🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the difference between the initial number of fish and the number the shark eats.
    535 - 461 = 74
    This means that 74 fish are left after the shark eats.
    The shark can't eat the remaining fish because there are less than 461 fish left.

    ### Answer: 74

Expected answer: 74

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many cookies the baker can give to each orphanage, we divide the total number of cookies by the number of orphanages: 928 cookies / 186 orphanages = 4.98 cookies per orphanage. Since the baker can only give out whole cookies, each orphanage receives 4 cookies. The baker gave out a total of 4 cookies/orphanage * 186 orphanages = 744 cookies. The baker has 928 cookies - 744 cookies = 184 cookies left.

    ### Answer: 184

Expected answer: 184

Correct? Yes

🔗 Follow-up

Problem: In the previously mentioned scenario, consider that the baker only baked 173 cookies instead of 928. He still plans on distributing equal amounts of cookies to the 186 orphanages. After giving out as many full sets as possible to each orphanage, how many cookies will the baker have left over this time?

Gemini-1.5 Flash:

    Reasoning:  Since the baker has fewer cookies than orphanages, he can only give out one cookie to each orphanage. He will give out a total of 1 cookie/orphanage * 186 orphanages = 186 cookies.
    He will then have 173 cookies - 186 cookies = -13 cookies. Since he can't have negative cookies, he'll have no cookies left over, and he'll be short 13 cookies.

    ### Answer: 0

Expected answer: 173

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find out how many slices of pizza fit into the boxes, so we divide the total slices by the capacity of each box: 975 / 196 = 4.97 (approximately). Since we can only have whole boxes, we know that 4 boxes will be full. To find out how many slices are left over, we multiply the number of full boxes by the capacity of each box and subtract that from the total slices: 4 * 196 = 784, and 975 - 784 = 191.

    ### Answer: 191

Expected answer: 191

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    This problem requires us to find the remainder after dividing the total number of stones by the number of stones needed per creature.

    We need to know how many creatures the wizard has summoned to determine the remainder.

    Let's say the wizard summoned 'x' creatures.  He would use 193 * x stones for those creatures.

    To find the remaining stones, we would subtract the stones used from the total stones: 932 - (193 * x)

    **We need the number of creatures summoned ('x') to calculate the remaining stones.**

Expected answer: 160

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The builder can install 660/335 = <<660/335=1.97>>1.97 tiles. Since the builder can only install whole tiles, he can install 1 tile completely. The last tile will need to cover the remaining 660-335 = <<660-335=325>> 325 square feet.

    ### Answer: 325

Expected answer: 325

Correct? Yes

🔗 Follow-up

Problem: A builder realizes that he made a mistake and the tiles can actually cover 337 square feet instead of 335 square feet. Given the same total area of 660 square feet, how many square feet will the last tile now need to cover?

Gemini-1.5 Flash:

    Reasoning: The builder can install 660/337 = <<660/337=1.95>> 1.95 tiles. Since the builder can only install whole tiles, he can install 1 tile completely. The last tile will need to cover the remaining 660-337 = <<660-337=323>> 323 square feet.

    ### Answer: 323

Expected answer: 323

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First, find out how many full containers the company can fill: 473 gallons / 22 gallons/container = 21 containers with some juice left over.
    Then, multiply the number of full containers by the size of each container to find out how much juice is used: 21 containers * 22 gallons/container = 462 gallons.
    Finally, subtract the amount of juice used from the total amount of juice to find out how much is left: 473 gallons - 462 gallons = 11 gallons.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: A juice company initially thought they produced 473 gallons of juice, but they realized they actually produced 599 gallons. They used the same 22-gallon containers as before. After filling up all the containers, how many gallons of juice do they now have left over?

Gemini-1.5 Flash:

    Reasoning: First, we need to determine how many full containers can be filled with 599 gallons: 599 gallons / 22 gallons/container = 27 containers with some juice left over.
    Next, we'll calculate how much juice is used to fill these containers: 27 containers * 22 gallons/container = 594 gallons.
    Finally, we subtract the amount of juice used from the total amount produced to find the leftover juice: 599 gallons - 594 gallons = 5 gallons.

    ### Answer: 5

Expected answer: 5

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  To find out how many boxes they can fill, we divide the total number of cars by the number of cars per box: 979 cars / 108 cars/box = 9.06 boxes. Since we can't have parts of boxes, they can fill 9 boxes completely.  To find out how many cars are left unpacked, we multiply the number of cars per box by the number of boxes filled and then subtract that from the total number of cars: 9 boxes * 108 cars/box = 972 cars.  979 cars - 972 cars = 7 cars left unpacked.

    ### Answer: 7

Expected answer: 7

Correct? Yes

🔗 Follow-up

Problem: The toy factory now produced 979 toy cars in a day and decided to package these cars into larger boxes, each containing 684 cars. After all the cars have been packed into the larger boxes, how many toy cars would be left unpacked at the end of the day?

Gemini-1.5 Flash:

    Reasoning:  Since each larger box holds 684 cars, and the factory produced 979 cars, we need to see how many times 684 goes into 979.  979 / 684 = 1.43 (approximately). This means they can completely fill 1 box (since we can't have parts of boxes).
    To find out how many cars are left unpacked, we subtract the number of cars in one full box from the total number of cars: 979 cars - 684 cars = 295 cars.

    ### Answer: 295

Expected answer: 295

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The factory can fill 994/425 = <<994/425 = 2.34>>2.34 boxes. Since we can't have a fraction of a box, the factory can fill 2 boxes.
    Each box holds 425 crayons, so 2 boxes hold 2*425 = <<2*425 = 850>>850 crayons.
    Therefore, 994 - 850 = <<994-850 = 144>>144 crayons will be left out of the boxes.
    ### Answer: 144

Expected answer: 144

Correct? Yes

🔗 Follow-up

Problem: Let's now consider that the crayon factory only made 223 crayons in one operation, while each box still holds 425 crayons. Again, how many crayons are left over and fail to make it into a box?

Gemini-1.5 Flash:

    Reasoning: Since the factory only made 223 crayons, and each box holds 425 crayons, there aren't enough crayons to fill even one box.
    Therefore, all 223 crayons will be left over.
    ### Answer: 223

Expected answer: 223

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First, divide the total number of tigers by the number of tigers per zone: 740 / 696 = 1.06. This means that each zone can hold 1 full group of 696 tigers, with some left over.
    To find the number left over, multiply the number of tigers per zone by the decimal part of the result: 0.06 * 696 = 41.6.  Since we can't have a fraction of a tiger, round down to the nearest whole number.

    ### Answer: 41

Expected answer: 44

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many hats are left over, we need to divide the total number of hats by the number of hats in each box and find the remainder.

    830 hats / 421 hats/box = 1 box with a remainder of 409 hats.

    ### Answer: 409

Expected answer: 409

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The fisherman catches 575 fish every month, and the fish repopulate at the same rate. This means that the number of fish in the lake remains constant.
    ### Answer: 871

Expected answer: 296

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: 891 beach balls divided by 119 beach balls per bag equals approximately 7.48 bags.  Since you can't have parts of a bag, we only have 7 full bags. To find out how many beach balls are left over, multiply the number of bags by the number of beach balls each bag can hold and subtract that amount from the total number of beach balls: 7 * 119 = 833 beach balls fit into 7 bags. 891 - 833 = 58 beach balls are left over.

    ### Answer: 58

Expected answer: 58

Correct? Yes

🔗 Follow-up

Problem: If instead there were 901 beach balls and every beach bag can fit 119 beach balls. After evenly placing the balls into bags, how many beach balls would be left over now?

Gemini-1.5 Flash:

    Reasoning: 901 beach balls divided by 119 beach balls per bag equals approximately 7.57 bags.  Since you can't have parts of a bag, we only have 7 full bags. To find out how many beach balls are left over, multiply the number of bags by the number of beach balls each bag can hold and subtract that amount from the total number of beach balls: 7 * 119 = 833 beach balls fit into 7 bags. 901 - 833 = 68 beach balls are left over.

    ### Answer: 68

Expected answer: 68

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: 544 divided by 446 is 1 with a remainder of 98. Since each cluster has 446 stars, 1 cluster can be formed, but 98 stars will be leftover.
    ### Answer: 98

Expected answer: 98

Correct? Yes

🔗 Follow-up

Problem: Considering the previous scenario with the constellation, suppose there were only 278 stars in the constellation instead of 544, and they were still to be grouped into smaller clusters of 446 stars each. If the clusters are evenly distributed, how many stars will now remain ungrouped?

Gemini-1.5 Flash:

    Reasoning: Since we can't form a complete cluster with 278 stars because we need 446 stars for each cluster, all the stars will remain ungrouped.
    ### Answer: 278

Expected answer: 278

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many sets of socks can be made, divide the total number of socks by the number of socks in each set: 805 / 132 = 6 with a remainder of 17.
    This means 6 sets of socks can be made, and there will be 17 socks remaining unpackaged.
    ### Answer: 17

Expected answer: 13

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First find out how many full nights of viewing they will need: 759 members / 228 members per night = 3.33 nights.
    Since they can't have a partial night, round up to the nearest whole number which is 4 nights.
    Then multiply the number of members per night by the number of full nights to find the total number of members who can view on the first three nights: 228 members per night * 3 nights = 684 members
    Then subtract that number from the total number of members to find the remainder for the final night: 759 members - 684 members = 75 members.
    ### Answer: 75

Expected answer: 75

Correct? Yes

🔗 Follow-up

Problem: A similar astronomy club from a neighboring town also wants to take part in viewing this rare celestial event. They have 593 members interested in participating. If they follow the same pattern of distributing the viewing nights evenly amongst all members, with only 228 people viewing the event each night, how many people from this club will view the event on the final night?

Gemini-1.5 Flash:

    Reasoning: We follow the same pattern as before.
    First find out how many full nights of viewing they will need: 593 members / 228 members per night = 2.6 nights.
    Since they can't have a partial night, round up to the nearest whole number which is 3 nights.
    Then multiply the number of members per night by the number of full nights to find the total number of members who can view on the first two nights: 228 members per night * 2 nights = 456 members
    Then subtract that number from the total number of members to find the remainder for the final night: 593 members - 456 members = 137 members.
    ### Answer: 137

Expected answer: 137

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The postman can put 891/616 = 1 mailbox full of letters.
    This means there are 891 - 616 = 275 letters remaining.
    ### Answer: 275

Expected answer: 275

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, assuming the postman had to originally deliver 524 letters instead of 891, and each mailbox can still only accommodate 616 letters. How many letters will remain in the last mailbox now?

Gemini-1.5 Flash:

    Reasoning: The postman can put 524/616 = 0 mailboxes full of letters, because you can't have a fraction of a mailbox.
    This means there will be 524 letters remaining, as none can be put in a mailbox.
    ### Answer: 524

Expected answer: 524

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    We need to figure out how many times the frog can eat 258 flies before there are not enough flies left.

    * **Divide the total flies by the number the frog eats per jump:** 941 / 258 = 3.65...

    Since we can't have a fraction of a frog jump, the frog eats 258 flies a total of 3 times.

    * **Calculate the total flies eaten:** 3 jumps * 258 flies/jump = 774 flies

    * **Subtract the eaten flies from the original number:** 941 flies - 774 flies = 167 flies

    ### Answer: 167

Expected answer: 167

Correct? Yes

🔗 Follow-up

Problem: Previously, a frog ate flies from a total of 941 flies with 258 flies eaten in each jump. Now, consider that instead of 941 flies there initially were 146 flies hopping around the pond. Given that the frog still eats 258 flies in each jump, how many flies would be left after a series of jumps?

Gemini-1.5 Flash:

    The frog can't eat 258 flies in a jump because there are only 146 flies to begin with.  Since the frog eats more flies than there are, there will be **0** flies left.

    ### Answer: 0

Expected answer: 146

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Each row can hold 991/66 = <<991/66=15>>15 cars.
    Since 15 cars fit in each row and there are 66 rows, that means that 66 * 15 = <<66*15=990>>990 spaces are filled.
    If there are 991 spaces in total and 990 are filled, that means there is 991-990 = <<991-990=1>>1 space left.
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: In the same large park, suppose they restructure the parking with larger spaces to accommodate bigger vehicles. Now, the adjusted parking lot configurations can hold 471 cars in each row. After filling up the rows, how many spare spaces would be there in the last row now?

Gemini-1.5 Flash:

    Reasoning: Since the park has 66 rows and each row can hold 471 cars, the park can now hold 66 * 471 = <<66*471=31086>>31086 cars.
    The park has a capacity of 991 spaces, so there will be 31086 - 991 = <<31086-991=30095>>30095 spaces left over.
    Since there are 471 spaces per row, the last row would have 30095 % 471 = <<30095%471=103>>103 spaces left over.
    ### Answer: 103

Expected answer: 49

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Each bottle can hold 193 / 167 = 1.15 liters of water.
    To figure out how much overflows, multiply the amount each bottle holds by the number of bottles: 1.15 * 167 = 192.55 liters.
    Subtract this amount from the total water: 193 - 192.55 = 0.45 liters.
    ### Answer: 0.45

Expected answer: 26

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many rows the dragon can fill completely, we divide the total number of eggs by the number of eggs per row: 996 / 319 = 3 rows with a remainder.

    To find the remainder, we multiply the number of full rows by the number of eggs per row and subtract that from the total number of eggs: 3 * 319 = 957, and 996 - 957 = 39.

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

    ### Answer: 39

Expected answer: 39

Correct? Yes

🔗 Follow-up

Problem: Now, consider if the dragon had only laid 8 jewel eggs and continued to distribute them among rows that could hold 319 eggs. How many eggs would be left over to be put in the last row?

Gemini-1.5 Flash:

    Reasoning: Since the dragon only laid 8 eggs, and each row can hold 319 eggs, the dragon can only fill a single row with 8 eggs.

    Therefore, there would be 8 eggs left over to be put in the last row.

    ### Answer: 8

Expected answer: 8

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many packs can be filled, we need to divide the total number of bulb units by the number of bulbs in a pack: 691 / 205 = 3 with a remainder of 81.
    This means 3 packs can be filled, and there will be 81 bulbs left unpacked.

    ### Answer: 81

Expected answer: 76

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to figure out how many bales of hay fit perfectly into the barns. We can do that by dividing the total number of bales by the number of bales each barn can hold: 330 / 259 = 1 with a remainder of 71.  This means that we can fill 1 barn completely, and we will have 71 bales left over for the last barn.

    ### Answer: 71

Expected answer: 71

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder after dividing the total number of windows by the number of windows a team can install per day.
    166 windows / 137 windows/day = 1 with a remainder of 29 windows.

    ### Answer: 29

Expected answer: 29

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when the total number of campers is divided by the capacity of each tent.
    533 divided by 445 is 1 with a remainder of 88.
    Therefore, there will be 88 campers left over.

    ### Answer: 88

Expected answer: 88

Correct? Yes

🔗 Follow-up

Problem: Now suppose that the park upgraded their tents and each tent can now host 886 people. With the same group of 533 campers, how many campers will be left over after all the tents are filled?

Gemini-1.5 Flash:

    Reasoning:  Since each tent can now host 886 people, and there are only 533 campers, all the campers will fit in a single tent.  There will be no campers left over.

    ### Answer: 0

Expected answer: 533

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We can figure out how many sets of seashells can be made by dividing the total number of seashells by the number of shells per set: 999 / 474 = 2.105.  Since we can only make whole sets, we know that 2 complete sets can be made. That means 2 sets * 474 shells/set = 948 shells will be used for the sets.  Finally, we subtract the shells used in the sets from the total number of shells to find how many are left over: 999 - 948 = 51 shells left over.

    ### Answer: 51

Expected answer: 51

Correct? Yes

🔗 Follow-up

Problem: In continuation of the previous scenario with seashells, imagine instead that there were initially only 234 seashells collected from the beach, but the souvenir sets are still made up of 474 shells each. How many shells would be left after attempting to form these sets?

Gemini-1.5 Flash:

    Reasoning: Since each set requires 474 shells and we only have 234 shells, we can't form any complete sets.  This is because we don't have enough shells to even fill one set.

    ### Answer: 234

Expected answer: 234

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The tailor can make 366/160 = 2 skirts with some fabric leftover.
    The tailor used 2 * 160 = 320 meters of fabric for the skirts.
    The tailor will have 366 - 320 = 46 meters of fabric left.
    ### Answer: 46

Expected answer: 46

Correct? Yes

🔗 Follow-up

Problem: A tailor realized that she has made a mistake. Actually, she has only 21 meters of fabric at her disposal, not 366. If each skirt requires 160 meters of fabric, how many meters of fabric will be left after making as many skirts as possible?

Gemini-1.5 Flash:

    Reasoning: The tailor cannot make any skirts because she only has 21 meters of fabric, and each skirt requires 160 meters.
    Therefore, she will have all 21 meters of fabric left.
    ### Answer: 21

Expected answer: 21

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The toymaker can fit 327 dolls into each box.
    To find out how many boxes she can fill, divide the total number of dolls by the number of dolls per box: 993 / 327 = 3 boxes.
    To find out how many dolls she has left over, multiply the number of boxes by the number of dolls per box and subtract that number from the total number of dolls: 3 * 327 = 981 dolls in the boxes. 993 - 981 = 12 dolls left over.
    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous problem, what if, instead of each box holding 327 dolls, each box can now hold 115 dolls? After packing each box to capacity, how many dolls will the toymaker have left?

Gemini-1.5 Flash:

    Reasoning: With each box holding 115 dolls, the toymaker can fit 993 / 115 = 8 boxes with some dolls left over.
    There will be 8 * 115 = 920 dolls in the boxes.
    The toymaker will have 993 - 920 = 73 dolls left over.
    ### Answer: 73

Expected answer: 73

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many stuffed animals each friend gets, we divide the total number of stuffed animals by the number of friends: 964 / 839 = 1 with a remainder of 125.  This means each friend gets 1 stuffed animal, and there are 125 stuffed animals left over.

    ### Answer: 125

Expected answer: 125

Correct? Yes

🔗 Follow-up

Problem: The child from the previous problem has gotten even more stuffed animals and now has a total of 964 stuffed animals. If they still want to divide them equally among their 892 friends, how many stuffed animals will be left over after distributing them?

Gemini-1.5 Flash:

    Reasoning: To find out how many stuffed animals each friend gets, we divide the total number of stuffed animals by the number of friends: 964 / 892 = 1 with a remainder of 72.  This means each friend gets 1 stuffed animal, and there are 72 stuffed animals left over.

    ### Answer: 72

Expected answer: 72

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many boxes are needed, we divide the total number of teddy bears by the number of teddy bears each box can hold: 369 / 270 = 1.366... Since we can't have a fraction of a box, we round down to 1 box.  This means we can pack 1 x 270 = 270 teddy bears into boxes.

    To find out how many teddy bears are left, we subtract the number of teddy bears packed from the total number of teddy bears: 369 - 270 = 99.

    ### Answer: 99

Expected answer: 99

Correct? Yes

🔗 Follow-up

Problem: Earlier, the toy factory produced 369 teddy bears in a day and they were packaged in boxes with each box holding 270 teddy bears. Now, suppose that the toy factory increased its production and now makes 813 teddy bears in a day while still packing them in boxes that can hold 270 teddy bears. How many teddy bears will be left now if all the teddy bears are evenly packed in the boxes?

Gemini-1.5 Flash:

    Reasoning: To find out how many boxes are needed, we divide the total number of teddy bears by the number of teddy bears each box can hold: 813 / 270 = 3.011...  Since we can't have a fraction of a box, we round down to 3 boxes. This means we can pack 3 x 270 = 810 teddy bears into boxes.

    To find out how many teddy bears are left, we subtract the number of teddy bears packed from the total number of teddy bears: 813 - 810 = 3

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The villagers can build 804 / 184 = <<804/184=4.37>> 4 snowmen.
    The villagers used 4 x 184 = <<4*184=736>> 736 snowballs to build the snowmen.
    There are 804 - 736 = <<804-736=68>> 68 snowballs left over.
    ### Answer: 68

Expected answer: 68

Correct? Yes

🔗 Follow-up

Problem: In the same village, another year, there were only 444 snowballs made to build the snowmen. If each snowman still requires exactly 184 snowballs, how many snowballs would be left over after as many complete snowmen as possible are built?

Gemini-1.5 Flash:

    Reasoning: The villagers can build 444 / 184 = <<444/184=2.41>> 2 complete snowmen.
    The villagers used 2 x 184 = <<2*184=368>> 368 snowballs to build the snowmen.
    There are 444 - 368 = <<444-368=76>> 76 snowballs left over.
    ### Answer: 76

Expected answer: 76

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  To find the number of rings left over, we need to figure out the remainder when 843 is divided by 839.

     843 divided by 839 equals 1 with a remainder of 4.

    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: The jewelry store just received an additional shipment and now has a total of 843 rings. However, this time they must be equally placed into 804 boxes. If every box is filled, how many rings will be left over now?

Gemini-1.5 Flash:

    Reasoning: To find the number of rings left over, we need to figure out the remainder when 843 is divided by 804.

    843 divided by 804 equals 1 with a remainder of 39.

    ### Answer: 39

Expected answer: 39

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The company can build 819/583 = <<819/583 = 1.40>>1 fireplace with a remainder of 819-583 = 236 bricks.
    ### Answer: 236

Expected answer: 236

Correct? Yes

🔗 Follow-up

Problem: The company received a new delivery of bricks, now they have 486 bricks in total. If they continue making fireplaces, each requiring 583 bricks as before, how many bricks will they have left after building as many full fireplaces as they can?

Gemini-1.5 Flash:

    Reasoning: Since they need 583 bricks for each fireplace, and they only have 486, they can't build a full fireplace.
    Therefore, they will have all 486 bricks left over.
    ### Answer: 486

Expected answer: 486

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  The factory produces 998 marshmallows, but the machine can only hold 957.  Therefore, 998 - 957 = 41 marshmallows will be left un-packaged.

    ### Answer: 41

Expected answer: 41

Correct? Yes

🔗 Follow-up

Problem: The marshmallow factory upgraded its packaging machine and now it can hold 804 marshmallows at a time instead of 957. If the factory continues to produce 998 marshmallows per minute, what will be the number of marshmallows left un-packaged in a minute after all the packaging machines are filled with the new capacity?

Gemini-1.5 Flash:

    Reasoning: The factory produces 998 marshmallows and the new machine can hold 804.  Therefore, 998 - 804 = 194 marshmallows will be left un-packaged.

    ### Answer: 194

Expected answer: 194

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  We need to find out how many tributes Princess can make by dividing the total number of roses by the number of roses in each tribute: 984 roses / 426 roses/tribute = 2.3 tributes. Since we can't have a fraction of a tribute, Princess can make 2 complete tributes.
    Now we need to find out how many roses are left: 2 tributes * 426 roses/tribute = 852 roses used.
    Therefore, 984 roses - 852 roses = 132 roses will be left undistributed.
    ### Answer: 132

Expected answer: 132

Correct? Yes

🔗 Follow-up

Problem: In the same castle's garden, there were originally 984 roses, but the princess has decided to use only 730 roses for each tribute to her loyal subjects instead of the previous 426. Now, if she distributes roses evenly to create as many tributes as possible, how many roses will be left undistributed in the castle's garden?

Gemini-1.5 Flash:

    Reasoning:  To find out how many tributes Princess can make with 730 roses per tribute, we divide the total roses by the roses per tribute: 984 roses / 730 roses/tribute = 1.35 tributes.  Since we can only have whole tributes, the Princess can create 1 tribute.
    Now we need to calculate how many roses are used in that tribute: 1 tribute * 730 roses/tribute = 730 roses used.
    Therefore, there are 984 roses - 730 roses = 254 roses left undistributed.
    ### Answer: 254

Expected answer: 254

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The song has 334/23 = <<334/23 = 14.52>> 14.52 lines if all lines had 23 words.
    Since the number of lines must be a whole number, we know that there are 14 complete lines with 23 words each, which makes a total of 14*23 = <<14*23 = 322>> 322 words.
    This leaves 334-322 = <<334-322 = 12>> 12 words in the incomplete line.
    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Follow-up

Problem: Suppose the song writer decided to change the structure of the song and made each line contain 314 words instead. Now with the same total of 334 words, how many words would be left in the incomplete line at the end of the song?

Gemini-1.5 Flash:

    Reasoning: We need to see how many lines with 314 words we can fit into the 334-word song.
    Dividing the total words by the new line length, we get 334/314 = <<334/314 = 1.06>> 1.06.
    This means we can fit one complete line of 314 words, and then have 334-314 = <<334-314 = 20>> 20 words left for the incomplete line at the end.
    ### Answer: 20

Expected answer: 20

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 928 is divided by 336.
    928 divided by 336 is 2 with a remainder of 256.
    This means the teacher can fill the printer 2 times completely, leaving 256 pages to print later.

    ### Answer: 256

Expected answer: 256

Correct? Yes

🔗 Follow-up

Problem: In the same scenario, suppose the teacher decides to use a different printer that can print 409 pages in one go. After filling this printer a number of times, how many pages will he have left over to print?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 928 is divided by 409.
    928 divided by 409 is 2 with a remainder of 110.
    This means the teacher can fill the printer 2 times completely, leaving 110 pages to print later.

    ### Answer: 110

Expected answer: 110

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  To find out how many groups of 667 sharks can be tagged, we divide the total number of sharks by the size of each group: 972 / 667 = 1 with a remainder of 305. This means they can tag 1 complete group of 667 sharks.  Since there's a remainder of 305, that's how many sharks are left untagged.
    ### Answer: 305

Expected answer: 305

Correct? Yes

🔗 Follow-up

Problem: Following up on the previous question, the scientists later spotted a new group of 758 sharks in a different area. Again, they were trying to tag the sharks in groups of 667. How many sharks were left untagged after all complete groups have been tagged in this new area?

Gemini-1.5 Flash:

    Reasoning: To find out how many complete groups of 667 sharks can be tagged in this new area, we divide the total number of sharks by the size of each group: 758 / 667 = 1 with a remainder of 91. This means they can tag 1 complete group of 667 sharks. Since there's a remainder of 91, that's how many sharks are left untagged.

    ### Answer: 91

Expected answer: 91

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First, find out how many boxes can be filled: 686 / 349 = 1 box with a remainder of 337.
    So, we can fill one box completely. Since there is a remainder of 337 blocks, that is how many blocks would be left over.
    ### Answer: 337

Expected answer: 337

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, say the dairy shop initially had 239 blocks of cheese instead of 686. Using the same boxes which can contain 349 blocks of cheese, how many blocks of cheese would be left over after all the boxes are filled?

Gemini-1.5 Flash:

    Reasoning: Since the dairy shop only has 239 blocks of cheese, and each box can hold 349 blocks, no boxes can be filled completely.  Therefore, all 239 blocks of cheese would be left over.
    ### Answer: 239

Expected answer: 239

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  To find out how many passes the snowplow will make, we need to divide the total snowfall by the amount of snow cleared per pass: 513 centimeters / 170 centimeters/pass = 3 passes with a remainder.

    To find out the remainder, we can multiply the amount cleared per pass by the number of full passes and subtract that from the total snowfall: (170 centimeters/pass * 3 passes) = 510 centimeters.

    Then, subtract that from the total snowfall: 513 centimeters - 510 centimeters = 3 centimeters.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: Suppose that instead of 513 centimeters, there were 460 centimeters of snowfall this winter. If the same snowplow, which can clear up to 170 centimeters of snow at a time, runs continuously, how many centimeters of snow would then be left over after the final pass?

Gemini-1.5 Flash:

    Reasoning: We divide the total snowfall by the amount of snow cleared per pass: 460 centimeters / 170 centimeters/pass = 2 passes with a remainder.

    To find the remainder, we multiply the amount cleared per pass by the number of full passes and subtract that from the total snowfall: (170 centimeters/pass * 2 passes) = 340 centimeters.

    Then, subtract that from the total snowfall: 460 centimeters - 340 centimeters = 120 centimeters.

    ### Answer: 120

Expected answer: 120

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many full compasses the maker can assemble, we divide the total number of needles by the number of needles per compass: 661 / 510 = 1 with a remainder of 151. This means he can make 1 full compass, and he will have 151 needles left over.

    ### Answer: 151

Expected answer: 151

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many chairs can be distributed evenly, we need to find the largest multiple of 310 that is less than 380. Since 310 x 1 = 310, and 310 x 2 = 620, we know 310 chairs can be distributed to each shop. This means 380 - 310 = 70 chairs will be left at the factory.
    ### Answer: 70

Expected answer: 70

Correct? Yes

🔗 Follow-up

Problem: Now suppose the factory decides to distribute these chairs amongst its smaller distributors, each of which can only hold 143 chairs. Now, how many chairs will be left at the factory after distributing them evenly?

Gemini-1.5 Flash:

    Reasoning:  We need to find the largest multiple of 143 that is less than 380.  143 x 2 = 286, and 143 x 3 = 429.  Since 429 is greater than 380, we know 286 chairs can be distributed evenly.  This means 380 - 286 = 94 chairs will be left at the factory.
    ### Answer: 94

Expected answer: 94

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 929 is divided by 154.
    We can do this using long division, or by repeatedly subtracting 154 from 929 until we get a number less than 154.

    929 divided by 154 is approximately 6, with a remainder of 1.

    This means the farmer can fill 6 boxes completely, but will have 1 tomato left over.

    ### Answer: 1

Expected answer: 5

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Each box will have 454/128 = 3 pairs of ice skates. There will be 454 - (3 * 128) = 10 pairs of ice skates left over.
    ### Answer: 10

Expected answer: 70

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how much power the village consumes, we need to find the highest multiple of 385 that is less than 506.  We can do this by dividing 506 by 385: 506 / 385 = 1.31...  The largest whole number less than 1.31 is 1.  So, the village consumes 1 * 385 = 385 units of power.

    To find the leftover power, we subtract the consumed power from the generated power: 506 - 385 = 121 units.

    ### Answer: 121

Expected answer: 121

Correct? Yes

🔗 Follow-up

Problem: Following the scenario of the windmill and the small village, let's now consider that the windmill had a great day and managed to generate 506 units of power. However, due to development demands, the daily consumption of the village has increased to 920 units. At the end of the day, with the power being consumed in complete units, how much power is left over?

Gemini-1.5 Flash:

    Reasoning:  The village can only consume power in full units of 920.  Since the windmill only generated 506 units, which is less than 920, the village can't consume any power at all.

    ### Answer: 506

Expected answer: 506

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    To find out how many blasts Blast Man can fire, we divide his total energy units by the energy units per blast: 338 energy units / 16 energy units/blast = 21.125 blasts.  Since Blast Man can't fire a fraction of a blast, he can fire a maximum of 21 blasts.

    To find out how many energy units he'll have left, we multiply the number of blasts by the energy used per blast and subtract that from his total energy units: 21 blasts * 16 energy units/blast = 336 energy units used.

    Then we subtract that from his total energy units: 338 energy units - 336 energy units = 2 energy units left.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: Now, imagine that Superhero Blast Man has boosted his power cells and now has 338 energy units in his power cells. But this time, each energy blast he fires now uses 46 energy units. After using equal units of energy firing blasts, how many energy units will Blast Man have left in his power cells?

Gemini-1.5 Flash:

    We'll follow the same process as before:

    1. **Calculate the maximum number of blasts:** 338 energy units / 46 energy units/blast = 7.348 blasts. Since Blast Man can't fire a fraction of a blast, he can fire a maximum of 7 blasts.

    2. **Calculate the total energy used:** 7 blasts * 46 energy units/blast = 322 energy units used.

    3. **Calculate the remaining energy:** 338 energy units - 322 energy units = 16 energy units left.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First, we need to find out how many buses are needed: 530 students / 144 students/bus = 3.68 buses. Since we can't have a fraction of a bus, we need to round up to 4 buses.  Now, we need to find how many students are on the first three buses: 3 buses * 144 students/bus = 432 students. Finally, we find the number of students on the last bus: 530 students - 432 students = 98 students.

    ### Answer: 98

Expected answer: 98

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many spells each apprentice gets, we divide the total spells by the number of apprentices: 999 / 951 = 1 (with a remainder). This means each apprentice gets 1 spell, and there's a remainder. The remainder is the number of spells the wizard has left over.  To find the remainder, we can subtract the number of spells given out (951) from the total number of spells (999): 999 - 951 = 48.

    ### Answer: 48

Expected answer: 48

Correct? Yes

🔗 Follow-up

Problem: If the wizard had instead 999 spells and he tries to distribute them equally among 801 apprentice wizards, how many spells will the wizard have left after giving out as many as he can to his apprentices?

Gemini-1.5 Flash:

    Reasoning: To find out how many spells each apprentice gets, we divide the total spells by the number of apprentices: 999 / 801 = 1 (with a remainder). This means each apprentice gets 1 spell, and there's a remainder. The remainder is the number of spells the wizard has left over.  To find the remainder, we can subtract the number of spells given out (801) from the total number of spells (999): 999 - 801 = 198.

    ### Answer: 198

Expected answer: 198

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many trucks are needed, divide the total number of scooters by the number of scooters each truck can carry: 767 / 369 = 2 (with a remainder). This means 2 trucks can be fully loaded.
    To find the remainder, we multiply the number of full trucks by the number of scooters per truck and subtract that from the total number of scooters: 2 * 369 = 738, and 767 - 738 = 29.
    ### Answer: 29

Expected answer: 29

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  The maximum number of raindrops that can be formed is 846 / 722 = 1.1714. Since we can't have a fraction of a raindrop, the maximum number of raindrops is 1.

    To find out how many droplets are left, we multiply the number of raindrops by the number of droplets needed per raindrop: 1 * 722 = 722

    Then we subtract that from the original number of droplets: 846 - 722 = 124

    ### Answer: 124

Expected answer: 124

Correct? Yes

🔗 Follow-up

Problem: There was a slight miscalculation in the cloud's droplet count. There are actually 846 water droplets in the cloud, but each raindrop needs 442 droplets to form instead of 722. With this updated droplet count per raindrop, how many droplets would be left unconverted in the cloud after reaching the maximum number of rain drops?

Gemini-1.5 Flash:

    Reasoning: The maximum number of raindrops that can be formed is 846 / 442 = 1.914.  Since we can't have a fraction of a raindrop, the maximum number of raindrops is 1.

    To find out how many droplets are left, we multiply the number of raindrops by the number of droplets needed per raindrop: 1 * 442 = 442

    Then we subtract that from the original number of droplets: 846 - 442 = 404

    ### Answer: 404

Expected answer: 404

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  We first need to figure out how many unicorns are in each complete section. We do this by dividing the total number of unicorns by the number of sections: 265 unicorns / 146 sections = 1.81 unicorns per section (approximately). Since we can't have parts of unicorns, each complete section has 1 unicorn.

    We then multiply the number of complete sections by the number of unicorns per section to find the number of unicorns in the complete sections: 145 sections * 1 unicorn/section = 145 unicorns.

    Finally, we subtract the number of unicorns in the complete sections from the total number of unicorns to find the number in the last incomplete section: 265 unicorns - 145 unicorns = 120 unicorns.

    ### Answer: 120

Expected answer: 119

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Divide the total number of players by the number of players per match: 923 / 383 = 2 with a remainder of 157.  This means 2 full matches can be filled, and there will be 157 players left waiting.
    ### Answer: 157

Expected answer: 157

Correct? Yes

🔗 Follow-up

Problem: In the same game, a new day dawns with 456 players waiting to join a match. The match capacity remains the same, permitting 383 players at a time. If players are allocated evenly across the matches, how many players will be left waiting after all available matches are filled?

Gemini-1.5 Flash:

    Reasoning: Divide the total number of players by the number of players per match: 456 / 383 = 1 with a remainder of 73.  This means 1 full match can be filled, and there will be 73 players left waiting.
    ### Answer: 73

Expected answer: 73

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many cannonballs go in each crate, we divide the total number of cannonballs by the number of crates: 923 / 499 = 1.849...  Since we can't have fractions of cannonballs, each crate gets 1 cannonball.

    To find the leftover cannonballs, we multiply the number of crates by the number of cannonballs per crate and subtract that from the total: 499 * 1 = 499, and 923 - 499 = 424.

    ### Answer: 424

Expected answer: 424

Correct? Yes

🔗 Follow-up

Problem: Keeping in line with the previous pirate ship themed problem, let's consider the following scenario: The same pirate ship initially started with 462 cannonballs instead of 923. After the pirates evenly distribute these cannonballs into the same 499 crates, can any be leftover? If so, how many cannonballs will be left uncrated?

Gemini-1.5 Flash:

    Reasoning: If we divide the total number of cannonballs by the number of crates, we get 462 / 499 = 0.925... This means each crate can hold less than one cannonball, which is not possible.

    Therefore, all 462 cannonballs will be used, and none will be left uncrated.

    ### Answer: 0

Expected answer: 462

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The store has 530-518 = <<530-518=12>>12 string spools left.
    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many jugs can be filled, we divide the total gallons of milk by the capacity of each jug: 913 gallons / 39 gallons/jug = 23.41 jugs. Since we can't have a fraction of a jug, we know that 23 jugs will be filled completely.
    To find the leftover milk, we multiply the number of filled jugs by the jug capacity and subtract that from the total milk produced: 23 jugs * 39 gallons/jug = 897 gallons.
    913 gallons - 897 gallons = 16 gallons.

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: The dairy farm has adjusted its production and now produces 913 gallons of milk in a day. If they started using larger milk jugs that hold 230 gallons each, how many gallons will be left over after all the jugs are filled?

Gemini-1.5 Flash:

    Reasoning: To find out how many jugs can be filled, we divide the total gallons of milk by the capacity of each jug: 913 gallons / 230 gallons/jug = 3.97 jugs. Since we can't have a fraction of a jug, we know that 3 jugs will be filled completely.
    To find the leftover milk, we multiply the number of filled jugs by the jug capacity and subtract that from the total milk produced: 3 jugs * 230 gallons/jug = 690 gallons.
    913 gallons - 690 gallons = 223 gallons.

    ### Answer: 223

Expected answer: 223

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many dolls were left unarranged, we need to divide the total number of dolls by the number of dolls in each row and find the remainder.
    603 divided by 369 is 1 with a remainder of 234.
    This means that 1 full row was filled with 369 dolls, and there were 234 dolls left over.

    ### Answer: 234

Expected answer: 234

Correct? Yes

🔗 Follow-up

Problem: In the previous doll problem, if the doll seller initially received a shipment of 44 new dolls instead of 603, and still arranged them in rows of 369 dolls, how many dolls would be left unarranged after filling up the rows as much as possible?

Gemini-1.5 Flash:

    Reasoning: The doll seller only has 44 dolls, which is less than the number of dolls needed to fill a single row (369).  Therefore, no rows can be filled, and all 44 dolls are left unarranged.

    ### Answer: 44

Expected answer: 44

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We can determine how many beads are leftover by dividing the total number of beads by the number of beads per necklace and looking at the remainder.

     850 divided by 631 is 1 with a remainder of 219.

     Therefore, the jewelry maker will have 219 beads left over.

    ### Answer: 219

Expected answer: 219

Correct? Yes

🔗 Follow-up

Problem: The jewelry maker decides to change the design and now each necklace uses only 150 beads instead of 631 beads. After they distribute the 850 beads as equally as possible among the new necklaces, how many beads will the jewelry maker have left over?

Gemini-1.5 Flash:

    Reasoning: We can determine how many beads are leftover by dividing the total number of beads by the number of beads per necklace and looking at the remainder.

    850 divided by 150 is 5 with a remainder of 100.

    Therefore, the jewelry maker will have 100 beads left over.

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The gardener can fill 952 / 380 = 2 boxes completely.
    This leaves 952 - (2 * 380) = 192 grapes leftover.
    ### Answer: 192

Expected answer: 192

Correct? Yes

🔗 Follow-up

Problem: The gardener's friend gave him an additional 183 grapes from his own garden. If the gardener decides to package these grapes as well into boxes with each box holding 380 grapes, how many grapes will remain after packaging the new grapes into as many boxes as possible?

Gemini-1.5 Flash:

    Reasoning: The gardener can fill 183 / 380 = 0 boxes completely with the new grapes, as 183 is less than 380.
    This means all 183 new grapes will be left over.
    ### Answer: 183

Expected answer: 183

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Divide the total number of steps by the number of steps between significant places: 236 steps / 44 steps/place = 5.36 places. Since we can only have whole places, we round down to 5 significant places.
    Multiply the number of steps between significant places by the number of significant places: 44 steps/place * 5 places = 220 steps.
    Subtract the total steps walked from the total steps on the map: 236 steps - 220 steps = 16 steps.
    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We first need to find out how many complete groups of bubbles Sarah's machine formed. We do this by dividing the total number of bubbles by the number of bubbles in each group: 932 / 507 = 1 with a remainder of 425. This means the machine formed 1 complete group, and it has 425 bubbles left over for its final incomplete group.

    ### Answer: 425

Expected answer: 425

Correct? Yes

🔗 Follow-up

Problem: Suppose Sarah uses her bubble machine again, this time to blow 904 bubbles. The machine is still 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?

Gemini-1.5 Flash:

    Reasoning: We need to figure out how many complete groups of bubbles Sarah's machine can make with 904 bubbles. We do this by dividing the total number of bubbles by the number of bubbles in each group: 904 / 507 = 1 with a remainder of 397. This means the machine formed 1 complete group, and it has 397 bubbles left over for its final incomplete group.

    ### Answer: 397

Expected answer: 397

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: If each swing set can hold 34 kids, then all the kids can fit on 931/34 = 27.41 swing sets. Since you can't have a fraction of a swing set, we round down to 27 swing sets.
    Now, let's find out how many kids can fit on 27 swing sets: 27 * 34 = 918 kids can fit on 27 swing sets.
    Therefore, 931 - 918 = 13 kids will be waiting.
    ### Answer: 13

Expected answer: 13

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, let's say that some of the kids finished their swinging and left the park. Now, there are only 708 kids waiting to use the swings. Each swing set can still accommodate 34 kids at a time. Given this new number, how many children will be waiting for their turn after all the swing sets are occupied?

Gemini-1.5 Flash:

    Reasoning:  With 708 kids and each swing set holding 34 kids, we can fit 708 / 34 = 20.82 swing sets. Again, we round down to 20 swing sets, as we can't have a fraction of a swing set.
    Now, let's find out how many kids can fit on 20 swing sets: 20 * 34 = 680 kids.
    Therefore, 708 - 680 = 28 kids will be waiting.

    ### Answer: 28

Expected answer: 28

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: John can fully load 943/433 = 2 wallets with a remainder of 943-866 = 77 dollar bills left over.
    ### Answer: 77

Expected answer: 77

Correct? Yes

🔗 Follow-up

Problem: Suppose John originally had 586 dollar bills instead of 943. He still 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 now?

Gemini-1.5 Flash:

    Reasoning: John can fully load 586/433 = 1 wallet with a remainder of 586-433 = 153 dollar bills left over.
    ### Answer: 153

Expected answer: 153

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The helicopter can carry 177 passengers, and there are 240 passengers total.
    To find out how many are left behind, subtract the number the helicopter carries from the total: 240 - 177 = 63.
    ### Answer: 63

Expected answer: 63

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The gardener can fill up 982 / 555 = 1 flowerbed with some flowers left over.
    The gardener has 982 - (1 * 555) = 982 - 555 = 427 flowers left to plant.
    ### Answer: 427

Expected answer: 427

Correct? Yes

🔗 Follow-up

Problem: The gardener received an additional shipment, bringing the total number of flowers up to 867. If he continues to plant the flowers in flowerbeds of 555 each, how many flowers will he have left to plant after filling up as many flowerbeds as possible?

Gemini-1.5 Flash:

    Reasoning: The gardener can fill up 867 / 555 = 1 flowerbed with some flowers left over.
    The gardener has 867 - (1 * 555) = 867 - 555 = 312 flowers left to plant.
    ### Answer: 312

Expected answer: 312

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many plants will be remaining, we need to see how many groups of 5 she can make and then see what's left over.
    She can make 203/5 = <<203/5=40.6>> 40.6 groups. Since we can't have a fraction of a group, we only consider the whole groups, which is 40 groups.
    This means she uses 40 * 5 = 200 plants.
    So, she has 203 - 200 = 3 plants remaining.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: The farmer harvested another field and got an additional 76 strawberry plants. Again, she wants to divide the new plants into groups of 5 to sell. How many plants will be remaining if she divides these new strawberries equally?

Gemini-1.5 Flash:

    Reasoning: To find out how many plants will be remaining, we need to see how many groups of 5 she can make from the new 76 plants and then see what's left over.
    She can make 76/5 = <<76/5=15.2>> 15.2 groups. Since we can't have a fraction of a group, we only consider the whole groups, which is 15 groups.
    This means she uses 15 * 5 = 75 plants.
    So, she has 76 - 75 = 1 plant remaining.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The gardener can create 355 / 16 = 22 bundles with a remainder of 3.  This means he will have 3 carrots left over.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Each day had 612/29 = 21.1 inches of rain.
    This means that 21 * 29 = 609 inches would be evenly distributed over 29 days.
    Therefore, the remaining amount of rain left to make the days evenly rainy is 612 - 609 = 3 inches.

    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: Suppose instead of 612 inches, a total rainfall of 505 inches fell over the city in those same 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?

Gemini-1.5 Flash:

    Reasoning: Each day had 505/29 = 17.4 inches of rain (approximately).
    This means that 17 * 29 = 493 inches would be evenly distributed over 29 days.
    Therefore, the remaining amount of rain left to make the days evenly rainy is 505 - 493 = 12 inches.

    ### Answer: 12

Expected answer: 12

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many boxes can fit in one truck, we divide the total number of boxes by the capacity of each truck: 514 / 371 = 1 with a remainder of 143.
    This means one truck can fit 371 boxes and there will be 143 boxes left over.

    ### Answer: 143

Expected answer: 143

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: First, find out how many complete sets of 230 sandcastles there are: 684 / 230 = 2 with a remainder of 224.
    This means there are 2 complete sets, and 224 sandcastles left over.
    ### Answer: 224

Expected answer: 224

Correct? Yes

🔗 Follow-up

Problem: Continuing from the prior problem, suppose that in another large sandbox, children now create 533 sandcastles over the summer instead of 684. If they still group the sandcastles in sets of 230 for a photography contest, how many sandcastles will be left now that don't form a complete set?

Gemini-1.5 Flash:

    Reasoning: To figure out how many sandcastles are left over, we need to see how many times 230 goes into 533.
    533 divided by 230 is 2 with a remainder of 73.
    This means there are 2 complete sets of sandcastles, and 73 sandcastles are left over that don't form a complete set.

    ### Answer: 73

Expected answer: 73

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many full packs can be made, we need to divide the total number of cars by the number of cars per pack: 735 / 348 = 2 with a remainder of 39.
    This means 2 full packs can be made, and there will be 39 toy cars left over.
    ### Answer: 39

Expected answer: 39

Correct? Yes

🔗 Follow-up

Problem: The toy manufacturer decides in the next production run to make only 77 toy cars instead of 735. Again, they package the cars in packs of 348 for bulk shipments. If all the toy cars are divided equally among these packs, how many toy cars will be left over after all full packs have been filled?

Gemini-1.5 Flash:

    Reasoning:  Since the manufacturer is making only 77 toy cars, and each pack holds 348 cars, they won't be able to fill even a single full pack.  Therefore, all 77 toy cars will be left over.

    ### Answer: 77

Expected answer: 77

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  We need to find out how many territories are fully occupied. We do this by dividing the total number of animals by the number of animals each territory can support: 386 animals / 95 animals/territory = 4.06 territories.  Since we can't have parts of territories, this means 4 territories are fully occupied.  Now, we need to figure out how many animals are left over. Since 4 territories hold 4 x 95 = 380 animals, there are 386 - 380 = 6 animals left over.

    ### Answer: 6

Expected answer: 6

Correct? Yes

🔗 Follow-up

Problem: In the same forest, a new report finds that there were actually 497 animals instead of the initially thought 386. If these animals were evenly distributed among the territories, each still supporting 95 animals, how many animals would be in the last not fully occupied territory now?

Gemini-1.5 Flash:

    Reasoning:  With 497 animals, we can fully occupy 497 animals / 95 animals/territory = 5.23 territories. Since we can't have parts of territories, this means 5 territories are fully occupied. Now, we need to figure out how many animals are left over. Since 5 territories hold 5 x 95 = 475 animals, there are 497 - 475 = 22 animals left over.

    ### Answer: 22

Expected answer: 22

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The number of trees that are expected to be cut down is 646.
    The number of trees that will stay healthy is 801 - 646 = <<801 - 646 = 155>> 155 trees.

    ### Answer: 155

Expected answer: 155

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The rope can be cut into 934/902 = 1 piece of rope with a remainder of 934 - 902 = 32 meters.
    ### Answer: 32

Expected answer: 32

Correct? Yes

🔗 Follow-up

Problem: Continuing from the previous scenario, suppose that the manufacturer only made a rope of 202 meters in length initially. Applying the same method of cutting rope into pieces that are each 902 meters long, how many meters would the piece of the rope be now?

Gemini-1.5 Flash:

    Reasoning:  Since the rope is only 202 meters long, and each piece needs to be 902 meters long, we cannot cut any pieces of the desired length.  Therefore, the entire rope will be the last piece.
    ### Answer: 202

Expected answer: 202

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  Since each container holds 550 liters, the farm can fill 550 liters * 1 container = 550 liters of milk into containers.
    This leaves 561 liters - 550 liters = 11 liters of milk left over.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Follow-up

Problem: If the dairy farm increased its production and started producing 729 liters of milk each day instead of 561 liters, how many liters of milk would be left over each day after filling the 550-liter containers?

Gemini-1.5 Flash:

    Reasoning: The farm can fill 550 liters * 1 container = 550 liters of milk into containers.
    This leaves 729 liters - 550 liters = 179 liters of milk left over.

    ### Answer: 179

Expected answer: 179

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Once Jon completes a puzzle, he will have 259-258 = <<259-258=1>>1 piece left over.
    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Follow-up

Problem: In the previous problem, Jon had 259 puzzle pieces and each puzzle requires 258 pieces. Suppose instead each puzzle needs 542 pieces. How many pieces would Jon have left over after finishing as many full puzzles as possible with his 259 pieces?

Gemini-1.5 Flash:

    Reasoning: Since Jon only has 259 pieces and each puzzle requires 542 pieces, he doesn't have enough to complete even one full puzzle.
    ### Answer: 259

Expected answer: 259

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The jewelry maker can create 673/49 = <<673/49=13.73>>13 complete bracelets with the beads she has. This means she uses 13*49 = <<13*49=637>>637 beads in total.
    The jewelry maker has 673-637 = <<673-637=36>>36 beads left after making the bracelets.
    ### Answer: 36

Expected answer: 36

Correct? Yes

🔗 Follow-up

Problem: The jewelry maker received an additional shipment, and now she has a total of 673 beads. This time, she wants to make larger bracelets which use exactly 545 beads each. After creating as many large bracelets as possible, how many beads will she have left over?

Gemini-1.5 Flash:

    Reasoning: The jewelry maker can create 673/545 = <<673/545=1.23>>1 complete large bracelet with the beads she has. This means she uses 1*545 = <<1*545=545>>545 beads in total.
    The jewelry maker has 673-545 = <<673-545=128>>128 beads left after making the large bracelet.
    ### Answer: 128

Expected answer: 128

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  Divide the total number of calls by the number of operators: 927 calls / 311 operators = 2.98 calls per operator. Since we can't have a fraction of a call, the last operator will handle 3 calls.
    ### Answer: 3

Expected answer: 305

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many packages John can make, we need to divide the total number of pieces by the number of pieces per package: 764 pieces / 589 pieces/package = 1.3 packages. Since we can't have a fraction of a package, we know John can only make 1 full package.  To find the number of pieces left over, we multiply the number of pieces per package by the number of packages and subtract that from the total number of pieces: 1 package * 589 pieces/package = 589 pieces. 764 pieces - 589 pieces = 175 pieces.
    ### Answer: 175

Expected answer: 175

Correct? Yes

🔗 Follow-up

Problem: If John had originally only 404 puzzle pieces, and each package can still only contain 589, how many pieces will be left outside the package now?

Gemini-1.5 Flash:

    Reasoning:  Since John has fewer pieces than needed for a full package, he can't make any full packages.  Therefore, all the pieces he has will be left outside the package.
    ### Answer: 404

Expected answer: 404

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The dressmaker can make 984/217 = 4 dresses with the fabric she has.
    She will use 4*217 = 868 meters of fabric to make the dresses.
    She will have 984-868 = 116 meters of fabric left.
    ### Answer: 116

Expected answer: 116

Correct? Yes

🔗 Follow-up

Problem: In the previous scenario, let's now suppose that the dressmaker has 984 meters of fabric, but this time she uses 585 meters of fabric to make each dress. Again, she uses all the fabric she can to make as many dresses as possible. With this change, how many meters of fabric will she have left after all the dresses are made?

Gemini-1.5 Flash:

    Reasoning: The dressmaker can only make 1 dress with the fabric because 585 meters is more than the 984 meters of fabric she has.
    Since she only makes one dress, she will have 984-585 = 399 meters of fabric left.

    ### Answer: 399

Expected answer: 399

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many sleeping bags are left over, we need to find the remainder when the total number of sleeping bags is divided by the number of sleeping bags per campsite.

    * Divide the total number of sleeping bags by the number of sleeping bags per campsite: 639 ÷ 374 = 1 with a remainder of 265

    * This means that 1 campsite will be fully supplied, and there will be 265 sleeping bags left over.

    ### Answer: 265

Expected answer: 265

Correct? Yes

🔗 Follow-up

Problem: The same company from our previous question receives an updated request for sleeping bags. Now instead of 639, they only need to donate 613. If each campsite is still supplied with 374 sleeping bags, how many sleeping bags will be left after all the campsites are filled?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when the new total number of sleeping bags is divided by the number of sleeping bags per campsite.

    * Divide the total number of sleeping bags by the number of sleeping bags per campsite: 613 ÷ 374 = 1 with a remainder of 239

    * This means that 1 campsite will be fully supplied, and there will be 239 sleeping bags left over.

    ### Answer: 239

Expected answer: 239

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 620 is divided by 578.  This can be done using long division or by recognizing that 620 is only slightly larger than 578.
    We know 620 - 578 = 42.
    Therefore, 42 pizzas will be left over.

    ### Answer: 42

Expected answer: 42

Correct? Yes

🔗 Follow-up

Problem: The owner of the pizza restaurant decides to make 74 more pizzas tomorrow, bringing the total to 694 pizzas. If they are again distributed into boxes that hold 578 pizzas each, how many pizzas will be left out without a box this time?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 694 is divided by 578. We can do this using long division or by recognizing that 694 is only slightly larger than 578.

    694 - 578 = 116.

    Since 116 is greater than 578, we know that there is at least one more box needed.

    116 - 578 = -462.  This negative result means we need to subtract one box.

    Therefore, 116 - 578 = -462  means there is only 116 left over.

    ### Answer: 116

Expected answer: 116

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  The factory needs 820/684 = <<820/684=1.198>> 1.198 storage units to store all the robots. Since you can't have parts of a storage unit, the factory needs 2 storage units. This means they can store 2*684 = <<2*684=1368>> 1368 robots in the storage units.  This leaves 820 - 1368 = <<820 - 1368=-548>> -548 robots outside. Since we can't have a negative number of robots, this tells us that all the robots can fit in the storage units.

    ### Answer: 0

Expected answer: 136

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To figure out how many cycles the cloud goes through, we divide the initial number of droplets by the number of droplets lost per cycle: 516 droplets / 289 droplets/cycle = 1.78 cycles. Since we can't have a fraction of a cycle, the cloud goes through 1 complete cycle.

    After the first cycle, the cloud loses 289 droplets.
    Therefore, the remaining droplets are 516 - 289 = 227 droplets.

    ### Answer: 227

Expected answer: 227

Correct? Yes

🔗 Follow-up

Problem: If initially, there were only 175 droplets in the cloud instead of 516. 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?

Gemini-1.5 Flash:

    Reasoning: Since the cloud loses water droplets in groups of 289, and there are only 175 droplets initially, the cloud will not go through a full cycle. It will lose all of its droplets before reaching the 289 threshold.

    ### Answer: 0

Expected answer: 175

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 330 is divided by 4.
    330 divided by 4 is 82 with a remainder of 2.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Follow-up

Problem: The transport company now needs to load a new batch of 274 boxes into trucks. Again, each truck can hold exactly 4 boxes. After filling each truck to its full capacity, how many boxes will be left unloaded this time?

Gemini-1.5 Flash:

    Reasoning: We need to find the remainder when 274 is divided by 4.
    274 divided by 4 is 68 with a remainder of 2.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the largest multiple of 183 that is less than 649. Dividing 649 by 183, we get approximately 3.55. This means that 3 crates can be filled completely.

     To find the remaining potatoes, we multiply the number of full crates by the number of potatoes per crate, and then subtract that amount from the total number of potatoes harvested: 3 crates * 183 potatoes/crate = 549 potatoes.

     Finally, we subtract the number of potatoes in full crates from the total number of potatoes: 649 potatoes - 549 potatoes = 100 potatoes.

    ### Answer: 100

Expected answer: 100

Correct? Yes

🔗 Follow-up

Problem: The farmer realized that he actually only harvested 238 potatoes this season instead of 649. If he still packs them into crates each holding 183 potatoes, how many potatoes will be left after all crates are filled to their maximum capacity?

Gemini-1.5 Flash:

    Reasoning: Since the farmer only has 238 potatoes, and each crate holds 183 potatoes, he can only fill one crate completely.

    To find out how many potatoes are left over, we subtract the number of potatoes in one crate from the total number of potatoes: 238 potatoes - 183 potatoes = 55 potatoes.

    ### Answer: 55

Expected answer: 55

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We can find out how many shirts fit in the boxes by dividing the total number of shirts by the number of shirts per box: 258 / 67 = 3 shirts with a remainder of 69. This means 3 boxes will be filled completely, but 69 shirts will be left over.

    ### Answer: 69

Expected answer: 57

Correct? No

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many coins are left over, we need to perform a division and look at the remainder. 995 divided by 267 is approximately 3.72. Since we can only have whole coins, each pirate receives 3 coins. To find the leftover coins, we multiply the number of pirates by the number of coins each pirate gets and subtract that from the total number of coins: 267 pirates * 3 coins/pirate = 801 coins. 995 - 801 = 194 coins leftover.
    ### Answer: 194

Expected answer: 194

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To figure this out, we need to see how many groups of 375 fit into 776 snails.  We can do this with division:

    776 / 375 = 2 with a remainder of 26.

    This means there are 2 full groups of 375 snails, and then 26 snails left over.

    ### Answer: 26

Expected answer: 26

Correct? Yes

🔗 Follow-up

Problem: Originally, you had grouped the snails in bunches of 375 snails each. Now, think about what would happen if each bunch had 18 snails instead. How many snails would be left in the final group then?

Gemini-1.5 Flash:

    Reasoning:  We need to see how many groups of 18 fit into 776 snails.  We can do this with division:

    776 / 18 = 43 with a remainder of 2.

    This means there are 43 full groups of 18 snails, and then 2 snails left over.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many full boxes they can pack, divide the total number of pillows by the number of pillows per box: 589 pillows / 198 pillows/box = 2.97 boxes. Since they can't pack a fraction of a box, they'll pack 2 full boxes. To find out how many pillows are left, multiply the number of pillows per box by the number of full boxes and subtract that from the total number of pillows: (2 boxes * 198 pillows/box) = 396 pillows.  589 pillows - 396 pillows = 193 pillows.

    ### Answer: 193

Expected answer: 193

Correct? Yes

🔗 Follow-up

Problem: The pillow factory has made an adjustment to the packaging process and recently upgraded their boxes so that each can now hold 810 pillows. If they still produce 589 pillows per day and pack as many full boxes as possible, how many pillows will be left outside the boxes at the end of the day?

Gemini-1.5 Flash:

    Reasoning: Since the factory produces 589 pillows and each box holds 810 pillows, they can't pack a full box. Therefore, all 589 pillows will be left outside the boxes.

    ### Answer: 589

Expected answer: 589

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The jewelry maker can make 633/30 = 21 necklaces with a remainder of 3 beads.
    ### Answer: 3

Expected answer: 3

Correct? Yes

🔗 Follow-up

Problem: The jewelry maker found an additional box of beads in her storage, increasing her total number of beads to 588. Now, if she uses these 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?

Gemini-1.5 Flash:

    Reasoning:  The jewelry maker can make 588/30 = 19 necklaces with a remainder of 18 beads.
    ### Answer: 18

Expected answer: 18

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many coins John can distribute evenly, we need to find the largest multiple of 140 that is less than 365.  We can do this by dividing 365 by 140: 365 / 140 = 2 with a remainder of 85. This means John can distribute 2 * 140 = 280 coins evenly.  He will have 365 - 280 = 85 coins left over.

    ### Answer: 85

Expected answer: 85

Correct? Yes

🔗 Follow-up

Problem: Now, suppose John comes across additional coins and his collection increases to 739 coins. He again tries to evenly distribute these coins among his 140 wallets. How many coins will John have left after this distribution?

Gemini-1.5 Flash:

    Reasoning:  To find out how many coins John can distribute evenly, we divide his total coins by the number of wallets: 739 / 140 = 5 with a remainder of 39. This means John can distribute 5 * 140 = 700 coins evenly.  He will have 739 - 700 = 39 coins left over.

    ### Answer: 39

Expected answer: 39

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: We need to find the largest multiple of 451 that is less than 743.
    743 divided by 451 is approximately 1.65.  This means we can fill one full carton (451 socks).
    The number of socks left unpacked is 743 - 451 = 292.

    ### Answer: 292

Expected answer: 292

Correct? Yes

🔗 Follow-up

Problem: Now suppose the sock manufacturer changes their packaging method and each carton contains 179 socks instead of 451 socks. After filling up as many cartons as possible with 743 socks, how many socks are left unpacked?

Gemini-1.5 Flash:

    Reasoning: We need to find the largest multiple of 179 that is less than 743.
    743 divided by 179 is approximately 4.15.  This means we can fill four full cartons (4 * 179 = 716 socks).
    The number of socks left unpacked is 743 - 716 = 27.

    ### Answer: 27

Expected answer: 27

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  We need to find the difference between the total number of children and the number who can go down without waiting.

      923 (total children) - 771 (children who can go without waiting) = 152 children.

    ### Answer: 152

Expected answer: 152

Correct? Yes

🔗 Follow-up

Problem: After the first 771 children go down the slide, another wave of children arrives and now there are 923 children in total waiting again. If 881 children can go down the slide without any break this time, how many children will be left waiting for their turn?

Gemini-1.5 Flash:

    Reasoning: We need to find the difference between the total number of children and the number who can go down without waiting.

    923 (total children) - 881 (children who can go without waiting) = 42 children

    ### Answer: 42

Expected answer: 42

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  Iron Punch can teleport 442 people / 104 people per trip = 4.25 trips. Since he can only make full trips, he'll make 4 trips.
    He will have teleported 4 trips * 104 people per trip = 416 people.
    There will be 442 people - 416 people = 26 people left in the building.

    ### Answer: 26

Expected answer: 26

Correct? Yes

🔗 Follow-up

Problem: What if there were actually 512 people in the collapsing building instead of 442? After Superhero Iron Punch teleports as many full groups of 104 people as he can to safety, how many people will be left in the building for his last round of rescue now?

Gemini-1.5 Flash:

    Reasoning: Iron Punch can teleport 512 people / 104 people per trip = 4.92 trips. Since he can only make full trips, he'll make 4 trips.
    He will have teleported 4 trips * 104 people per trip = 416 people.
    There will be 512 people - 416 people = 96 people left in the building.

    ### Answer: 96

Expected answer: 96

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning:  To find out how many packs the manufacturer can create, divide the total number of cards by the number of cards in each pack: 569 / 68 = 8 with a remainder of 25. This means the manufacturer can create 8 full packs and will have 25 cards left over.

    ### Answer: 25

Expected answer: 25

Correct? Yes

🔗 Follow-up

Problem: After realizing the popularity of the game, the card manufacturer decides to produce another deck of cards, this time with 205 cards. Once again, each card pack can hold 68 cards. After creating as many full packs as possible, how many cards will the manufacturer have left over this time around?

Gemini-1.5 Flash:

    Reasoning: To find out how many full packs the manufacturer can create with the new deck, divide the total number of cards by the number of cards in each pack: 205 / 68 = 3 with a remainder of 1.  This means the manufacturer can create 3 full packs and will have 1 card left over.

    ### Answer: 1

Expected answer: 1

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many boxes can be filled, we divide the total number of erasers by the number of erasers per box: 842 / 719 = 1 with a remainder of 123.
    This means 1 box can be filled completely, and there will be 123 erasers left over.

    ### Answer: 123

Expected answer: 123

Correct? Yes

🔗 Follow-up

Problem: Suppose the stationery store owner later decided to display the erasers in smaller boxes, with each box containing 420 erasers instead. After filling as many boxes as possible, how many erasers will be left over now?

Gemini-1.5 Flash:

    Reasoning:  To find out how many boxes can be filled with the smaller boxes, we divide the total number of erasers by the number of erasers per box: 842 / 420 = 2 with a remainder of 2.

    This means 2 boxes can be filled completely, and there will be 2 erasers left over.

    ### Answer: 2

Expected answer: 2

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many full boxes the farmer can pack, we need to divide the total number of carrots by the number of carrots each box can hold: 461 carrots / 244 carrots/box = 1.89 boxes. Since we can't have a fraction of a box, the farmer can pack 1 full box.

    Now, to find out how many carrots are left unpacked, we multiply the number of carrots per box by the number of full boxes packed and subtract that from the total number of carrots: 244 carrots/box * 1 box = 244 carrots.

    Finally, we subtract the number of carrots packed from the total number of carrots: 461 carrots - 244 carrots = 217 carrots.
    ### Answer: 217

Expected answer: 217

Correct? Yes

🔗 Follow-up

Problem: The farmer found out that he had initially miscounted and he actually only harvested 11 carrots. After he tries to pack these into the boxes which each can hold up to 244 carrots, how many carrots will be left unpacked now?

Gemini-1.5 Flash:

    Reasoning: The farmer only has 11 carrots, and each box can hold up to 244 carrots. Since 11 is less than 244, he won't be able to fill even one box.

    ### Answer: 11

Expected answer: 11

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how many penguins are left over, we need to see how many times 293 goes into 309.
    309 divided by 293 is approximately 1.05.
    Since we can't have a partial penguin, we know that there was 1 group of 293 penguins.
    To find the number of penguins in the final group, we subtract the number of penguins in the full group from the total: 309 - 293 = 16

    ### Answer: 16

Expected answer: 16

Correct? Yes

🔗 Follow-up

Problem: The penguin scientist realizes she made a mistake and there were actually only 262 penguins in each group. How many penguins will be in the final, possibly incomplete, group now?

Gemini-1.5 Flash:

    Reasoning: We need to see how many times 262 goes into 309.
    309 divided by 262 is approximately 1.18.
    Again, since we can't have a partial penguin, there was 1 group of 262 penguins.
    To find the number of penguins in the final group, we subtract the number of penguins in the full group from the total: 309 - 262 = 47

    ### Answer: 47

Expected answer: 47

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: The shop can make 580/18 = <<580/18=32.2222...>> 32 complete batches of sandwiches (we can't make parts of a sandwich).
    Since 32 batches use 32*18 = <<32*18=576>> 576 slices of bread, they will have 580 - 576 = <<580-576=4>> 4 slices of bread left.
    ### Answer: 4

Expected answer: 4

Correct? Yes

🔗 Follow-up

Problem: The sandwich shop's supplier delivered an additional batch of bread, bringing their total to 580 slices. If the shop still makes sandwiches using 477 slices of bread per batch, how many slices will they have left after the latest batch of sandwiches is made?

Gemini-1.5 Flash:

    Reasoning: After using 477 slices of bread for the latest batch, the shop will have 580 - 477 = <<580-477=103>> 103 slices of bread left.
    ### Answer: 103

Expected answer: 103

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: To find out how much fabric is left over, we need to figure out how much fabric is used to make dresses.
    We divide the total fabric by the fabric needed per dress: 925 meters / 529 meters/dress = 1.75 dresses.
    Since we can't make parts of dresses, the tailor can make only 1 dress.
    The amount of fabric left over is 925 meters - 529 meters = 396 meters.

    ### Answer: 396

Expected answer: 396

Correct? Yes

🔗 Follow-up

Problem: After making some dresses, the tailor now only has 62 meters of fabric left. If the tailor continues to use 529 meters of fabric to make each dress, how many meters of fabric will be left over after making the dresses?

Gemini-1.5 Flash:

    Reasoning: The tailor has 62 meters of fabric left, but needs 529 meters to make each dress.  This means the tailor cannot make any more dresses, as they do not have enough fabric.

    ### Answer: 62

Expected answer: 62

Correct? Yes

🔗 Problem

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?

Gemini-1.5 Flash:

    Reasoning: Since each tour group can only hold 530 people, we find out how many full groups can be made by dividing the total number of tourists by the group capacity: 976 / 530 = 1.84.
    Because we cannot have a partial group, we know that 1 full group will be able to go on a tour, leaving 976 - 530 = 446 tourists for the last group.
    ### Answer: 446

Expected answer: 446

Correct? Yes

🔗 Follow-up

Problem: What would happen if the number of tourists wanting to explore the castle was still 976, but this time each group could accommodate up to 726 people? How many tourists would be left for the last group of the day now?

Gemini-1.5 Flash:

    Reasoning:  If each tour group can now hold 726 people, we divide the total number of tourists by the group capacity: 976 / 726 = 1.34.  Since we cannot have a partial group, only 1 full group can go on a tour, leaving 976 - 726 = 250 tourists for the last group of the day.

    ### Answer: 250

Expected answer: 250

Correct? Yes