed to be cut into smaller pieces, each piece being 902 meters in length. After cutting into the maximum possible number of equal pieces, how many meters will the last piece of the rope be?

Claude-3 Sonnet:

To solve this problem, we need to find the number of pieces of 902 meters that can be cut from the 934-meter rope, and then calculate the remaining length of the rope.

Given information:
- Total length of the rope = 934 meters.
- Length of each piece to be cut = 902 meters.

Step 1: Find the number of pieces of 902 meters that can be cut from the 934-meter rope.
Number of pieces = Total length of the rope / Length of each piece
Number of pieces = 934 meters / 902 meters
Number of pieces = 1.035 (rounded down to 1)

Step 2: Calculate the remaining length of the rope after cutting the maximum possible number of pieces.
Remaining length of the rope = Total length of the rope - (Number of pieces × Length of each piece)
Remaining length of the rope = 934 meters - (1 × 902 meters)
Remaining length of the rope = 32 meters

Therefore, after cutting the maximum possible number of equal pieces of 902 meters from the 934-meter rope, the last piece of the rope will be 32 meters long.

### Answer: 32

Expected answer: 32

Correct? Yes

Problem: A dairy farm produces 561 liters of milk each day. The milk is packaged into 550-liter containers. How many liters of milk are left over each day after filling the containers?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder after dividing the total milk production by the container size.

Given information:
- The dairy farm produces 561 liters of milk each day.
- The milk is packaged into 550-liter containers.

Step 1: Divide the total milk production by the container size.
Total milk production / Container size = Number of containers filled
561 liters / 550 liters = 1.02 containers

Step 2: Find the number of liters that can be filled into whole containers.
Number of whole containers × Container size = Liters filled into whole containers
1 container × 550 liters = 550 liters

Step 3: Find the remaining liters of milk after filling the whole containers.
Total milk production - Liters filled into whole containers = Remaining liters
561 liters - 550 liters = 11 liters

Therefore, 11 liters of milk are left over each day after filling the containers.

### Answer: 11

Expected answer: 11

Correct? Yes

Problem: Jon has 259 puzzle pieces. If each puzzle requires 258 pieces, how many pieces will be left over once he completes a full puzzle?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when 259 is divided by 258.

Given information:
- Jon has 259 puzzle pieces.
- Each puzzle requires 258 pieces.

Step 1: Divide the total number of puzzle pieces by the number of pieces required for one puzzle.
259 ÷ 258 = 1 (with a remainder)

Step 2: Find the remainder.
259 - (258 × 1) = 1

Therefore, after completing one full puzzle, Jon will have 1 puzzle piece left over.

### Answer: 1

Expected answer: 1

Correct? Yes

Problem: A jewelry maker has 673 beads. She plans to use exactly 49 beads for each bracelet. How many beads will she have left after creating as many bracelets as possible with the exact number of beads?

Claude-3 Sonnet:

To solve this problem, we need to find out how many bracelets the jewelry maker can create with the available beads, and then calculate the remaining beads.

Given information:
- The jewelry maker has 673 beads.
- Each bracelet requires 49 beads.

Step 1: Find the number of bracelets the jewelry maker can create with the available beads.
Number of bracelets = Total number of beads / Number of beads per bracelet
Number of bracelets = 673 / 49
Number of bracelets = 13 (since we need to use an exact number of beads for each bracelet)

Step 2: Calculate the number of beads used for creating the bracelets.
Number of beads used = Number of bracelets × Number of beads per bracelet
Number of beads used = 13 × 49
Number of beads used = 637

Step 3: Calculate the number of remaining beads.
Number of remaining beads = Total number of beads - Number of beads used
Number of remaining beads = 673 - 637
Number of remaining beads = 36

Therefore, after creating as many bracelets as possible with the exact number of beads, the jewelry maker will have 36 beads left.

### Answer: 36

Expected answer: 36

Correct? Yes

Problem: A police station received 927 calls within a week. They have 311 operators who can handle the same number of calls each week. However, when the calls are divided equally, how many calls will the last operator handle?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when the total number of calls is divided by the number of operators.

Given information:
- The police station received 927 calls within a week.
- There are 311 operators.

Step 1: Divide the total number of calls by the number of operators to find the number of calls each operator would handle if the calls were divided equally.
Number of calls per operator = Total number of calls / Number of operators
Number of calls per operator = 927 / 311
Number of calls per operator = 2 (integer division)

Step 2: Find the remainder after dividing the total number of calls by the number of operators.
Remainder = Total number of calls % Number of operators
Remainder = 927 % 311
Remainder = 305

Therefore, the last operator will handle the remaining 305 calls.

### Answer: 305

Expected answer: 305

Correct? Yes

Problem: John has 764 pieces for his jigsaw puzzle, and every package should contain 589 pieces. If he separates these pieces into full packages, how many pieces will be left outside without a package?

Claude-3 Sonnet:

To solve this problem, we need to find the number of full packages John can make with the 764 pieces, and then calculate the remaining pieces that will be left outside without a package.

Given information:
- John has 764 pieces for his jigsaw puzzle.
- Each package should contain 589 pieces.

Step 1: Find the number of full packages John can make.
Number of full packages = Total pieces / Pieces per package
Number of full packages = 764 / 589
Number of full packages = 1 (since we need to consider only full packages)

Step 2: Calculate the number of pieces used in the full packages.
Pieces used in full packages = Number of full packages × Pieces per package
Pieces used in full packages = 1 × 589 = 589 pieces

Step 3: Calculate the remaining pieces left outside without a package.
Remaining pieces = Total pieces - Pieces used in full packages
Remaining pieces = 764 - 589 = 175 pieces

Therefore, 175 pieces will be left outside without a package.

### Answer: 175

Expected answer: 175

Correct? Yes

Problem: A dressmaker has 984 meters of fabric. She uses 217 meters of fabric to make each dress. After using all the fabric she can to make as many dresses as possible, how many meters of fabric will she have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many dresses the dressmaker can make with the available fabric, and then calculate the remaining fabric after making those dresses.

Given information:
- The dressmaker has 984 meters of fabric.
- Each dress requires 217 meters of fabric.

Step 1: Find the number of dresses the dressmaker can make with the available fabric.
Number of dresses = Total fabric / Fabric required for one dress
Number of dresses = 984 meters / 217 meters
Number of dresses = 4 dresses (since we can't have a partial dress)

Step 2: Calculate the fabric used for making the dresses.
Fabric used for making dresses = Number of dresses × Fabric required for one dress
Fabric used for making dresses = 4 × 217 meters
Fabric used for making dresses = 868 meters

Step 3: Calculate the remaining fabric after making the dresses.
Remaining fabric = Total fabric - Fabric used for making dresses
Remaining fabric = 984 meters - 868 meters
Remaining fabric = 116 meters

Therefore, after using all the fabric she can to make as many dresses as possible, the dressmaker will have 116 meters of fabric left.

### Answer: 116

Expected answer: 116

Correct? Yes

Problem: A company donates 639 sleeping bags for a camping event. Each campsite is supplied with 374 sleeping bags. If all the sleeping bags are divided equally among the campsites, how many sleeping bags will there be left?

Claude-3 Sonnet:

To solve this problem, we need to find the number of campsites that can be supplied with the available sleeping bags, and then calculate the remaining sleeping bags.

Given information:
- The company donates 639 sleeping bags.
- Each campsite is supplied with 374 sleeping bags.

Step 1: Find the number of campsites that can be supplied with the available sleeping bags.
Number of campsites = Total number of sleeping bags / Number of sleeping bags per campsite
Number of campsites = 639 / 374
Number of campsites = 1 (since we cannot have a fraction of a campsite)

Step 2: Calculate the remaining sleeping bags.
Remaining sleeping bags = Total number of sleeping bags - (Number of campsites × Number of sleeping bags per campsite)
Remaining sleeping bags = 639 - (1 × 374)
Remaining sleeping bags = 639 - 374
Remaining sleeping bags = 265

Therefore, there will be 265 sleeping bags left after supplying one campsite with 374 sleeping bags.

### Answer: 265

Expected answer: 265

Correct? Yes

Problem: A pizza restaurant made 620 pizzas today. They package up the pizzas in boxes that hold 578 each for delivery. If the pizzas are evenly distributed into these boxes, how many pizzas will be left over that don't fit into a box?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes required to pack all the pizzas and then calculate the remaining pizzas that don't fit into a box.

Given information:
- The pizza restaurant made 620 pizzas today.
- Each box can hold 8 pizzas.

Step 1: Find the number of boxes required to pack all the pizzas.
Number of boxes required = Total number of pizzas / Number of pizzas per box
Number of boxes required = 620 / 8
Number of boxes required = 77.5

Since we cannot have a fractional number of boxes, we need to round up to the nearest whole number.
Number of boxes required = 78 boxes

Step 2: Calculate the number of pizzas that can be packed into the boxes.
Number of pizzas packed = Number of boxes × Number of pizzas per box
Number of pizzas packed = 78 × 8
Number of pizzas packed = 624 pizzas

Step 3: Calculate the number of pizzas left over that don't fit into a box.
Number of pizzas left over = Total number of pizzas - Number of pizzas packed
Number of pizzas left over = 620 - 624
Number of pizzas left over = -4

Since the number of pizzas left over is negative, it means that all the pizzas can be packed into the boxes, and there are no pizzas left over.

### Answer: 0

Expected answer: 42

Correct? No

Problem: A factory made a total of 820 robots. It can store 684 robots in one storage unit. If the robots are evenly stored, how many robots will not fit and remain outside of the storage units?

Claude-3 Sonnet:

To solve this problem, we need to find the number of storage units required to store all the robots and then calculate the remaining robots that won't fit in the storage units.

Given information:
- The factory made a total of 820 robots.
- Each storage unit can store 684 robots.

Step 1: Find the number of storage units required to store all the robots.
Number of storage units required = Total number of robots / Number of robots per storage unit
Number of storage units required = 820 / 684
Number of storage units required = 1.2 (rounded down to 1)

Step 2: Calculate the number of robots that can be stored in the storage units.
Number of robots that can be stored = Number of storage units × Number of robots per storage unit
Number of robots that can be stored = 1 × 684 = 684

Step 3: Calculate the number of robots that won't fit in the storage units.
Number of robots that won't fit = Total number of robots - Number of robots that can be stored
Number of robots that won't fit = 820 - 684 = 136

Therefore, 136 robots will not fit and remain outside of the storage units.

### Answer: 136

Expected answer: 136

Correct? Yes

Problem: A cloud changes its shape by reducing its water droplets. Initially, there were 516 droplets in the cloud. If the cloud loses water droplets at an equal rate and becomes entirely dry after every 289 droplets, how many droplets will be left when the cloud is dry after the final cycle?

Claude-3 Sonnet:

To solve this problem, we need to find the number of complete cycles the cloud goes through before becoming entirely dry, and then calculate the remaining droplets after the last cycle.

Given information:
- Initially, there are 516 droplets in the cloud.
- The cloud loses water droplets at an equal rate.
- The cloud becomes entirely dry after every 289 droplets.

Step 1: Find the number of complete cycles the cloud goes through.
Number of complete cycles = Total droplets / Droplets lost per cycle
Number of complete cycles = 516 / 289
Number of complete cycles = 1 (with a remainder)

Step 2: Calculate the remaining droplets after the last cycle.
Remaining droplets = Total droplets - (Number of complete cycles × Droplets lost per cycle)
Remaining droplets = 516 - (1 × 289)
Remaining droplets = 227

Therefore, when the cloud is dry after the final cycle, there will be 227 droplets left.

### Answer: 227

Expected answer: 227

Correct? Yes

Problem: A transport company needs to load 330 boxes into trucks. Each truck can hold exactly 4 boxes. After filling each truck to its full capacity, how many boxes will be left unloaded?

Claude-3 Sonnet:

To solve this problem, we need to find out how many trucks are needed to transport all the boxes, and then calculate the remaining boxes that cannot be loaded into the trucks.

Given information:
- There are 330 boxes to be loaded.
- Each truck can hold exactly 4 boxes.

Step 1: Find the number of trucks needed to transport all the boxes.
Number of trucks needed = Total number of boxes / Number of boxes per truck
Number of trucks needed = 330 / 4
Number of trucks needed = 82.5

Since we cannot have a fractional number of trucks, we need to round up to the nearest whole number.
Number of trucks needed = 83 trucks

Step 2: Calculate the number of boxes that can be loaded into the trucks.
Number of boxes that can be loaded = Number of trucks × Number of boxes per truck
Number of boxes that can be loaded = 83 × 4
Number of boxes that can be loaded = 332 boxes

Step 3: Calculate the number of boxes that will be left unloaded.
Number of boxes left unloaded = Total number of boxes - Number of boxes that can be loaded
Number of boxes left unloaded = 330 - 332
Number of boxes left unloaded = -2

Since we cannot have a negative number of boxes left unloaded, it means that all the boxes can be loaded into the trucks, and there will be no boxes left unloaded.

### Answer: 0

Expected answer: 2

Correct? No

Problem: A farmer harvested 649 potatoes this season. He decides to pack them into crates each containing 183 potatoes. How many potatoes will be left after all crates are filled to their maximum capacity?

Claude-3 Sonnet:

To solve this problem, we need to find out how many crates the farmer can fill with the total number of potatoes, and then calculate the remaining potatoes after filling the crates.

Given information:
- The farmer harvested 649 potatoes.
- Each crate can hold 183 potatoes.

Step 1: Find the number of crates the farmer can fill with 649 potatoes.
Number of crates = Total potatoes / Potatoes per crate
Number of crates = 649 / 183
Number of crates = 3.54 (rounded down to 3 since we can't have a partial crate)

Step 2: Calculate the number of potatoes that can be packed into the crates.
Potatoes packed in crates = Number of crates × Potatoes per crate
Potatoes packed in crates = 3 × 183 = 549

Step 3: Calculate the remaining potatoes after filling the crates.
Remaining potatoes = Total potatoes - Potatoes packed in crates
Remaining potatoes = 649 - 549 = 100

Therefore, after filling all the crates to their maximum capacity, there will be 100 potatoes left.

### Answer: 100

Expected answer: 100

Correct? Yes

Problem: A t-shirt company has a batch of 258 shirts in production. Each box can pack 67 shirts. If all the shirts are evenly distributed in the boxes, how many shirts would be left outside the boxes?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes required to pack all the shirts and then calculate the remaining shirts that cannot be packed in the boxes.

Given information:
- The company has 258 shirts in production.
- Each box can pack 67 shirts.

Step 1: Find the number of boxes required to pack all the shirts.
Number of boxes required = Total number of shirts / Number of shirts per box
Number of boxes required = 258 / 67
Number of boxes required = 3.85 (rounded down to 3 since we cannot have a fractional number of boxes)

Step 2: Calculate the number of shirts that can be packed in the boxes.
Number of shirts packed in boxes = Number of boxes × Number of shirts per box
Number of shirts packed in boxes = 3 × 67 = 201

Step 3: Calculate the number of shirts left outside the boxes.
Number of shirts left outside the boxes = Total number of shirts - Number of shirts packed in boxes
Number of shirts left outside the boxes = 258 - 201 = 57

Therefore, 57 shirts would be left outside the boxes.

### Answer: 57

Expected answer: 57

Correct? Yes

Problem: On a pirate ship, there are 995 gold coins that need to be evenly divided among the 267 pirates. If they split the gold up as evenly as possible, how many gold coins will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find the quotient and remainder when dividing 995 gold coins by 267 pirates.

Given information:
- There are 995 gold coins.
- There are 267 pirates.

Step 1: Find the number of gold coins each pirate will receive when divided evenly.
Number of gold coins per pirate = Total gold coins / Number of pirates
Number of gold coins per pirate = 995 / 267
Number of gold coins per pirate = 3 (quotient)

Step 2: Find the number of gold coins left over after the even distribution.
Number of gold coins left over = Total gold coins - (Number of pirates × Number of gold coins per pirate)
Number of gold coins left over = 995 - (267 × 3)
Number of gold coins left over = 995 - 801
Number of gold coins left over = 194 (remainder)

Therefore, after dividing the 995 gold coins evenly among the 267 pirates, there will be 194 gold coins left over.

### Answer: 194

Expected answer: 194

Correct? Yes

Problem: There are 776 snails all lined up in a row. If you group them in bunches of 375 snails, how many snails will be left in the final group?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when 776 is divided by 375.

Given information:
- There are 776 snails in total.
- We need to group them in bunches of 375 snails.

Step 1: Divide 776 by 375 to find the number of complete bunches of 375 snails.
776 ÷ 375 = 2 (with a remainder)

Step 2: Find the number of snails in the remaining incomplete bunch.
Number of snails in the remaining incomplete bunch = 776 - (2 × 375)
Number of snails in the remaining incomplete bunch = 776 - 750
Number of snails in the remaining incomplete bunch = 26

Therefore, the final group will have 26 snails.

### Answer: 26

Expected answer: 26

Correct? Yes

Problem: A pillow factory produces 589 pillows per day. They package these pillows in boxes, and each box holds 198 pillows. If they pack as many full boxes as possible, how many pillows will be left outside the boxes at the end of the day?

Claude-3 Sonnet:

To solve this problem, we need to find the number of full boxes that can be packed and then subtract the total number of pillows packed in those boxes from the total number of pillows produced.

Given information:
- The factory produces 589 pillows per day.
- Each box holds 198 pillows.

Step 1: Find the number of full boxes that can be packed.
Number of full boxes = Total pillows produced / Pillows per box
Number of full boxes = 589 / 198
Number of full boxes = 2 (with a remainder)

Step 2: Find the total number of pillows packed in the full boxes.
Total pillows packed in full boxes = Number of full boxes × Pillows per box
Total pillows packed in full boxes = 2 × 198
Total pillows packed in full boxes = 396

Step 3: Find the number of pillows left outside the boxes.
Pillows left outside the boxes = Total pillows produced - Total pillows packed in full boxes
Pillows left outside the boxes = 589 - 396
Pillows left outside the boxes = 193

Therefore, 193 pillows will be left outside the boxes at the end of the day.

### Answer: 193

Expected answer: 193

Correct? Yes

Problem: A jewelry maker has 633 beads. If she uses beads to make necklaces, with each necklace using exactly 30 beads, how many beads will she have left after making as many necklaces as she can?

Claude-3 Sonnet:

To solve this problem, we need to find out how many necklaces the jewelry maker can make with the available beads, and then calculate the remaining beads.

Given information:
- The jewelry maker has 633 beads.
- Each necklace requires 30 beads.

Step 1: Find the number of necklaces the jewelry maker can make.
Number of necklaces = Total number of beads / Number of beads per necklace
Number of necklaces = 633 / 30
Number of necklaces = 21

Step 2: Calculate the number of beads used for making necklaces.
Number of beads used = Number of necklaces × Number of beads per necklace
Number of beads used = 21 × 30
Number of beads used = 630

Step 3: Calculate the number of remaining beads.
Number of remaining beads = Total number of beads - Number of beads used
Number of remaining beads = 633 - 630
Number of remaining beads = 3

Therefore, after making as many necklaces as possible, the jewelry maker will have 3 beads left.

### Answer: 3

Expected answer: 3

Correct? Yes

Problem: John has collected 365 coins. He decided to put equal numbers of them in his 140 wallets. However, he found out he would still have some coins left after evenly distributing them into these wallets. How many coins will John have left?

Claude-3 Sonnet:

To solve this problem, we need to find the maximum number of coins that can be evenly distributed among the 140 wallets, and then subtract that number from the total number of coins John has.

Given information:
- John has 365 coins.
- John has 140 wallets.

Step 1: Find the greatest number that divides both 365 and 140.
The greatest common divisor (GCD) of 365 and 140 is 5.

Step 2: Divide 365 by the GCD to find the maximum number of coins that can be evenly distributed among the wallets.
365 ÷ 5 = 73

Step 3: Subtract the maximum number of coins that can be evenly distributed from the total number of coins.
365 - (73 × 140) = 365 - 10,220 = -9,855

Since the result is negative, it means that John cannot evenly distribute all the coins among the wallets.

Step 4: Find the number of coins left by taking the remainder of 365 divided by 140.
365 ÷ 140 = 2 with a remainder of 85

Therefore, John will have 85 coins left after evenly distributing the coins among the 140 wallets.

### Answer: 85

Expected answer: 85

Correct? Yes

Problem: A sock manufacturer produces 743 socks in a single production run. The socks are packed into cartons, each containing 451 socks. After filling up as many cartons as possible, how many socks are left unpacked?

Claude-3 Sonnet:

To solve this problem, we need to find out how many cartons can be filled with the given number of socks, and then calculate the remaining unpacked socks.

Given information:
- Total number of socks produced = 743
- Number of socks per carton = 451

Step 1: Find the number of cartons that can be filled.
Number of cartons = Total number of socks / Number of socks per carton
Number of cartons = 743 / 451
Number of cartons = 1 (since we cannot have a fractional number of cartons)

Step 2: Calculate the number of socks packed in the cartons.
Number of socks packed = Number of cartons × Number of socks per carton
Number of socks packed = 1 × 451 = 451

Step 3: Calculate the number of unpacked socks.
Number of unpacked socks = Total number of socks - Number of socks packed
Number of unpacked socks = 743 - 451 = 292

Therefore, after filling up as many cartons as possible, there are 292 socks left unpacked.

### Answer: 292

Expected answer: 292

Correct? Yes

Problem: A total of 923 children want to slide down a slide at an amusement park. If 771 children can go down the slide without rest, how many children will be left waiting for their turn?

Claude-3 Sonnet:

To solve this problem, we need to find the difference between the total number of children and the number of children who can go down the slide without rest.

Given information:
- Total number of children = 923
- Number of children who can go down the slide without rest = 771

Step 1: Find the number of children who will be left waiting for their turn.
Number of children left waiting = Total number of children - Number of children who can go down the slide without rest
Number of children left waiting = 923 - 771
Number of children left waiting = 152

Therefore, 152 children will be left waiting for their turn to slide down the slide.

### Answer: 152

Expected answer: 152

Correct? Yes

Problem: Superhero Iron Punch has to save 442 people from a collapsing building. He can teleport a maximum of 104 people at a time to safety. After teleporting as many full groups as he can, how many people will be left in the building for his last round of rescue?

Claude-3 Sonnet:

To solve this problem, we need to find out how many full groups of 104 people Iron Punch can teleport, and then calculate the remaining people left in the building.

Given information:
- There are 442 people in the collapsing building.
- Iron Punch can teleport a maximum of 104 people at a time.

Step 1: Find the number of full groups of 104 people that Iron Punch can teleport.
Number of full groups = Total people / Maximum people per group
Number of full groups = 442 / 104
Number of full groups = 4 (with a remainder)

Step 2: Calculate the number of people teleported in the full groups.
Number of people teleported in full groups = Number of full groups × Maximum people per group
Number of people teleported in full groups = 4 × 104
Number of people teleported in full groups = 416

Step 3: Calculate the remaining people left in the building.
Remaining people = Total people - Number of people teleported in full groups
Remaining people = 442 - 416
Remaining people = 26

Therefore, after teleporting as many full groups as possible, there will be 26 people left in the building for Iron Punch's last round of rescue.

### Answer: 26

Expected answer: 26

Correct? Yes

Problem: A card game manufacturer creates a deck of cards with 569 cards. Each card pack has 68 cards. After creating as many packs as possible, how many cards will the manufacturer have left over?

Claude-3 Sonnet:

To solve this problem, we need to find the number of packs that can be created with 569 cards, and then calculate the remaining cards after creating those packs.

Given information:
- The manufacturer has 569 cards.
- Each card pack has 68 cards.

Step 1: Find the number of packs that can be created with 569 cards.
Number of packs = Total number of cards / Number of cards per pack
Number of packs = 569 / 68
Number of packs = 8 (with a remainder)

Step 2: Calculate the number of cards used to create the packs.
Number of cards used = Number of packs × Number of cards per pack
Number of cards used = 8 × 68
Number of cards used = 544

Step 3: Calculate the number of cards left over.
Number of cards left over = Total number of cards - Number of cards used
Number of cards left over = 569 - 544
Number of cards left over = 25

Therefore, after creating as many packs as possible, the manufacturer will have 25 cards left over.

### Answer: 25

Expected answer: 25

Correct? Yes

Problem: A stationery store received a shipment of 842 erasers. The store owner wants to display them in boxes, with each box containing 719 erasers. After filling as many boxes as possible, how many erasers will be left over?

Claude-3 Sonnet:

To solve this problem, we need to find the number of boxes that can be filled with 719 erasers each, and then calculate the remaining erasers.

Given information:
- The stationery store received 842 erasers.
- Each box can hold 719 erasers.

Step 1: Find the number of boxes that can be filled with 719 erasers each.
Number of boxes = Total number of erasers / Number of erasers per box
Number of boxes = 842 / 719
Number of boxes = 1 (since we cannot have a fractional number of boxes)

Step 2: Calculate the number of erasers that can be placed in the boxes.
Number of erasers in the boxes = Number of boxes × Number of erasers per box
Number of erasers in the boxes = 1 × 719 = 719

Step 3: Calculate the number of erasers left over.
Number of erasers left over = Total number of erasers - Number of erasers in the boxes
Number of erasers left over = 842 - 719 = 123

Therefore, after filling as many boxes as possible with 719 erasers each, there will be 123 erasers left over.

### Answer: 123

Expected answer: 123

Correct? Yes

Problem: A farmer harvested 461 carrots from his garden. He packs them into boxes, each box can hold up to 244 carrots. After packing as many full boxes as possible, how many carrots will be left unpacked?

Claude-3 Sonnet:

To solve this problem, we need to find out how many full boxes the farmer can pack with the 461 carrots, and then calculate the remaining carrots that will be left unpacked.

Given information:
- The farmer harvested 461 carrots.
- Each box can hold up to 244 carrots.

Step 1: Find the number of full boxes the farmer can pack.
Number of full boxes = Total carrots / Carrots per box
Number of full boxes = 461 / 244
Number of full boxes = 1 (with a remainder of 217)

Step 2: Calculate the remaining carrots that will be left unpacked.
Remaining carrots = Total carrots - (Number of full boxes × Carrots per box)
Remaining carrots = 461 - (1 × 244)
Remaining carrots = 461 - 244
Remaining carrots = 217

Therefore, after packing as many full boxes as possible, there will be 217 carrots left unpacked.

### Answer: 217

Expected answer: 217

Correct? Yes

Problem: A penguin scientist counts 309 penguins in a colony. She decides to tag them in groups of 293 for easier tracking. How many penguins will be in the final, possibly incomplete, group?

Claude-3 Sonnet:

To solve this problem, we need to find the remainder when 309 is divided by 293.

Given information:
- There are 309 penguins in the colony.
- The penguin scientist wants to tag them in groups of 293.

Step 1: Divide 309 by 293 to find the number of complete groups.
309 ÷ 293 = 1 (with a remainder)

Step 2: Find the remainder by subtracting the product of the number of complete groups and the group size from the total number of penguins.
Remainder = 309 - (1 × 293)
Remainder = 309 - 293
Remainder = 16

Therefore, the final, possibly incomplete, group will have 16 penguins.

### Answer: 16

Expected answer: 16

Correct? Yes

Problem: A sandwich shop has 580 slices of bread. They use 18 slices of bread for each sandwich-making batch. After using up the bread in these batches, how many slices will they have left?

Claude-3 Sonnet:

To solve this problem, we need to find out how many batches of sandwiches can be made with the available 580 slices of bread, and then calculate the remaining slices after using up the bread for those batches.

Given information:
- The sandwich shop has 580 slices of bread.
- Each sandwich-making batch requires 18 slices of bread.

Step 1: Find the number of batches that can be made with 580 slices of bread.
Number of batches = Total slices of bread / Slices required per batch
Number of batches = 580 / 18
Number of batches = 32.22 (rounded down to 32 since we cannot have a partial batch)

Step 2: Calculate the number of slices of bread used for 32 batches.
Slices of bread used = Number of batches × Slices required per batch
Slices of bread used = 32 × 18
Slices of bread used = 576

Step 3: Calculate the remaining slices of bread after using up the bread for the batches.
Remaining slices of bread = Total slices of bread - Slices of bread used
Remaining slices of bread = 580 - 576
Remaining slices of bread = 4

Therefore, after using up the bread in these batches, the sandwich shop will have 4 slices of bread left.

### Answer: 4

Expected answer: 4

Correct? Yes

Problem: A tailor has 925 meters of fabric. The tailor uses 529 meters of fabric to make each dress. If the tailor uses the fabric evenly for each dress, how many meters of fabric will be left over after completing the dresses?

Claude-3 Sonnet:

To solve this problem, we need to find out how many dresses the tailor can make with the available fabric and then calculate the remaining fabric after making those dresses.

Given information:
- The tailor has 925 meters of fabric.
- The tailor uses 529 meters of fabric to make each dress.

Step 1: Find the number of dresses the tailor can make with the available fabric.
Number of dresses = Total fabric / Fabric required for one dress
Number of dresses = 925 meters / 529 meters per dress
Number of dresses = 1.75 (rounded down to the nearest whole number, which is 1)

Step 2: Calculate the remaining fabric after making the dresses.
Remaining fabric = Total fabric - (Number of dresses × Fabric required for one dress)
Remaining fabric = 925 meters - (1 × 529 meters)
Remaining fabric = 925 meters - 529 meters
Remaining fabric = 396 meters

Therefore, after completing the dresses, the tailor will have 396 meters of fabric left over.

### Answer: 396

Expected answer: 396

Correct? Yes

Problem: There are 976 tourists wanting to explore a castle. Each tour group throughout the day accommodates up to 530 people. After all the groups have taken off, how many tourists will be left for the last group of the day?

Claude-3 Sonnet:

To solve this problem, we need to find out how many tour groups can accommodate the total number of tourists, and then calculate the remaining tourists for the last group.

Given information:
- There are 976 tourists wanting to explore the castle.
- Each tour group can accommodate up to 530 people.

Step 1: Find the number of tour groups needed to accommodate all the tourists.
Number of tour groups = Total number of tourists / Maximum capacity of each tour group
Number of tour groups = 976 / 530
Number of tour groups = 1.84 (rounded down to 1 since we cannot have a partial group)

Step 2: Calculate the number of tourists accommodated in the first tour group.
Number of tourists accommodated in the first tour group = 530

Step 3: Calculate the remaining number of tourists for the last group.
Remaining tourists for the last group = Total number of tourists - Number of tourists accommodated in the first tour group
Remaining tourists for the last group = 976 - 530
Remaining tourists for the last group = 446

Therefore, there will be 446 tourists left for the last group of the day.

### Answer: 446

Expected answer: 446

Correct? Yes