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 Opus:

Let's solve this problem step by step:

1. Initially, there are 535 fish in the tank.
2. The shark eats 461 fish in one sitting.
3. To find the number of fish left after the shark's dinner, we subtract the number of fish eaten from the total number of fish:

   535 - 461 = 74

4. The shark only eats when there are 461 or more fish to consume. Since there are only 74 fish left, which is less than 461, the shark will not eat again.

Therefore, after the shark's dinner, there will be 74 fish leftover in the 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The baker baked a total of 928 cookies.
   * He wants to distribute equal amounts of cookies to 186 orphanages.
   * We need to find out how many cookies are left after distributing as many entire sets of cookies as possible.

2. Calculate the number of cookies each orphanage will receive:
   * Number of cookies per orphanage = Total cookies ÷ Number of orphanages
   * Number of cookies per orphanage = 928 ÷ 186
   * Number of cookies per orphanage = 4 remainder 184
   * So, each orphanage will receive 4 cookies.

3. Calculate the total number of cookies distributed:
   * Total cookies distributed = Number of orphanages × Cookies per orphanage
   * Total cookies distributed = 186 × 4
   * Total cookies distributed = 744

4. Calculate the number of cookies left:
   * Cookies left = Total cookies - Total cookies distributed
   * Cookies left = 928 - 744
   * Cookies left = 184

Therefore, the baker will have 184 cookies left after distributing equal amounts of cookies to 186 orphanages.

### Answer: 184

Expected answer: 184

Correct? Yes

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 Opus:

Let's solve this problem step by step:

1. Find the number of full pizza boxes:
   * Each pizza box can contain 196 slices.
   * Number of full boxes = Total slices ÷ Slices per box
   * Number of full boxes = 975 ÷ 196 = 4.97 (rounded down to 4 since we can't have a partial box)

2. Calculate the number of slices in the full boxes:
   * Slices in full boxes = Number of full boxes × Slices per box
   * Slices in full boxes = 4 × 196 = 784

3. Calculate the number of leftover slices:
   * Leftover slices = Total slices - Slices in full boxes
   * Leftover slices = 975 - 784 = 191

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

### 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 Opus:

Let's solve this problem step by step:

1. The wizard starts with 932 stones.
2. Each creature he summons requires 193 stones.
3. To find out how many creatures the wizard can summon, we divide the total number of stones by the number of stones required for each creature:
   932 ÷ 193 = 4 remainder 160
   This means the wizard can summon 4 creatures, and he will have 160 stones left over.

So, after summoning 4 creatures, the wizard will have 160 stones left.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The builder needs to install 660 square foot tiles.
   * Each tile can cover 335 square feet.

2. Calculate the number of full tiles needed:
   * Number of full tiles = Total area ÷ Area covered by each tile
   * Number of full tiles = 660 ÷ 335
   * Number of full tiles = 1.97 (rounded to 1 full tile)

3. Calculate the area covered by the full tiles:
   * Area covered by full tiles = Number of full tiles × Area covered by each tile
   * Area covered by full tiles = 1 × 335
   * Area covered by full tiles = 335 square feet

4. Calculate the area that the last tile needs to cover:
   * Area for the last tile = Total area - Area covered by full tiles
   * Area for the last tile = 660 - 335
   * Area for the last tile = 325 square feet

Therefore, the last tile will need to cover 325 square feet.

### Answer: 325 square feet.

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 Opus:

Let's solve this step by step:

1. Find the number of 22-gallon containers that can be filled:
   * 473 ÷ 22 = 21 remainder 11
   * This means 21 containers can be filled completely.

2. Find the number of gallons left after filling the containers:
   * The remainder from the division is 11 gallons.
   * This means 11 gallons of juice will be left after filling 21 containers.

Therefore, after filling up all the 22-gallon containers, there will be 11 gallons of juice left.

### Answer: 11 gallons

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 Opus:

To solve this problem, let's follow these steps:

1. Find out how many boxes can be filled with 108 cars each:
   * 979 ÷ 108 = 9 remainder 7
   * This means 9 boxes can be completely filled with 108 cars each.

2. Calculate the number of cars packed in these 9 boxes:
   * 9 × 108 = 972 cars

3. Find the number of cars left unpacked:
   * Total cars produced - Cars packed in boxes = Cars left unpacked
   * 979 - 972 = 7 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The crayon factory can make 994 crayons in one operation.
   * Each box can hold 425 crayons.

2. Find the number of boxes that can be filled with 994 crayons:
   * Number of boxes = 994 ÷ 425
   * 994 ÷ 425 = 2 remainder 144
   * This means 2 boxes can be completely filled, and there will be some crayons left over.

3. Calculate the number of crayons left out of the boxes:
   * Crayons left out = Remainder from the division
   * Crayons left out = 144

Therefore, if the crayon factory operates at full capacity, 144 crayons will be left out of the boxes after the operation.

### 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 Opus:

Let's solve this step by step:

1. We need to find out how many zones can be filled with 696 tigers each.
   * 740 ÷ 696 = 1.063... 
   * This means we can fill 1 zone completely with 696 tigers.

2. Now, let's calculate how many tigers will be left after filling 1 zone.
   * Tigers left = Total tigers - Tigers in filled zones
   * Tigers left = 740 - (1 × 696)
   * Tigers left = 740 - 696 = 44

Therefore, after distributing the tigers evenly among the zones, 44 tigers will be left in the last zone.

### 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * The hat shop makes 830 hats every week.
   * They plan to put 421 hats in each special edition box.
   * We need to find out how many hats will be left over after evenly distributing the hats among the boxes.

2. Divide the total number of hats by the number of hats in each box:
   * 830 ÷ 421 = 1 remainder 409
   * This means they can fill 1 complete box, and there will be 409 hats left over.

3. Therefore, after evenly distributing the hats among the special edition boxes, there will be 409 hats left over.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the 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.

2. Calculate the number of fish left after the fisherman catches 575 fish:
   * Fish left = Initial number of fish - Fish caught by the fisherman
   * Fish left = 871 - 575 = 296

3. Since the fish repopulate at the same rate that the fisherman is depleting them, the number of fish will increase by 575 after repopulation:
   * Fish after repopulation = Fish left + Fish repopulated
   * Fish after repopulation = 296 + 575 = 871

Therefore, after a month, the number of fish in the lake will be the same as the initial number of fish.

### 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 Opus:

To solve this problem, let's follow these steps:

1. Find the number of beach bags that can be filled completely:
   * Number of beach balls = 891
   * Beach balls per bag = 119
   * Number of full bags = 891 ÷ 119 = 7 bags (with a remainder)

2. Calculate the number of beach balls that can fit in the full bags:
   * Beach balls in full bags = 7 × 119 = 833 beach balls

3. Calculate the number of beach balls left over:
   * Beach balls left over = Total beach balls - Beach balls in full bags
   * Beach balls left over = 891 - 833 = 58 beach balls

Therefore, 58 beach balls will not fit in the bags 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 Opus:

Let's approach this step by step:

1) First, we need to find out how many clusters of 6 stars can be formed from 544 stars.

   To do this, we divide 544 by 6:
   544 ÷ 6 = 90 remainder 4

   This means that 90 complete clusters of 6 stars can be formed, and there will be 4 stars left over.

2) Now, we can calculate the total number of stars in these 90 clusters:
   
   90 clusters × 6 stars per cluster = 540 stars

3) Finally, we can find the number of stars that remain ungrouped:
   
   Total stars - Stars in clusters = Ungrouped stars
   544 - 540 = 4

Therefore, 4 stars will remain ungrouped.

### Answer: 4

Expected answer: 98

Correct? No

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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * The manufacturer produces 805 socks in one shift.
   * The socks are packaged into sets of 132 each.

2. Find the number of complete sets of 132 socks that can be made from 805 socks:
   * Number of complete sets = 805 ÷ 132
   * 805 ÷ 132 = 6 remainder 13
   * So, 6 complete sets of 132 socks can be made.

3. Calculate the number of socks in the complete sets:
   * Socks in complete sets = 6 × 132
   * 6 × 132 = 792

4. Calculate the number of socks that remain unpackaged:
   * Unpackaged socks = Total socks - Socks in complete sets
   * Unpackaged socks = 805 - 792 = 13

Therefore, 13 socks will remain unpackaged after making complete sets of 132 socks each.

### 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 Opus:

Let's solve this problem step by step:

1. Find the number of full nights needed:
   * Total members: 759
   * Members per night: 228
   * Full nights = 759 ÷ 228 = 3.32...
   * Since we can't have a fraction of a night, there will be 3 full nights.

2. Find the number of members who will view the event in the first 3 nights:
   * Members in 3 nights = 228 × 3 = 684

3. Find the remaining members who will view the event on the final night:
   * Remaining members = Total members - Members in 3 nights
   * Remaining members = 759 - 684 = 75

Therefore, 75 people will view the event on the final night.

### Answer: 75

Expected answer: 75

Correct? Yes

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 Opus:

Let's solve this step by step:

1. Find the number of mailboxes needed:
   * Number of letters = 891
   * Capacity of each mailbox = 616
   * Number of mailboxes = 891 ÷ 616 = 1.446 (rounded to 3 decimal places)
   * Since we can't have a fraction of a mailbox, we need to round up to the next whole number.
   * Number of mailboxes needed = 2

2. Find the number of letters in the last mailbox:
   * Total number of letters = 891
   * Number of letters in the first mailbox = 616
   * Number of letters in the last mailbox = Total letters - Letters in the first mailbox
   * Number of letters in the last mailbox = 891 - 616 = 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 Opus:

Let's approach this step by step:

1) We know the total number of flies is 941.

2) Each time a frog jumps, it eats 258 flies.

3) We need to find out how many times the frog can jump while eating 258 flies each time, without exceeding the total number of flies.

4) We can do this by dividing 941 by 258 and taking the integer part of the result:

   941 ÷ 258 = 3.64...

   The integer part is 3, meaning the frog can jump 3 times, eating 258 flies each time.

5) So, the total number of flies eaten is:

   3 × 258 = 774

6) The remaining flies are:

   941 - 774 = 167

Therefore, after the frog has jumped as many times as it can, eating 258 flies per jump, there will be 167 flies 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 Opus:

Let's solve this step by step:

1. Find the number of spaces in each row:
   * Total spaces = 991
   * Number of rows = 66
   * Spaces per row = 991 ÷ 66 = 15

2. Calculate the total number of spaces that will be filled:
   * Filled spaces = Spaces per row × (Number of rows - 1)
   * Filled spaces = 15 × (66 - 1) = 15 × 65 = 975

3. Calculate the number of spare spaces in the last row:
   * Spare spaces = Total spaces - Filled spaces
   * Spare spaces = 991 - 975 = 16

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 Opus:

Let's approach this step by step:

1) First, let's find out how many liters of water can be put in each bottle if we divide the water evenly:
   
   193 ÷ 167 = 1.155689... liters per bottle

2) However, we can't have a fraction of a liter in a bottle. So, each bottle will contain 1 liter, and the rest will overflow.

3) To find the number of liters that will overflow, we multiply the number of bottles by the liters each bottle can hold, and subtract that from the total liters:

   Overflow = Total liters - (Bottles × Liters per bottle)
            = 193 - (167 × 1)
            = 193 - 167
            = 26 liters

Therefore, 26 liters of water will overflow and can't 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 Opus:

Let's approach this step by step:

1) We know the total number of eggs is 996.
2) Each row can hold 319 eggs.
3) We need to find out how many rows can be filled completely, and how many eggs will be left over for the last row.

4) To find the number of complete rows, we divide the total number of eggs by the number of eggs per row:
   996 ÷ 319 = 3 remainder 39
   This means there will be 3 complete rows.

5) The remainder, 39, tells us how many eggs will be in the last (incomplete) row.

Therefore, there will be 39 eggs 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 Opus:

To solve this problem, let's follow these steps:

1. Find out how many complete packs can be filled with 691 bulbs, given that each pack includes 205 bulbs.
   - To do this, we divide 691 by 205 and take the integer part (i.e., round down).
   - 691 ÷ 205 = 3.37 (rounded to 2 decimal places)
   - The integer part is 3, so 3 complete packs can be filled.

2. Calculate the number of bulbs in the 3 complete packs.
   - Each pack has 205 bulbs, so multiply 3 by 205.
   - 3 × 205 = 615 bulbs in the 3 complete packs.

3. Calculate the number of bulbs left unpacked by subtracting the bulbs in the complete packs from the total bulbs.
   - Total bulbs = 691
   - Bulbs in complete packs = 615
   - Unpacked bulbs = 691 - 615 = 76

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

### 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 Opus:

Let's approach this step by step:

1. Find the number of barns that can be filled completely:
   * 330 ÷ 259 = 1.27 (rounded down to 1 as we can't have a fraction of a barn)
   * So, 1 barn can be filled completely with 259 bales.

2. Calculate the number of bales stored in the completely filled barn(s):
   * 1 barn × 259 bales per barn = 259 bales

3. Calculate the number of bales left for the last barn:
   * Total bales - Bales in completely filled barns = Bales left for the last barn
   * 330 - 259 = 71 bales

Therefore, 71 bales of hay will be left for the last barn.

### Answer: 71

Expected answer: 71

Correct? Yes

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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * The construction company is installing a total of 166 windows.
   * One installation team can install 137 windows per day.
   * The windows are equally distributed amongst teams each day.

2. Find the number of windows that will be installed on the first day:
   * Windows installed on the first day = 137

3. Calculate the remaining windows after the first day:
   * Remaining windows = Total windows - Windows installed on the first day
   * Remaining windows = 166 - 137 = 29

Therefore, 29 windows will remain for the team to install on the next day.

### Answer: 29

Expected answer: 29

Correct? Yes

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 Opus:

Let's approach this step by step:

1. We know that there are 533 campers in total.
2. Each tent can accommodate 445 people.
3. To find out how many campers will be left over, we need to find the remainder when 533 is divided by 445.

We can do this division:

533 ÷ 445 = 1 remainder 88

This means that 1 tent will be completely filled (with 445 campers), and there will be 88 campers left over.

### 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 Opus:

To solve this problem, let's follow these steps:

1. Find the number of complete souvenir sets that can be made from 999 seashells, given that each set contains 474 shells.
   - To do this, we divide 999 by 474 and take the integer part (floor division).
   - 999 ÷ 474 = 2 remainder 51
   - This means we can make 2 complete sets of 474 shells each.

2. Calculate the number of seashells used in the complete sets.
   - Number of complete sets × Shells per set = 2 × 474 = 948 shells

3. Find the number of seashells left without a set by subtracting the number of shells used in complete sets from the total number of shells.
   - Total seashells - Shells used in complete sets = Seashells left without a set
   - 999 - 948 = 51 seashells

Therefore, after grouping the seashells into beach-themed 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 Opus:

Let's solve this problem step by step:

1. Find out how many skirts can be made with 366 meters of fabric.
   * To do this, divide 366 by 160: 366 ÷ 160 = 2 remainder 46
   * This means the tailor can make 2 skirts.

2. Calculate the total fabric used for making the skirts.
   * Each skirt requires 160 meters of fabric.
   * Total fabric used = 2 × 160 = 320 meters

3. Calculate the remaining fabric.
   * Remaining fabric = Total fabric - Fabric used for skirts
   * Remaining fabric = 366 - 320 = 46 meters

Therefore, after making as many skirts as possible, the tailor will have 46 meters of fabric left.

### Answer: 46 meters

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 Opus:

Let's approach this step by step:

1) First, let's find out how many boxes can be filled with 327 dolls each. We can do this by dividing the total number of dolls by the capacity of each box:

   993 ÷ 327 = 3.03669724771 boxes

2) Since we can't have a fraction of a box, we round down to the nearest whole number of boxes. So, 3 boxes can be filled to capacity.

3) Now, let's calculate how many dolls are packed in these 3 boxes:

   327 dolls/box × 3 boxes = 981 dolls

4) Finally, we can find the number of dolls left by subtracting the packed dolls from the total dolls:

   993 dolls - 981 dolls = 12 dolls

Therefore, the toymaker will have 12 dolls left after packing the boxes 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 Opus:

To solve this problem, let's use the division algorithm:
964 ÷ 839 = quotient + remainder/839

We can calculate the quotient and remainder by performing long division:

  1 R 125
839 | 964
     839
     ---
     125

So, the quotient is 1, and the remainder is 125.

This means that if the child distributes the stuffed animals evenly among their 839 friends, each friend will receive 1 stuffed animal, and 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The toy factory produces 369 teddy bears in a day.
   * Each box can hold 270 teddy bears.
   * We need to find out how many teddy bears will be left after evenly packing them in boxes.

2. Divide the total number of teddy bears by the number of bears each box can hold:
   * 369 ÷ 270 = 1 remainder 99
   * This means that 1 box will be completely filled, and there will be 99 teddy bears left.

3. The remaining teddy bears are the ones that will be left after evenly packing them in boxes.

Therefore, 99 teddy bears will be left after evenly packing the 369 teddy bears in boxes that can hold 270 bears each.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The villagers made 804 snowballs in total.
   * Each snowman requires 184 snowballs.

2. Find out how many complete snowmen can be built with 804 snowballs:
   * Number of complete snowmen = 804 ÷ 184
   * 804 ÷ 184 = 4 remainder 68
   * This means they can build 4 complete snowmen.

3. Calculate the number of leftover snowballs:
   * Leftover snowballs = Total snowballs - (Number of complete snowmen × Snowballs per snowman)
   * Leftover snowballs = 804 - (4 × 184)
   * Leftover snowballs = 804 - 736
   * Leftover snowballs = 68

Therefore, after building 4 complete snowmen, there will be 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 Opus:

Let's approach this step by step:

1) We need to find out how many rings will go into each box if they are distributed equally. To do this, we can divide the total number of rings by the number of boxes.

   843 ÷ 839 = 1 remainder 4

   This means that if we distribute the rings equally, each box will get 1 ring, and there will be 4 rings left over.

2) We can verify this by multiplying the number of boxes by the number of rings per box, and then adding the remainder:

   839 × 1 = 839
   839 + 4 = 843

   This confirms that if we put 1 ring in each of the 839 boxes, and then add the 4 leftover rings, we get the total of 843 rings.

Therefore, if each box is filled with an equal number of rings, there will be 4 rings left over.

### 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 Opus:

Let's solve this problem step by step:

1. Find the number of fireplaces that can be built with 819 bricks:
   * To do this, we divide 819 by 583 and take the integer part (floor division).
   * 819 ÷ 583 = 1.40480274442538 (rounded)
   * Using floor division: 819 // 583 = <<819//583=1>>1

2. Calculate the number of bricks used to build the fireplaces:
   * Number of bricks used = Number of fireplaces × Bricks per fireplace
   * Number of bricks used = 1 × 583 = <<1*583=583>>583

3. Calculate the number of bricks left over:
   * Bricks left over = Total bricks - Bricks used
   * Bricks left over = 819 - 583 = <<819-583=236>>236

### 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 Opus:

Let's organize the information we have:
- The factory produces 998 marshmallows per minute.
- Each packaging machine can hold 957 marshmallows.

To find the number of marshmallows left un-packaged, we need to find the remainder when the total number of marshmallows produced in a minute is divided by the capacity of each packaging machine.

Mathematically, this can be represented as:
998 ÷ 957 = 1 remainder 41

This means that after filling one packaging machine, there will be 41 marshmallows left un-packaged.

### Answer: 41 marshmallows will be left un-packaged in a minute after all the packaging machines are filled.

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 Opus:

Let's solve this problem step by step:

1. The castle's garden has 984 roses.
2. Each tribute requires 426 roses.
3. To find the number of tributes the Princess can create, we need to divide the total number of roses by the number of roses in each tribute.

984 ÷ 426 = 2 remainder 132

This means the Princess can create 2 complete tributes, and there will be 132 roses left over.

4. To find the number of roses left undistributed, we simply need to consider the remainder from the division above.

Therefore, 132 roses will be left undistributed in the castle's garden.

### 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 Opus:

Let's approach this step by step:

1) First, let's find out how many complete lines are in the song. We can do this by dividing the total number of words by the number of words in each line:

   334 ÷ 23 = 14 remainder 12

   This means there are 14 complete lines in the song.

2) Now, we know that the remaining words will form an incomplete line at the end of the song. The number of words in this incomplete line will be the remainder from the division above:

   Remainder = 12

Therefore, the incomplete line at the end of the song will have 12 words.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The teacher has 928 pages of study materials to print.
   * The printer can print 336 pages at a time.
   * We need to find out how many pages will be left over after filling the printer a number of times.

2. Divide the total number of pages by the printer's capacity to find the number of times the printer can be filled completely:
   * Number of times the printer can be filled = 928 ÷ 336
   * 928 ÷ 336 = 2 with a remainder of 256
   * This means the printer can be filled 2 times completely, and there will be some pages left over.

3. Calculate the number of pages that will be printed after filling the printer 2 times:
   * Pages printed = 2 × 336
   * Pages printed = 672

4. Calculate the number of pages left over by subtracting the printed pages from the total pages:
   * Pages left over = Total pages - Pages printed
   * Pages left over = 928 - 672
   * Pages left over = 256

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 Opus:

Let's solve this step by step:

1. We know that the scientists have spotted 972 sharks in total.
2. They tag the sharks in groups of 667 each.
3. To find out how many complete groups of 667 sharks can be tagged, we divide 972 by 667:
   972 ÷ 667 = 1 remainder 305
   This means the scientists can tag 1 complete group of 667 sharks.

4. Now, to find the number of sharks left untagged, we subtract the number of sharks tagged from the total number of sharks:
   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 Opus:

To solve this problem, let's follow these steps:

1. Find out how many boxes can be filled with the available blocks of cheese.
   - Total blocks of cheese = 686
   - Blocks of cheese per box = 349
   - Number of boxes that can be filled = 686 ÷ 349 = 1.965... rounded down to 1 (since we can't have a partial box)

2. Calculate the number of blocks of cheese that will be placed in the boxes.
   - Blocks of cheese in the boxes = Number of boxes × Blocks of cheese per box
   - Blocks of cheese in the boxes = 1 × 349 = 349

3. Calculate the number of blocks of cheese left over.
   - Leftover blocks of cheese = Total blocks of cheese - Blocks of cheese in the boxes
   - Leftover blocks of cheese = 686 - 349 = 337

Therefore, after filling all the boxes evenly, 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * Total snowfall recorded this winter = 513 centimeters
   * A snowplow can clear up to 170 centimeters of snow at a time

2. Find out how many full passes the snowplow can make:
   * Number of full passes = 513 ÷ 170
   * 513 ÷ 170 = 3 with a remainder of 3
   * This means the snowplow can make 3 full passes

3. Calculate the amount of snow cleared in the full passes:
   * Snow cleared in full passes = 3 × 170
   * 3 × 170 = 510 centimeters

4. Calculate the amount of snow left after the final pass:
   * Snow left = Total snowfall - Snow cleared in full passes
   * Snow left = 513 - 510
   * Snow left = 3 centimeters

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

### Answer: 3 centimeters

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 Opus:

Let's solve this problem step by step:

1. Find the number of full compasses that can be made:
   * The compass maker has 661 needles in total.
   * Each compass requires 510 needles.
   * Number of full compasses = 661 ÷ 510 = 1 remainder 151
   * So, the compass maker can make 1 full compass.

2. Find the number of needles left after making the full compass:
   * The compass maker used 510 needles for the full compass.
   * Needles left = Total needles - Needles used
   * Needles left = 661 - 510 = 151

Therefore, after installing as many full compasses as he can, 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The factory has manufactured 380 chairs.
   * Each shop can hold 310 chairs in its storage.
   * The factory wants to distribute the chairs evenly among the shops.

2. Find the number of shops that can receive the full 310 chairs:
   * Number of shops = 380 ÷ 310
   * Number of shops = 1 remainder 70
   * This means 1 shop can receive the full 310 chairs, and there will be 70 chairs left.

3. Calculate the number of chairs left at the factory:
   * Chairs left at the factory = 70 (the remainder from step 2)

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

### 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 Opus:

Let's solve this step by step:

1. We need to find out how many boxes the farmer can fill with 929 tomatoes, if each box holds 154 tomatoes.

2. To do this, we can divide 929 by 154:
   929 ÷ 154 = 6 remainder 5
   This means the farmer can fill 6 boxes completely, and there will be some tomatoes left over.

3. To find the number of tomatoes left over, we can use the remainder from the division:
   Remainder = 5
   So, there will be 5 tomatoes left over after filling the boxes.

Therefore, after packing the tomatoes evenly in boxes, 5 tomatoes will be 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 Opus:

Let's solve this step by step:

1. We have 454 pairs of ice skates in total.
2. We want to distribute these skates evenly among 128 boxes.
3. To find out how many skates will be in each box, we divide the total number of skates by the number of boxes:
   454 ÷ 128 = 3 remainder 70
   This means each box will contain 3 pairs of skates.

4. Now, we have 70 pairs of skates left over. These are the skates that will not fit evenly into the boxes.

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

### 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 Opus:

Let's solve this problem step by step:

1. The windmill generates 506 units of power per day.
2. The village consumes power in increments of 385 units.
3. We need to find out how many full increments of 385 units can be consumed from the 506 units generated.

To do this, we can divide 506 by 385:
506 ÷ 385 = 1 remainder 121

This means that the village can consume 1 full increment of 385 units, and there will be 121 units left over.

Therefore, at the end of the day, after the village has consumed as much power as it can in full increments, there will be 121 units of power 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * Blast Man has 338 energy units in his power cells.
   * Each energy blast uses 16 energy units.
   * He uses equal units of energy firing blasts.

2. Find out how many complete blasts Blast Man can fire:
   * Number of blasts = Total energy units ÷ Energy units per blast
   * Number of blasts = 338 ÷ 16 = 21 blasts with a remainder of 2 energy units

3. Calculate the total energy units used for the blasts:
   * Energy units used = Number of complete blasts × Energy units per blast
   * Energy units used = 21 × 16 = 336 energy units

4. Calculate the remaining energy units:
   * Remaining energy units = Total energy units - Energy units used
   * Remaining energy units = 338 - 336 = 2 energy units

Therefore, after using equal units of energy firing 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 Opus:

Let's solve this step by step:

1. Find the number of full buses needed:
   * Number of students = 530
   * Capacity of each bus = 144
   * Number of full buses = 530 ÷ 144 = 3.68
   * Since we can't have a fraction of a bus, we round down to 3 full buses.

2. Find the number of students on the full buses:
   * Students on full buses = 3 × 144 = 432

3. Find the number of students on the last bus:
   * Students on the last bus = Total students - Students on full buses
   * Students on the last bus = 530 - 432 = 98

Therefore, there will be 98 students on the last bus.

### 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 Opus:

Let's approach this step by step:

1) The wizard has 999 spells and 951 apprentices.

2) To find out how many spells each apprentice would get if divided equally, we do integer division:
   
   999 ÷ 951 = 1 (with a remainder)

3) This means that each apprentice will get 1 spell.

4) To find out how many spells are left, we need to find the remainder. We can do this by subtracting the total number of spells given out from the original number of spells:
   
   Total spells given out = Number of apprentices × Spells per apprentice
                          = 951 × 1 = 951

   Remaining spells = Total spells - Spells given out
                    = 999 - 951 = 48

Therefore, the wizard will have 48 spells left after giving out as many as he can to his apprentices.

### 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 Opus:

Let's approach this step by step:

1) We know that the company has produced 767 scooters in total.

2) Each delivery truck can carry 369 scooters.

3) To find out how many scooters will be left, we need to find the remainder when 767 is divided by 369.

4) We can do this by using the division algorithm:
   
   767 ÷ 369 = 2 remainder 29

   This means that 2 trucks will be fully loaded (each with 369 scooters), and there will be 29 scooters left over.

5) Therefore, after all the trucks are loaded, 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 Opus:

Let's approach this step by step:

1. Find the number of raindrops that can be formed:
   * Each raindrop needs 722 droplets to form.
   * Number of raindrops = Total number of droplets ÷ Droplets per raindrop
   * Number of raindrops = 846 ÷ 722 = 1.17 (rounded to 2 decimal places)
   * Since we can't have a fraction of a raindrop, we round down to 1 raindrop.

2. Find the number of droplets used to form the raindrops:
   * Droplets used = Number of raindrops × Droplets per raindrop
   * Droplets used = 1 × 722 = 722

3. Find the number of droplets left unconverted:
   * Droplets left = Total number of droplets - Droplets used
   * Droplets left = 846 - 722 = 124

Therefore, after forming the maximum number of raindrops, there will 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 Opus:

Let's approach this step by step:

1) First, let's find out how many unicorns would be in each section if they were divided equally. We can do this by dividing the total number of unicorns by the number of sections:

   265 ÷ 146 = 1.8150684931506849...

2) Since we can't have a fraction of a unicorn, this means that each complete section will have 1 unicorn, and there will be some unicorns left over for the last incomplete section.

3) To find out how many complete sections there are, let's perform integer division:

   265 // 146 = 1

4) This means there is 1 complete section, each with 1 unicorn.

5) To find the number of unicorns in the last incomplete section, we subtract the number of unicorns in the complete sections from the total number of unicorns:

   265 - (1 * 146) = 265 - 146 = 119

Therefore, the last incomplete section will have 119 unicorns.

### Answer: 119

Expected answer: 119

Correct? Yes

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 Opus:

Let's solve this step by step:

1. Find the number of full matches that can be formed:
   * 923 players ÷ 383 players per match = 2.4099 matches
   * Since we can't have a fraction of a match, we round down to 2 full matches.

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

3. Calculate the number of players left waiting:
   * Total players - Players who entered matches = Players left waiting
   * 923 players - 766 players = 157 players left waiting

Therefore, after filling all the matches evenly, 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 Opus:

To solve this problem, let's follow these steps:

1. Divide the total number of cannonballs by the number of crates to find out how many cannonballs can be evenly distributed in each crate.
   923 ÷ 499 = 1 remainder 424
   This means that each crate can have 1 cannonball, and there will be 424 cannonballs left over.

2. Calculate the number of cannonballs that will be placed in the crates:
   1 cannonball per crate × 499 crates = 499 cannonballs in crates

3. Subtract the number of cannonballs in crates from the total number of cannonballs to find the number of uncrated cannonballs:
   923 total cannonballs - 499 cannonballs in crates = 424 uncrated cannonballs

Therefore, after evenly distributing the cannonballs among the crates, there will be 424 cannonballs 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 Opus:

To solve this problem, let's organize the given information:
* The kite store has 530 string spools.
* They distribute the spools to 518 kites.
* Each kite gets one string spool.

Now, let's find the number of spools left in the store after distribution:
* Spools left = Total spools - Spools distributed
* Spools left = 530 - 518
* Spools left = <<530-518=12>>12

Therefore, after each kite gets a spool, there are 12 spools left in the 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 Opus:

To solve this problem, let's follow these steps:

1. Find the number of milk jugs that can be filled with 913 gallons of milk.
   - To do this, divide 913 by 39 and round down to the nearest whole number.
   - 913 ÷ 39 = 23.4102564...
   - Rounding down, we get 23 milk jugs.

2. Calculate the total number of gallons that will be put into the milk jugs.
   - Multiply the number of milk jugs by the capacity of each jug.
   - 23 × 39 = 897 gallons

3. Calculate the number of gallons left over by subtracting the total gallons in the jugs from the total gallons produced.
   - 913 - 897 = 16 gallons left over

Therefore, after filling all the milk 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * The doll seller received 603 dolls.
   * She arranged the dolls in rows, with 369 dolls in each row.
   * We need to find out how many dolls were left unarranged.

2. Calculate the number of complete rows:
   * Number of complete rows = 603 ÷ 369
   * 603 ÷ 369 = 1 remainder 234
   * So, there is 1 complete row of 369 dolls.

3. Calculate the number of dolls left unarranged:
   * Dolls left unarranged = Total dolls - Dolls in complete rows
   * Dolls left unarranged = 603 - (1 × 369)
   * Dolls left unarranged = 603 - 369
   * 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 Opus:

Let's solve this step by step:

1. We know that the jewelry maker has 850 beads in total.
2. Each necklace requires 631 beads.
3. To find out how many necklaces can be made, we divide the total number of beads by the number of beads needed for each necklace:
   850 ÷ 631 = 1 remainder 219
   This means the jewelry maker can make 1 complete necklace.

4. To find the number of beads left over, we take the remainder from the division:
   219 beads will be 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 Opus:

Let's solve this step by step:

1. Find the number of boxes the gardener can fill:
   * The gardener has 952 grapes in total.
   * Each box can hold 380 grapes.
   * Number of boxes = 952 ÷ 380 = 2.505
   * Since we can't have a fraction of a box, the gardener can fill 2 boxes completely.

2. Find the number of grapes in the filled boxes:
   * Each box holds 380 grapes.
   * Grapes in filled boxes = 2 × 380 = 760

3. Find the number of grapes left after filling the boxes:
   * Total grapes - Grapes in filled boxes = Grapes left
   * 952 - 760 = 192

Therefore, 192 grapes will be left after the gardener has filled as many boxes as possible.

### 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * The treasure map has a total of 236 steps.
   * Every 44 steps lead to a significant place or clue.

2. Find out how many significant places or clues there are:
   * Number of significant places or clues = Total steps ÷ Steps per clue
   * Number of significant places or clues = 236 ÷ 44
   * Number of significant places or clues = 5 remainder 16
   * This means there are 5 significant places or clues, and 16 steps remain after the last clue.

3. Calculate the number of steps taken to reach the last significant place or clue:
   * Steps to the last clue = Number of clues × Steps per clue
   * Steps to the last clue = 5 × 44
   * Steps to the last clue = 220

4. Find the remaining steps after the last significant place or clue:
   * Remaining steps = Total steps - Steps to the last clue
   * Remaining steps = 236 - 220
   * Remaining steps = 16

Therefore, 16 steps will be left after reaching the last significant place or clue.

### 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 Opus:

Let's approach this step by step:

1) First, let's find out how many complete groups of 507 bubbles Sarah's machine made. We can do this by dividing 932 by 507:

   932 ÷ 507 = 1 remainder 425

   This means the machine made 1 complete group of 507 bubbles.

2) Now, we need to find out how many bubbles were in the final, incomplete group. The remainder from the division tells us this:

   The remainder is 425, so there were 425 bubbles in the final, incomplete group.

Therefore, after forming complete groups, the machine made 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * There are 931 kids who want to use the swings.
   * Each swing set can accommodate 34 kids at a time.
   * We need to find out how many kids will be waiting after all the swing sets are occupied.

2. Find the number of swing sets that can be fully occupied by the kids:
   * Number of swing sets = 931 ÷ 34
   * 931 ÷ 34 = 27 remainder 13
   * So, 27 swing sets can be fully occupied.

3. Calculate the number of kids accommodated in the fully occupied swing sets:
   * Kids accommodated = 27 × 34
   * 27 × 34 = 918

4. Find the number of kids waiting for their turn:
   * Kids waiting = Total kids - Kids accommodated
   * Kids waiting = 931 - 918
   * Kids waiting = 13

Therefore, 13 kids will be waiting for their turn after all the swing sets are occupied.

### Answer: 13

Expected answer: 13

Correct? Yes

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 Opus:

Let's solve this step by step:

1. First, we need to find out how many wallets John can fully load with 943 dollar bills, given that each wallet can hold 433 dollar bills.

   To do this, we divide 943 by 433:
   943 ÷ 433 = 2 remainder 77

   This means John can fully load 2 wallets, and he will have some dollar bills left over.

2. Now, we need to find out how many dollar bills are left after loading the 2 wallets.

   Each wallet holds 433 dollar bills, so 2 wallets hold:
   433 × 2 = 866 dollar bills

   So, the number of dollar bills left is:
   943 - 866 = 77

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

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The helicopter pilot needs to transport a total of 240 passengers.
   * The helicopter can carry 177 passengers in one trip.

2. Calculate the number of passengers left behind after the first full trip:
   * Passengers left behind = Total passengers - Passengers in one full trip
   * Passengers left behind = 240 - 177
   * Passengers left behind = 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 Opus:

Let's solve this step by step:

1. Find the number of complete flowerbeds the gardener can fill:
   * 982 flowers ÷ 555 flowers per flowerbed = 1.76936...
   * Since we can't have a partial flowerbed, the gardener can fill 1 complete flowerbed.

2. Calculate the number of flowers used in the complete flowerbed:
   * 1 flowerbed × 555 flowers per flowerbed = 555 flowers

3. Calculate the number of flowers left after filling the complete flowerbed:
   * Total flowers - Flowers used in complete flowerbeds
   * 982 - 555 = 427 flowers left

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 Opus:

Let's solve this problem step by step:

1. The farmer has 203 strawberry plants.
2. She wants to divide the plants into groups of 5.
3. To find the number of complete groups, we divide 203 by 5:
   203 ÷ 5 = 40 remainder 3
   This means there will be 40 complete groups of 5 plants.

4. The remaining plants that don't form a complete group of 5 are 3.

Therefore, if the farmer divides her 203 strawberry plants equally 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 Opus:

Let's solve this step by step:

1) First, let's find out how many bundles of 16 carrots the gardener can make. We can do this by dividing the total number of carrots by 16.

   355 ÷ 16 = 22 remainder 3

   This means the gardener can make 22 bundles of 16 carrots.

2) Now, let's calculate how many carrots were used in these 22 bundles.

   22 bundles × 16 carrots per bundle = 352 carrots

3) Finally, we can find the number of carrots left by subtracting the number of carrots used in the bundles from the total number of carrots.

   355 total carrots - 352 carrots in bundles = 3 carrots left

Therefore, after creating as many bundles of 16 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 Opus:

Let's approach this step by step:

1. Find the total number of inches of rainfall:
   * Total rainfall = 612 inches

2. Find the number of days:
   * Number of days = 29 days

3. To find the amount of rainfall per day, divide the total rainfall by the number of days:
   * Rainfall per day = Total rainfall ÷ Number of days
   * Rainfall per day = 612 ÷ 29 = <<612/29=21.1034482758621>>21.1034482758621 inches

4. Round down the rainfall per day to the nearest whole number:
   * Rounded rainfall per day = 21 inches

5. Calculate the total rainfall if it were evenly distributed:
   * Even total rainfall = Rounded rainfall per day × Number of days
   * Even total rainfall = 21 × 29 = <<21*29=609>>609 inches

6. Calculate the difference between the actual total rainfall and the even total rainfall:
   * Leftover rainfall = Total rainfall - Even total rainfall
   * Leftover rainfall = 612 - 609 = <<612-609=3>>3 inches

Therefore, 3 inches of rain would be left to make the days evenly rainy.

### Answer: 3

Expected answer: 3

Correct? Yes

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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The truck company has 514 boxes for delivery.
   * Each truck can hold up to 371 boxes.
   * We need to find out how many boxes will be left over if each truck is loaded to its full capacity.

2. Calculate the number of trucks needed:
   * Number of trucks = Total boxes ÷ Boxes per truck
   * Number of trucks = 514 ÷ 371
   * Number of trucks = 1.385 (rounded to 3 decimal places)
   * Since we can't have a fraction of a truck, we round up to 2 trucks.

3. Calculate the total number of boxes that can be loaded in the trucks:
   * Boxes loaded = Number of trucks × Boxes per truck
   * Boxes loaded = 2 × 371
   * Boxes loaded = 742

4. Calculate the number of boxes left over:
   * Boxes left over = Total boxes - Boxes loaded
   * Boxes left over = 514 - 742
   * Boxes left over = -228

However, it's not possible to have a negative number of boxes left over. This means that all the boxes can be loaded into the trucks without any boxes being left over.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * Children created 684 sandcastles in total.
   * The sandcastles were grouped into sets of 230 for a photography contest.
   * We need to find out how many sandcastles were left that didn't form a complete set.

2. Calculate the number of complete sets of sandcastles:
   * Number of complete sets = Total sandcastles ÷ Sandcastles per set
   * Number of complete sets = 684 ÷ 230
   * Number of complete sets = 2 with a remainder of 224
   * This means there are 2 complete sets of 230 sandcastles.

3. Calculate the number of sandcastles in the complete sets:
   * Sandcastles in complete sets = Number of complete sets × Sandcastles per set
   * Sandcastles in complete sets = 2 × 230
   * Sandcastles in complete sets = 460

4. Calculate the number of sandcastles left that didn't form a complete set:
   * Sandcastles left = Total sandcastles - Sandcastles in complete sets
   * Sandcastles left = 684 - 460
   * Sandcastles left = 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 Opus:

Let's approach this step by step:

1) We know that the manufacturer has 735 toy cars in total.

2) They are packaging these cars into packs of 348 each.

3) To find out how many full packs can be made, we need to divide 735 by 348:

   735 ÷ 348 = 2 remainder 39

   This means that 2 full packs can be made, and there will be 39 cars left over.

4) To confirm, let's check: 2 packs of 348 cars each is 2 × 348 = 696 cars. 
   If we add the remaining 39 cars, we get 696 + 39 = 735, which is the total number of cars.

Therefore, after filling all the full packs, 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 Opus:

Let's solve this step by step:

1. Find the number of fully occupied territories:
   * 386 ÷ 95 = 4 remainder 6
   * This means there are 4 fully occupied territories, and the remaining animals are in the last not fully occupied territory.

2. Calculate the number of animals in the fully occupied territories:
   * 4 territories × 95 animals per territory = 380 animals

3. Calculate the number of animals in the last not fully occupied territory:
   * Total animals - Animals in fully occupied territories
   * 386 - 380 = 6 animals

Therefore, there will be 6 animals 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 Opus:

Let's organize the given information and solve the problem step by step:
* The forest has a total of 801 trees.
* The tree disease is expected to affect 646 trees.
* We need to find out how many trees will likely stay healthy after the disease has affected all possible trees.

To find the number of healthy trees, we need to subtract the number of diseased trees from the total number of trees in the forest.

Healthy trees = Total trees - Diseased trees
Healthy trees = 801 - 646 = 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 Opus:

Let's approach this step by step:

1) We need to find out how many 902-meter pieces can be cut from the 934-meter rope.

2) We can do this by dividing 934 by 902 and taking the integer part of the result:

   934 ÷ 902 = 1.035... 
   The integer part is 1.

3) This means that we can cut one 902-meter piece from the rope.

4) After cutting this piece, the remaining length of the rope will be:

   934 - 902 = 32 meters

Therefore, after cutting the maximum possible number of 902-meter pieces (which is 1), 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The dairy farm produces 561 liters of milk each day.
   * The milk is packaged into containers that hold 550 liters each.

2. To find out how many liters of milk are left over, we need to calculate the remainder when dividing the total milk produced by the capacity of each container.

3. Divide the total milk produced by the container capacity:
   * 561 ÷ 550 = 1 remainder 11

4. The quotient (1) tells us that one full container can be filled, and the remainder (11) is the amount of milk left over.

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

### Answer: 11 liters

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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * Jon has 259 puzzle pieces in total.
   * Each puzzle requires 258 pieces to be completed.

2. To find the number of pieces left over, we need to divide the total number of pieces by the number of pieces required for each puzzle and find the remainder.

3. Dividing 259 by 258:
   * 259 ÷ 258 = 1 remainder 1
   * This means Jon can complete 1 full puzzle, and he will have 1 piece left over.

Therefore, once Jon completes a full puzzle, he will have 1 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 Opus:

Let's solve this step by step:

1. Find the number of bracelets the jewelry maker can create:
   * Each bracelet requires 49 beads.
   * Number of bracelets = Total beads ÷ Beads per bracelet
   * Number of bracelets = 673 ÷ 49 = 13 remainder 36
   * So, she can make 13 bracelets.

2. Calculate the number of beads used:
   * Beads used = Number of bracelets × Beads per bracelet
   * Beads used = 13 × 49 = 637

3. Calculate the number of beads left:
   * Beads left = Total beads - Beads used
   * Beads left = 673 - 637 = 36

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

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The police station received 927 calls within a week.
   * They have 311 operators.
   * Each operator handles the same number of calls.
   * We need to find out how many calls the last operator will handle.

2. Divide the total number of calls by the number of operators:
   * 927 ÷ 311 = 2 remainder 305
   * This means each operator will handle 2 calls, and there will be 305 calls left.

3. The remaining 305 calls will be handled by the last operator.

Therefore, the last operator will handle 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 Opus:

Let's solve this step by step:

1. Understand the given information:
   * John has 764 pieces for his jigsaw puzzle.
   * Each package should contain 589 pieces.
   * We need to find out how many pieces will be left outside without a package.

2. Divide the total number of pieces by the number of pieces per package:
   * 764 ÷ 589 = 1 remainder 175
   * This means John can make 1 full package, and there will be 175 pieces left.

3. The remaining pieces are the ones that will be left outside without a package.

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 Opus:

Let's solve this problem step by step:

1. Find the number of dresses the dressmaker can make with 984 meters of fabric.
   * To do this, divide 984 by 217.
   * 984 ÷ 217 = 4 remainder 116
   * This means she can make 4 complete dresses.

2. Calculate the amount of fabric used for making the 4 dresses.
   * Each dress requires 217 meters of fabric.
   * Fabric used = 4 × 217 = 868 meters

3. Calculate the remaining fabric.
   * Total fabric - Fabric used = Remaining fabric
   * 984 - 868 = 116 meters

Therefore, the dressmaker will have 116 meters of fabric left after making as many dresses as possible.

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The company donates 639 sleeping bags in total.
   * Each campsite is supplied with 374 sleeping bags.
   * We need to find out how many sleeping bags will be left after dividing them equally among the campsites.

2. Determine the number of campsites:
   * Number of campsites = Total sleeping bags ÷ Sleeping bags per campsite
   * Number of campsites = 639 ÷ 374
   * 639 ÷ 374 = 1 remainder 265
   * So, there is 1 complete campsite, and 265 sleeping bags are left.

3. Calculate the number of sleeping bags left:
   * Sleeping bags left = 265

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The restaurant made 620 pizzas today.
   * Each delivery box can hold 8 pizzas.

2. Calculate the number of full boxes that can be filled:
   * Number of full boxes = 620 ÷ 8
   * 620 ÷ 8 = 77 remainder 4
   * So, 77 boxes can be filled completely.

3. Determine the number of pizzas left over:
   * The remainder from the division is the number of pizzas left over.
   * Pizzas left over = 4

Therefore, 4 pizzas will be left over that don't fit into a full box.

### Answer: 4

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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The factory made a total of 820 robots.
   * Each storage unit can store 684 robots.
   * The robots are evenly stored in the storage units.

2. Find the number of storage units needed:
   * Number of storage units = 820 ÷ 684
   * 820 ÷ 684 = 1 remainder 136
   * This means 1 storage unit will be completely filled, and there will be 136 robots left.

3. Calculate the number of robots that will not fit in the storage units:
   * Robots not fitting in the storage units = 136

Therefore, 136 robots will 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 Opus:

Let's approach this step by step:

1) The cloud starts with 516 droplets.

2) The cloud loses water droplets at an equal rate and becomes entirely dry after every 289 droplets. This means that the cloud will go through several cycles of losing 289 droplets until it has less than 289 droplets left.

3) To find out how many complete cycles the cloud will go through, we can divide 516 by 289:

   516 ÷ 289 = 1.7855... 
   
   This means the cloud will go through 1 complete cycle of losing 289 droplets.

4) After this cycle, the number of droplets left will be:

   516 - 289 = 227

5) Since 227 is less than 289, the cloud will not go through another complete cycle. Instead, it will lose all remaining 227 droplets in the final cycle.

6) After the final cycle, the cloud will be completely dry, meaning there will be 0 droplets left.

### Answer: 0

Expected answer: 227

Correct? No

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 Opus:

Let's solve this step by step:

1. Find the number of trucks that can be fully loaded:
   * Each truck can hold 4 boxes.
   * Number of fully loaded trucks = 330 ÷ 4 = 82 remainder 2
   * This means 82 trucks can be fully loaded, and there will be 2 boxes left.

2. Find the number of boxes left unloaded:
   * Boxes left unloaded = 2 (the remainder from the division above)

Therefore, after filling each truck to its full capacity, 2 boxes will be left unloaded.

### Answer: 2

Expected answer: 2

Correct? Yes

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 Opus:

Let's solve this step by step:

1. The farmer harvested 649 potatoes in total.
2. Each crate can hold 183 potatoes.
3. To find out how many crates can be filled, we divide the total number of potatoes by the number of potatoes per crate:
   649 ÷ 183 = 3 remainder 100
   This means 3 crates can be filled completely, and there will be some potatoes left over.

4. To find the number of potatoes left over, we multiply the number of full crates by the number of potatoes per crate, and subtract this from the total number of potatoes:
   3 × 183 = 549
   649 - 549 = 100

Therefore, after filling 3 crates to their maximum capacity, there will be 100 potatoes left over.

### 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 Opus:

Let's solve this step by step:

1. We have a total of 258 shirts.
2. Each box can hold 67 shirts.
3. To find out how many boxes can be filled completely, we divide 258 by 67:
   258 ÷ 67 = 3 remainder 57
   This means 3 boxes can be filled completely, and there will be some shirts left over.

4. To find the number of shirts left outside the boxes, we take the remainder from the division:
   Shirts left outside boxes = 57

Therefore, if all the shirts are evenly distributed in the boxes, 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 Opus:

To solve this problem, we need to find the remainder when dividing the total number of gold coins by the number of pirates.

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

Step 1: Divide the total number of gold coins by the number of pirates.
995 ÷ 267 = 3 remainder 194

This means that each pirate will receive 3 gold coins, and there will be 194 gold coins left over.

### Answer: 194 gold coins will be left over.

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 Opus:

Let's approach this step by step:

1) First, let's find out how many complete groups of 375 snails we can make from 776 snails.

   To do this, we divide 776 by 375:
   776 ÷ 375 = 2 remainder 26

   This means we can make 2 complete groups of 375 snails.

2) Now, we need to find out how many snails are left over.

   The remainder from the division tells us this. There are 26 snails left over.

3) Therefore, in the final group, there will be 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 Opus:

Let's approach this step by step:

1) First, we need to find out how many full boxes can be packed with 589 pillows, given that each box holds 198 pillows.

   To do this, we divide 589 by 198 and take the integer part of the result:
   589 ÷ 198 = 2.97 (rounded to 2 decimal places)
   The integer part of 2.97 is 2, so they can pack 2 full boxes.

2) Now, we need to find out how many pillows are in these 2 full boxes:
   2 boxes × 198 pillows per box = 396 pillows

3) Finally, we subtract the number of pillows in the full boxes from the total number of pillows to find out how many are left outside the boxes:
   589 pillows - 396 pillows in full boxes = 193 pillows left outside the boxes

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 Opus:

Let's solve this step by step:

1. Find the number of necklaces the jewelry maker can make with 633 beads, if each necklace requires 30 beads.
   * Number of necklaces = Total beads ÷ Beads per necklace
   * Number of necklaces = 633 ÷ 30 = 21 necklaces with a remainder of 3 beads

2. Calculate the total number of beads used in making the necklaces.
   * Beads used = Number of necklaces × Beads per necklace
   * Beads used = 21 × 30 = 630 beads

3. Find the number of beads left after making the necklaces.
   * Beads left = Total beads - Beads used
   * Beads left = 633 - 630 = 3 beads

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

### 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * John has 365 coins in total.
   * He wants to distribute the coins equally among 140 wallets.
   * Some coins will be left after the distribution.

2. Find the number of coins that can be evenly distributed in each wallet:
   * Number of coins per wallet = 365 ÷ 140
   * 365 ÷ 140 = 2 remainder 85
   * So, each wallet will have 2 coins.

3. Calculate the total number of coins distributed in the wallets:
   * Total coins distributed = Number of coins per wallet × Number of wallets
   * Total coins distributed = 2 × 140 = 280

4. Calculate the number of coins left after the distribution:
   * Coins left = Total coins - Total coins distributed
   * Coins left = 365 - 280 = 85

Therefore, John will have 85 coins left after evenly distributing the coins into 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 Opus:

Let's solve this step by step:

1. We need to find out how many cartons can be filled with 743 socks, if each carton contains 451 socks.

2. To do this, we can divide 743 by 451:
   743 ÷ 451 = 1 remainder 292
   
   This means that 1 carton can be completely filled, and there will be some socks left over.

3. The number of socks that are left over is the remainder from the division:
   Socks left unpacked = 292

Therefore, after filling up as many cartons as possible, 292 socks are 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 Opus:

To solve this problem, let's organize the given information:
* Total number of children who want to slide down: 923
* Number of children who can go down the slide without rest: 771

Now, let's find the number of children left waiting for their turn:
* Children left waiting = Total children - Children who can go down without rest
* Children left waiting = 923 - 771
* 923 - 771 = 152

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

### 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 Opus:

Let's solve this step by step:

1. Find the number of full groups Iron Punch can teleport:
   * 442 ÷ 104 = 4 remainder 26
   * This means Iron Punch can teleport 4 full groups of 104 people.

2. Calculate the total number of people teleported in the full groups:
   * 4 groups × 104 people per group = 416 people

3. Find the number of people left in the building for the last round of rescue:
   * Total people - People in full groups = People left
   * 442 - 416 = 26 people

Therefore, after teleporting as many full groups as he can, 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 Opus:

Let's solve this step by step:

1. We need to find out how many complete packs of 68 cards can be made from 569 cards.
2. To do this, we can divide 569 by 68 and take the integer part of the result (as we can't have a fraction of a pack).
   569 ÷ 68 = 8.367... 
   The integer part is 8, so 8 complete packs can be made.

3. Now, to find the number of cards left over, we multiply the number of complete packs by the number of cards per pack, and subtract this from the total number of cards.
   Cards in complete packs = 8 × 68 = 544
   Cards left over = Total cards - Cards in complete packs
                   = 569 - 544 = 25

Therefore, 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 Opus:

Let's solve this step by step:

1. We need to find out how many boxes can be filled with 719 erasers each, given a total of 842 erasers.

2. To do this, we can divide 842 by 719 and take the integer part of the result (as we can't have a partial box):
   842 ÷ 719 = 1.17 (rounded to 2 decimal places)
   The integer part of 1.17 is 1, so we can fill 1 box completely.

3. Now, we need to find out how many erasers are left after filling 1 box:
   Erasers left = Total erasers - (Number of boxes × Erasers per box)
               = 842 - (1 × 719)
               = 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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * The farmer harvested 461 carrots.
   * Each box can hold up to 244 carrots.
   * We need to find out how many carrots will be left unpacked after filling as many boxes as possible.

2. Determine the number of full boxes:
   * Number of full boxes = 461 ÷ 244
   * 461 ÷ 244 = 1 remainder 217
   * So, the farmer can fill 1 full box.

3. Calculate the number of carrots left unpacked:
   * Carrots left unpacked = Remainder from the division
   * Remainder = 217
   * So, 217 carrots will be 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 Opus:

Let's approach this step by step:

1) To find out how many groups of 293 penguins can be formed from 309 penguins, we divide 309 by 293:

   309 ÷ 293 = 1 remainder 16

   This means that 1 complete group of 293 penguins can be formed.

2) The remainder, 16, tells us that there are 16 penguins left over after forming the complete group.

3) These 16 penguins will form the final, incomplete group.

Therefore, the final group will contain 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 Opus:

Let's solve this problem step by step:

1. Find the number of sandwich-making batches:
   * The shop uses 18 slices of bread for each batch.
   * Number of batches = Total slices ÷ Slices per batch
   * Number of batches = 580 ÷ 18 = 32 remainder 4
   * They can make 32 complete batches.

2. Find the number of slices used in the batches:
   * Slices used = Number of batches × Slices per batch
   * Slices used = 32 × 18 = 576

3. Find the number of slices left:
   * Slices left = Total slices - Slices used
   * Slices left = 580 - 576 = 4

Therefore, after using up the bread in these batches, they will have 4 slices 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 Opus:

Let's solve this problem step by step:

1. Find out how many dresses the tailor can make with the available fabric:
   * The tailor has 925 meters of fabric.
   * Each dress requires 529 meters of fabric.
   * Number of dresses = 925 ÷ 529 = 1.74 (rounded down to 1 because the tailor can't make a fraction of a dress)

2. Calculate the amount of fabric used for making the dresses:
   * Fabric used = Number of dresses × Fabric per dress
   * Fabric used = 1 × 529 = 529 meters

3. Calculate the amount of fabric left over:
   * Leftover fabric = Total fabric - Fabric used
   * Leftover fabric = 925 - 529 = 396 meters

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

### Answer: 396 meters

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 Opus:

Let's solve this problem step by step:

1. Understand the given information:
   * There are 976 tourists in total.
   * Each tour group can accommodate up to 530 people.
   * We need to find out how many tourists will be left for the last group.

2. Find the number of complete tour groups:
   * Number of complete groups = 976 ÷ 530
   * 976 ÷ 530 = 1 remainder 446
   * So, there will be 1 complete tour group.

3. Find the number of tourists left for the last group:
   * Tourists left = Total tourists - (Number of complete groups × Tourists per group)
   * Tourists left = 976 - (1 × 530)
   * Tourists left = 976 - 530 = 446

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

### Answer: 446

Expected answer: 446

Correct? Yes