id stringlengths 71 71 | problem stringlengths 8 3.62k | reference_answers listlengths 1 7 | original_problem_variants listlengths 1 3 | problem_sources listlengths 0 4 | source_splits listlengths 1 4 | source_split_row_counts unknown | source_row_count int64 1 364 | missing_reference_answer_rows int64 0 0 | blank_reference_answer_rows int64 0 25 |
|---|---|---|---|---|---|---|---|---|---|
omr-ws-aa1ca6219442591887e7722e1c908dc1e63e60f2a2439b42d79fa266c0ed2a45 | A magician has 100 letters, numbered from 1 to 100. He distributes them into three boxes (red, white, and blue) such that each box contains at least one letter. Two distributions are considered different if at least one letter is in a different box. A spectator chooses two of the three boxes, removes one letter from ea... | [
"12"
] | [
"A magician has 100 letters, numbered from 1 to 100. He distributes them into three boxes (red, white, and blue) such that each box contains at least one letter. Two distributions are considered different if at least one letter is in a different box. A spectator chooses two of the three boxes, removes one letter fr... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 3,
"genselect": 7
} | 10 | 0 | 0 |
omr-ws-b9e2b4721a6051ce5be88ce6ca20a615b2266bc2d224509d634dc1e0c417a7aa | A magician has a deck of 52 cards (13 of each suit: spades, clubs, hearts, diamonds). A random person selects 5 cards with different colors. The magician's helper arranges these 5 cards in a specific order and flips 4 of them face up while leaving one card face down. The magician can then correctly guess the face-down ... | [
"Using the majority color to determine the hidden card's suit and permuting the remaining cards to encode its rank."
] | [
"A magician has a deck of 52 cards (13 of each suit: spades, clubs, hearts, diamonds). A random person selects 5 cards with different colors. The magician's helper arranges these 5 cards in a specific order and flips 4 of them face up while leaving one card face down. The magician can then correctly guess the face-... | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems",
"genselect"
] | {
"additional_problems": 1,
"genselect": 5
} | 6 | 0 | 0 |
omr-ws-a1829b3081fca9ba0a957d07f2a98c6b41ffa368f1737968ffc6817e8bf54c50 | A magician has cards numbered 1 to 100 and distributes them into three boxes (blue, red, and yellow) such that each box contains at least one card. A spectator chooses two boxes, takes one card from each, and sums the numbers on the cards. The magician must be able to determine which two boxes were chosen based on the ... | [
"The magician can distribute the cards either by their residue classes modulo 3 or as {1}, {2 to 99}, {100}."
] | [
"A magician has cards numbered 1 to 100 and distributes them into three boxes (blue, red, and yellow) such that each box contains at least one card. A spectator chooses two boxes, takes one card from each, and sums the numbers on the cards. The magician must be able to determine which two boxes were chosen based on... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 9,
"genselect": 4,
"tir": 13
} | 26 | 0 | 0 |
omr-ws-dd2573ebe087efc5b53d02574cf791eb671141b15e84e72b97a8b1ce880e4381 | A magician has one hundred cards numbered 1 to 100. He puts them into three boxes (red, white, and blue) such that each box contains at least one card. A member of the audience draws two cards from two different boxes and announces the sum of the numbers on those cards. Given this information, the magician can identify... | [
"6"
] | [
"A magician has one hundred cards numbered 1 to 100. He puts them into three boxes (red, white, and blue) such that each box contains at least one card. A member of the audience draws two cards from two different boxes and announces the sum of the numbers on those cards. Given this information, the magician can ide... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 10,
"genselect": 1
} | 11 | 0 | 0 |
omr-ws-c2a91148969665e8910adb6904a05f6e02f111f5eafb3c05454b9ce2853235e4 | A magician has one hundred cards numbered from 1 to 100. He distributes these cards into three boxes (red, white, and blue) such that each box contains at least one card. An audience member selects two of the three boxes, picks one card from each, and announces the sum of the numbers on the chosen cards. Given this sum... | [
"Red box: \\(3k+1\\), White box: \\(3k+2\\), Blue box: \\(3k\\)"
] | [
"A magician has one hundred cards numbered from 1 to 100. He distributes these cards into three boxes (red, white, and blue) such that each box contains at least one card. An audience member selects two of the three boxes, picks one card from each, and announces the sum of the numbers on the chosen cards. Given thi... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 11,
"genselect": 1,
"tir": 27
} | 39 | 0 | 0 |
omr-ws-b9af89e8de071814559d6753d4658c0053eb61b0a77ac6b7f850e106de2ea391 | A magician needs to determine the area of a hidden convex 2008-gon \( A_1A_2 \ldots A_{2008} \). In each step, the magician chooses two points on the perimeter (which can be vertices or points dividing selected sides in selected ratios). The helper then divides the polygon into two parts by the line through these two p... | [
"2007"
] | [
"A magician needs to determine the area of a hidden convex 2008-gon \\( A_1A_2 \\ldots A_{2008} \\). In each step, the magician chooses two points on the perimeter (which can be vertices or points dividing selected sides in selected ratios). The helper then divides the polygon into two parts by the line through the... | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-9e425a2c25c677705f92d59697d658044655667aeff6c654f716c0a2ec8cf5c9 | A magician needs to determine the area of a hidden convex 2008-gon \( A_{1}A_{2}\cdots A_{2008} \). In each step, he chooses two points on the perimeter (which can be vertices or points dividing selected sides in selected ratios). His helper then divides the polygon into two parts by the line through these two points a... | [
"2007"
] | [
"A magician needs to determine the area of a hidden convex 2008-gon \\( A_{1}A_{2}\\cdots A_{2008} \\). In each step, he chooses two points on the perimeter (which can be vertices or points dividing selected sides in selected ratios). His helper then divides the polygon into two parts by the line through these two ... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 5,
"genselect": 3
} | 8 | 0 | 0 |
omr-ws-f4833581739d070a48a5092cbeab9a54dd5aabab1ff22f47f83604377e85cf03 | A magician performs a trick with a deck of $n$ cards numbered from $1$ to $n$. The magician arranges the cards in a specific order and challenges an audience member to write an integer on a board. The magician turns over the cards one by one, and each time, the audience member multiplies the number on the board by $-1$... | [
"n \\equiv 3 \\pmod{4}"
] | [
"A magician performs a trick with a deck of $n$ cards numbered from $1$ to $n$. The magician arranges the cards in a specific order and challenges an audience member to write an integer on a board. The magician turns over the cards one by one, and each time, the audience member multiplies the number on the board by... | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-d21b2787299eea301cac4961aba36ad352db0a16560db04266500a91dfaa86f7 | A magician randomly lays out 13 distinct-valued cards in a row and repeatedly removes the least or greatest-valued card, passing over all cards to the left of the removed card. If $x$ is the expected number of cards he will pass over, compute $x - \sum^{13}_{n=2}\frac{1}{n}$. | [
"27"
] | [
"A magician randomly lays out 13 distinct-valued cards in a row and repeatedly removes the least or greatest-valued card, passing over all cards to the left of the removed card. If $x$ is the expected number of cards he will pass over, compute $x - \\sum^{13}_{n=2}\\frac{1}{n}$."
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-d47e67b9c8d92d2a18a3e6472c60ee1db1b0c49bc5a3b5ff83c0039f3d8e9a6d | A magician randomly picks a three-digit positive integer to put into her hat and pulls out the same number with its digits in reverse order. What is the probability the magician pulls out a multiple of $22$? | [
"\\(\\frac{1}{20}\\)"
] | [
"A magician randomly picks a three-digit positive integer to put into her hat and pulls out the same number with its digits in reverse order. What is the probability the magician pulls out a multiple of $22$?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-90bb1d3a727412564474baee760cf1408b7feb63d32bac6dc703fa7894575b78 | A magician wants to demonstrate a trick to an audience of $n \ge 16$ people. He gives them 15 hats and after giving instructions to his assistant (which the audience does not hear), leaves the hall. Some 15 people in the audience put on one of the hats. The assistant then marks one of the hats with a marker, and the pe... | [
"\\( n = 16 \\) and \\( n = 17 \\)"
] | [
"A magician wants to demonstrate a trick to an audience of $n \\ge 16$ people. He gives them 15 hats and after giving instructions to his assistant (which the audience does not hear), leaves the hall. Some 15 people in the audience put on one of the hats. The assistant then marks one of the hats with a marker, and ... | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-bcf5ba07c3a27b672be3e7c40b636775776428cc16d05e27ba941e62320acf6f | A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notes that no two adjacent houses ever get mail on the same day, but there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible? | [
"351"
] | [
"A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notes that no two adjacent houses ever get mail on the same day, but there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-5c7f6ba6f25023d2acddb6ef0cf817a9f6db28883bf765e597a7fe06b35bad49 | A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible? | [
"351"
] | [
"A mail carrier delivers mail to the nineteen houses on the east side of Elm Street. The carrier notices that no two adjacent houses ever get mail on the same day, but that there are never more than two houses in a row that get no mail on the same day. How many different patterns of mail delivery are possible?",
... | [
"MATH_training_set",
"aops_c4_high_school_math",
"aops_c5_contests_amp_programs"
] | [
"cot",
"genselect"
] | {
"cot": 109,
"genselect": 8
} | 117 | 0 | 0 |
omr-ws-16c2a55131522d0be4ee6710b3e74a7ae0a055f55a9c07c6407ce62add780fb5 | A mail train leaves station $A$ at 5 a.m. for station $B$, 1080 km away. At 8 a.m. a fast train leaves $B$ for $A$ and runs 15 km/h faster than the mail train. When do the trains pass each other if this occurs midway between $A$ and $B$? | [
"In 9 hours after the fact train departure"
] | [
"A mail train leaves station $A$ at 5 a.m. for station $B$, 1080 km away. At 8 a.m. a fast train leaves $B$ for $A$ and runs 15 km/h faster than the mail train. When do the trains pass each other if this occurs midway between $A$ and $B$?"
] | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-1cf7f10872780aa8d5fbaad1dc51f9c75a93ac7374439dfbc515c62d1cb8c52f | A mailman is delivering mail to 10 houses on one side of the street. No two adjacent houses both get mail, and at most three houses in a row don't get any mail. How many ways can this occur? | [
"69"
] | [
"A mailman is delivering mail to 10 houses on one side of the street. No two adjacent houses both get mail, and at most three houses in a row don't get any mail. How many ways can this occur?"
] | [
"aops_c5_contests_amp_programs",
"c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 46,
"tir": 29
} | 75 | 0 | 0 |
omr-ws-5f2c4faf48053e0e0e4851f0e7bb26642d80226f88e975458e07760959ea266f | A mailman must deliver letters to 8 houses along a street, starting at house 1 and finishing at house 8. The houses are arranged such that houses 1, 3, 5, and 7 are on one side, and houses 2, 4, 6, and 8 are on the other side, with each house directly opposite its counterpart (e.g., house 2 is opposite house 1). The ma... | [
"8"
] | [
"A mailman must deliver letters to 8 houses along a street, starting at house 1 and finishing at house 8. The houses are arranged such that houses 1, 3, 5, and 7 are on one side, and houses 2, 4, 6, and 8 are on the other side, with each house directly opposite its counterpart (e.g., house 2 is opposite house 1). T... | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 3
} | 3 | 0 | 0 |
omr-ws-feb9f95457fa0636d7e107cd6b22207499f6a5e29ab07f9d4e6115e7ba5d737e | A maintenance man takes 30 seconds to run down a moving escalator. It takes him 45 seconds to descend along the escalator when motionless. How long would it take him to descend by simply standing on the escalator when moving? | [
"90 s"
] | [
"A maintenance man takes 30 seconds to run down a moving escalator. It takes him 45 seconds to descend along the escalator when motionless. How long would it take him to descend by simply standing on the escalator when moving?"
] | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-98e85b044bfc48a8d4b63b5e83765438797f9e191a142d2f7eef704bc922d9cd | A majority of the 30 students in Ms. Deameanor's class bought pencils at the school bookstore. Each student bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was \$17.71. ... | [
"11"
] | [
"A majority of the 30 students in Ms. Deameanor's class bought pencils at the school bookstore. Each student bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was \\$1... | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 17
} | 33 | 0 | 0 |
omr-ws-49c2c78aba56b2d43a4923d2a7f69be2cc8139a5b9978b808576c54e95d05ba6 | A majority of the 30 students in Ms. Demeanor's class bought pencils at the school bookstore. Each student bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.71. Wh... | [
"11"
] | [
"A majority of the 30 students in Ms. Demeanor's class bought pencils at the school bookstore. Each student bought the same number of pencils, and this number was greater than 1. The cost of a pencil in cents was greater than the number of pencils each student bought, and the total cost of all the pencils was $17.7... | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 20
} | 36 | 0 | 0 |
omr-ws-1215deaa8db10a0f75fbe154238bbad0a7407a8e91a6976b7c256d6eabe044e6 | A man 1.8 meters tall, standing due east of a street light, notices that his shadow is 6.5 meters long. He walks on a bearing of $150^{\circ}T$ from his first position for a distance of 12 meters and now finds his shadow is 9.1 meters long. Find the height of the street light to 1.d.p. | [
"5.5"
] | [
"A man 1.8 meters tall, standing due east of a street light, notices that his shadow is 6.5 meters long. He walks on a bearing of $150^{\\circ}T$ from his first position for a distance of 12 meters and now finds his shadow is 9.1 meters long. Find the height of the street light to 1.d.p."
] | [
"aops_c4_high_school_math"
] | [
"tir"
] | {
"tir": 4
} | 4 | 0 | 0 |
omr-ws-2d4db8d04313317358cb16794da5227d6a07fec69404be16a770989e846d689d | A man 2 meters tall walks at \( \frac{5}{3} \) meters per second along one edge of a straight road that is 10 meters wide. On the other side of the road is a light atop a pole that is 6 meters tall. How fast is the length of the man's shadow (on the ground) increasing when he is 15 meters beyond the point directly acro... | [
"\\dfrac{5\\sqrt{13}}{26}"
] | [
"A man 2 meters tall walks at \\( \\frac{5}{3} \\) meters per second along one edge of a straight road that is 10 meters wide. On the other side of the road is a light atop a pole that is 6 meters tall. How fast is the length of the man's shadow (on the ground) increasing when he is 15 meters beyond the point direc... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 15,
"genselect": 4
} | 19 | 0 | 0 |
omr-ws-7759ffb9aaee9aaa3ba7ec02d4553f48a0de900e09058af33cd63f581629a992 | A man 5 ft tall walks at the rate of 4 ft/sec directly away from a street light which is 20 ft above the street. At what rate is the length of his shadow changing? | [
"\\dfrac{4}{3}"
] | [
"A man 5 ft tall walks at the rate of 4 ft/sec directly away from a street light which is 20 ft above the street. At what rate is the length of his shadow changing?"
] | [
"aops_c7_college_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-1b7032b20cebfaa45b2078d663dca74b067cbbb146919f7c1e394e873ff5b8f3 | A man 5 ft tall walks at the rate of 4 ft/sec directly away from a street light which is 20 ft above the street. At what rate is the tip of his shadow changing? | [
"\\dfrac{16}{3}"
] | [
"A man 5 ft tall walks at the rate of 4 ft/sec directly away from a street light which is 20 ft above the street. At what rate is the tip of his shadow changing?"
] | [
"aops_c7_college_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-b1c92887cd6798bcb2a5b267b84903a179b66f95cce69fa976d89f4113e593f7 | A man 6 feet tall is walking at a rate of 3 feet per second towards a streetlight 18 feet high. At what rate is his shadow changing? | [
"-\\dfrac{3}{2}"
] | [
"A man 6 feet tall is walking at a rate of 3 feet per second towards a streetlight 18 feet high. At what rate is his shadow changing?"
] | [
"aops_c7_college_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-f912e9d218fb6b150a251ddae7e31eddc7d70e3ba81c74eb6dc47c128945a77a | A man 6 feet tall is walking at a rate of 3 feet per second towards a streetlight 18 feet high. How fast is the tip of the shadow moving? | [
"\\dfrac{9}{2}"
] | [
"A man 6 feet tall is walking at a rate of 3 feet per second towards a streetlight 18 feet high. How fast is the tip of the shadow moving?"
] | [
"aops_c7_college_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-5cf18c5584e358a467671c8a89adea22cc74d63afa24f6cfeaab8a134d5c09f3 | A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When the man is 10 feet from the base of the light, at what rate is the tip of his shadow moving and at what rate is the length of his shadow changing? | [
"$\\frac{25}{3}$ and $\\frac{10}{3}$"
] | [
"A man 6 feet tall walks at a rate of 5 feet per second away from a light that is 15 feet above the ground. When the man is 10 feet from the base of the light, at what rate is the tip of his shadow moving and at what rate is the length of his shadow changing?"
] | [
"aops_c7_college_math"
] | [
"tir"
] | {
"tir": 19
} | 19 | 0 | 0 |
omr-ws-9849e1765f6434a1a1efbaf378331f772f7a18b62041f8a8b8c80345f73d98f2 | A man 6 ft tall is walking at a rate of 3 ft/sec toward a street light 15 ft above the ground. How fast is the length of his shadow changing? | [
"\\(-\\frac{9}{5}\\) ft/sec"
] | [
"A man 6 ft tall is walking at a rate of 3 ft/sec toward a street light 15 ft above the ground. How fast is the length of his shadow changing?"
] | [
"aops_c7_college_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-06a6a0947a5d0e56d1e77cace245a2224fca37e1e33e9dc51c59ceb684545ac0 | A man 6 ft tall is walking at a rate of f feet per second toward a streetlight 18 ft high. a) At what rate is his shadow changing? b) How fast is the tip of the shadow moving? | [
"-\\dfrac{3f}{2}"
] | [
"A man 6 ft tall is walking at a rate of f feet per second toward a streetlight 18 ft high.\n a) At what rate is his shadow changing?\n b) How fast is the tip of the shadow moving?"
] | [
"aops_c7_college_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-6c7e317beb0e9b502eabc37ed0f64366800492bb4961ea069eea36d2c92d31c9 | A man 6 ft tall walks at the rate of 200 feet per minute towards a street light which is 18 ft above the ground. At what rate is the tip of his shadow moving? | [
"300 feet per minute"
] | [
"A man 6 ft tall walks at the rate of 200 feet per minute towards a street light which is 18 ft above the ground. At what rate is the tip of his shadow moving?"
] | [
"aops_c7_college_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 15,
"genselect": 8,
"tir": 7
} | 30 | 0 | 0 |
omr-ws-21f8771d41dc086db1952e4a447914a73b16dcad63990f93e1445d127203260c | A man and a woman agree to meet at a certain location around 12:30 P.M. The man arrives at a time uniformly distributed between 12:15 and 12:45, and the woman arrives at a time uniformly distributed between 12:00 and 1:00 P.M. Find the probability that the first to arrive waits no longer than 5 minutes. | [
"\\(\\frac{1}{6}\\)"
] | [
"A man and a woman agree to meet at a certain location around 12:30 P.M. The man arrives at a time uniformly distributed between 12:15 and 12:45, and the woman arrives at a time uniformly distributed between 12:00 and 1:00 P.M. Find the probability that the first to arrive waits no longer than 5 minutes."
] | [
"aops_c7_college_math"
] | [
"cot",
"tir"
] | {
"cot": 14,
"tir": 28
} | 42 | 0 | 0 |
omr-ws-a71f6a072dfd2f2a105e8ae3982906a8212b9819f5d0b96375a8d0edafbfa2a8 | A man and a woman agree to meet at a certain location around 12:30 P.M. The man arrives at a time uniformly distributed between 12:15 and 12:45, and the woman arrives at a time uniformly distributed between 12:00 and 1:00 P.M. Find the probability that the man arrives first. | [
"\\(\\frac{1}{2}\\)"
] | [
"A man and a woman agree to meet at a certain location around 12:30 P.M. The man arrives at a time uniformly distributed between 12:15 and 12:45, and the woman arrives at a time uniformly distributed between 12:00 and 1:00 P.M. Find the probability that the man arrives first."
] | [
"aops_c7_college_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 10
} | 26 | 0 | 0 |
omr-ws-327138ad9cc2375edc2bb698faae2b586be79726dc143d38dd5f139d2d19145d | A man and his grandson have the same birthday. For 6 consecutive birthdays, the man is an integral number of times as old as his grandson. How old is each at the 6th of these birthdays? | [
"Man is 66, grandson is 6."
] | [
"A man and his grandson have the same birthday. For 6 consecutive birthdays, the man is an integral number of times as old as his grandson. How old is each at the 6th of these birthdays?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 3,
"tir": 24
} | 27 | 0 | 0 |
omr-ws-b74f0d6eb815fe91aafc2a25d605633a40ffbb15aa89da954091988ac36bffb1 | A man and his grandson have the same birthday. For six consecutive birthdays the man is an integral number of times as old as his grandson. How old is the man at the sixth of these birthdays? | [
"66"
] | [
"A man and his grandson have the same birthday. For six consecutive birthdays the man is an integral number of times as old as his grandson. How old is the man at the sixth of these birthdays?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 15,
"tir": 9
} | 24 | 0 | 0 |
omr-ws-9c4ab56bc2ea8d329821e118ac7ed35183397c280436285d103f948e2aaf4e73 | A man arrives at an airport between 11:00 and 12:00 and waits for 20 minutes for his wife to pick him up. If she does not arrive, he leaves. His wife arrives between 11:00 and 11:40 and waits for him for 10 minutes. If he does not arrive, she leaves. What is the probability that the wife picks up the man? | [
"\\dfrac{5}{12}"
] | [
"A man arrives at an airport between 11:00 and 12:00 and waits for 20 minutes for his wife to pick him up. If she does not arrive, he leaves. His wife arrives between 11:00 and 11:40 and waits for him for 10 minutes. If he does not arrive, she leaves. What is the probability that the wife picks up the man?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 15
} | 15 | 0 | 0 |
omr-ws-b256592b964ddd6ac5b65d81343e61e736a28147f4dea2c55c9a7209f30a9da2 | A man between 30 and 60 years old, born between 1901 and 1955, is celebrating his birthday on the same day of the week as the day he was born. What is the sum of the possible values of his age at the time of his celebration? | [
"182"
] | [
"A man between 30 and 60 years old, born between 1901 and 1955, is celebrating his birthday on the same day of the week as the day he was born. What is the sum of the possible values of his age at the time of his celebration?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-21d148237d7a7fb5d1e22ef196ef8260dcdd06aa96ad890ca2b8bccd5a8abbbf | A man borrows $2000 and agrees to repay $2560 at the end of 4 years. What is the rate of simple interest? | [
"28%"
] | [
"A man borrows $2000 and agrees to repay $2560 at the end of 4 years. What is the rate of simple interest?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-9e32fd145c6b9a413d1f1d4345cdf44ceb7244744920c74b75030f0e9244e9ed | A man bought a factory for Rs 20,00,000 and earns Rs 12,00,000 at the end of 5 years. He did not allow depreciation for the first 2 years. If the rate of depreciation for the remaining years was 10% p.a., find the gain or loss percent from the factory. | [
"32.9%"
] | [
"A man bought a factory for Rs 20,00,000 and earns Rs 12,00,000 at the end of 5 years. He did not allow depreciation for the first 2 years. If the rate of depreciation for the remaining years was 10% p.a., find the gain or loss percent from the factory."
] | [
"aops_c4_high_school_math"
] | [
"tir"
] | {
"tir": 19
} | 19 | 0 | 0 |
omr-ws-9e25a59b6f2f6827f05dfd2c8c838cee18d1635ada5b9926880212b16cd48995 | A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, how much should he sell the other to make a profit of 20% on the whole? | [
"3350"
] | [
"A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, how much should he sell the other to make a profit of 20% on the whole?"
] | [
"aops_c7_college_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-c6667f423978c28b2afea145316ca2343f1fe397b815bf157a34eff42f9a94f6 | A man buys 4 items at a store. The sum and the product of the prices of these items are both $7.11. What are the prices of each of the items? | [
"1.20, 1.25, 1.50, 3.16"
] | [
"A man buys 4 items at a store. The sum and the product of the prices of these items are both $7.11. What are the prices of each of the items?"
] | [
"aops_c4_high_school_math"
] | [
"tir"
] | {
"tir": 25
} | 25 | 0 | 0 |
omr-ws-51f8fa1c5b7d44b8d6fd1f8f260c1ff5b06bbf35978e7f9c008e31ccfe38b558 | A man buys a house for $10,000 and rents it. He puts 12.5% of each month's rent aside for repairs and upkeep, pays $325 a year in taxes, and realizes a 5.5% return on his investment. What is the monthly rent? | [
"550\n\nThe first post in the forum discussions directly provides the answer to the problem, stating that the monthly rent is 550 dollars."
] | [
"A man buys a house for $10,000 and rents it. He puts 12.5% of each month's rent aside for repairs and upkeep, pays $325 a year in taxes, and realizes a 5.5% return on his investment. What is the monthly rent?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-a74bbda163f2cd917c5b5b8e98676189bdc4c9dac66d488601a61b6a170a8c66 | A man buys an item for 50 dollars using a 100-dollar bill. The clerk exchanges the 100-dollar bill for change from an adjacent shop and gives the man the item and his change. Later, the adjacent shop clerk returns, stating the 100-dollar bill is fake. The first clerk then gives a real 100-dollar bill to the adjacent sh... | [
"-100"
] | [
"A man buys an item for 50 dollars using a 100-dollar bill. The clerk exchanges the 100-dollar bill for change from an adjacent shop and gives the man the item and his change. Later, the adjacent shop clerk returns, stating the 100-dollar bill is fake. The first clerk then gives a real 100-dollar bill to the adjace... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-c1c1e1d3a5ab8f3a7bcd9a02f34de6138e29b93c250e775b94f730133116606f | A man buys drinks from two manufacturers: - One bottle of drink A is made up from alcohol and water in the ratio 1:3. - One bottle of drink B is made up from alcohol and water in the ratio 1:7. What is the least number of bottles he would need of each type of drink in order to produce drinks containing alcohol and wate... | [
"26"
] | [
"A man buys drinks from two manufacturers:\n- One bottle of drink A is made up from alcohol and water in the ratio 1:3.\n- One bottle of drink B is made up from alcohol and water in the ratio 1:7.\nWhat is the least number of bottles he would need of each type of drink in order to produce drinks containing alcohol ... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 13
} | 13 | 0 | 0 |
omr-ws-052711045cdde199d4200b9523b28edf47ac1b02630e84da3a3a60cef0fe3c74 | A man can only keep bass between 8 lb and 14 lb. There are 24 bass in the lake, ranging from 4 lb to 22 lb. What is the probability that he will catch two keepers, given that if he catches one keeper, he won't release it back into the lake? Express your answer in percent and round to the nearest tenth if necessary. | [
"10.1\\%"
] | [
"A man can only keep bass between 8 lb and 14 lb. There are 24 bass in the lake, ranging from 4 lb to 22 lb. What is the probability that he will catch two keepers, given that if he catches one keeper, he won't release it back into the lake? Express your answer in percent and round to the nearest tenth if necessary... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-3c8301418b447e12790544fa2c1509d4c57f9905ee63a8463af066a00cd6f3cf | A man commutes to work either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon, and vice versa. During a total of \( x \) working days, the man took the bus to work in the morning 8 times, came home by bus in the afternoon 15 times, and commuted by train (eit... | [
"16"
] | [
"A man commutes to work either by train or by bus. If he goes to work on the train in the morning, he comes home on the bus in the afternoon, and vice versa. During a total of \\( x \\) working days, the man took the bus to work in the morning 8 times, came home by bus in the afternoon 15 times, and commuted by tra... | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 9,
"genselect": 7
} | 16 | 0 | 0 |
omr-ws-e313c9c46b0d78781a18bb38a5adda03a28d213bac508f75a20097da78a05701 | A man cycles to his destination with the wind at a speed of 8 m/s and back to his starting point at 4 m/s. Calculate his average speed for the entire trip. | [
"\\dfrac{16}{3}"
] | [
"A man cycles to his destination with the wind at a speed of 8 m/s and back to his starting point at 4 m/s. Calculate his average speed for the entire trip."
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-3e4bd33cb02671628d6a98022b2f366210c03ab15926f7a5c003597f2f8f689f | A man deposits $2000 on June 1st each year for 20 years. If interest at 8% is compounded annually, what is the value of his account after 20 years? Use the formula \( S_{n} = \frac{x_{1} ( r^{n} - 1)}{r - 1} \). | [
"91523.93"
] | [
"A man deposits $2000 on June 1st each year for 20 years. If interest at 8% is compounded annually, what is the value of his account after 20 years? Use the formula \\( S_{n} = \\frac{x_{1} ( r^{n} - 1)}{r - 1} \\)."
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 29
} | 45 | 0 | 0 |
omr-ws-d67b7bbd2558a1c9a8e1892ece729fa31dd1c7574af1f62a6618a63bedddd1b7 | A man descends 3 stairs per second and counts 140 stairs. When he descends 2 stairs per second, he counts 168 stairs. How many stairs are there in total? | [
"105"
] | [
"A man descends 3 stairs per second and counts 140 stairs. When he descends 2 stairs per second, he counts 168 stairs. How many stairs are there in total?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 14,
"genselect": 7
} | 21 | 0 | 0 |
omr-ws-a7e8348b6fe6712419e02dc180ed7867ae3c50e183d52e094a179ea71f65b815 | A man drives at a constant speed. He travels from A to C in 30 minutes, from A through B to C in 35 minutes, and from A through D to C in 40 minutes. The distance from B to C is 10 miles, the same as from C to D. Angle C is a right angle, and points A, B, C, and D form a quadrilateral in a counterclockwise manner. Dete... | [
"40"
] | [
"A man drives at a constant speed. He travels from A to C in 30 minutes, from A through B to C in 35 minutes, and from A through D to C in 40 minutes. The distance from B to C is 10 miles, the same as from C to D. Angle C is a right angle, and points A, B, C, and D form a quadrilateral in a counterclockwise manner.... | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 4,
"genselect": 5
} | 9 | 0 | 0 |
omr-ws-fc543aba265f75984f08bb295a0184f8fe9b234228bd388719b847b4b317f346 | A man drives from city \( A \) to city \( B \) and back. The average speed he has on the trip from \( A \) to \( B \) is \( r \). The average speed he has for the entire trip is \( s \). What is his average speed on the trip from \( B \) to \( A \)? (in terms of \( s \) and \( r \)). | [
"\\dfrac{rs}{2r - s}"
] | [
"A man drives from city \\( A \\) to city \\( B \\) and back. The average speed he has on the trip from \\( A \\) to \\( B \\) is \\( r \\). The average speed he has for the entire trip is \\( s \\). What is his average speed on the trip from \\( B \\) to \\( A \\)? (in terms of \\( s \\) and \\( r \\))."
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-d783fcb15f328321d5010153930d1ae45ed5c256ebfe50b4d0d1afe9f10a885a | A man engages in a shooting contest. Each time he hits a target he receives $10$ cents, while each time he misses he pays $5$ cents. If after $20$ shots he has lost $10$ cents, how many times has he hit the target? | [
"6"
] | [
"A man engages in a shooting contest. Each time he hits a target he receives $10$ cents, while each time he misses he pays $5$ cents. If after $20$ shots he has lost $10$ cents, how many times has he hit the target?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 1
} | 17 | 0 | 0 |
omr-ws-b21fd4dea80c736b949abedd2c454ac7271767de770f1a5132cb2156eaad1b9c | A man goes into a bank to cash a check. The teller mistakenly reverses the amounts and gives the man cents for dollars and dollars for cents. After spending five cents, the man finds that he still has twice as much as the original check amount. What was the original check amount? Find all possible solutions. | [
"31.63"
] | [
"A man goes into a bank to cash a check. The teller mistakenly reverses the amounts and gives the man cents for dollars and dollars for cents. After spending five cents, the man finds that he still has twice as much as the original check amount. What was the original check amount? Find all possible solutions."
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-002ec3ba8d582ca92383189f44198db10e737207bf05cb7f0d09fb2ae596eb20 | A man goes out between 4 and 5 P.M. and returns between 5 and 6 P.M. to find that the positions of the hour and minute hands of the clock have exactly swapped. At what time does he go out? | [
"4:27 or more precisely \\( 4:\\frac{3840}{143} \\)"
] | [
"A man goes out between 4 and 5 P.M. and returns between 5 and 6 P.M. to find that the positions of the hour and minute hands of the clock have exactly swapped. At what time does he go out?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 13,
"genselect": 5,
"tir": 27
} | 45 | 0 | 0 |
omr-ws-e90d0a9b00515e71290f2a8ff2dc0282ec871dc249fd20edeced746210a3ba4d | A man had to cover the distance from a village to a railway station. Having covered 3 km during the first hour, he understood that he could be late for the train and began walking at a speed of 4 km/h. He reached the station 45 minutes before the train departed. If he had gone at a speed of 3 km/h, he would have been 4... | [
"20 km"
] | [
"A man had to cover the distance from a village to a railway station. Having covered 3 km during the first hour, he understood that he could be late for the train and began walking at a speed of 4 km/h. He reached the station 45 minutes before the train departed. If he had gone at a speed of 3 km/h, he would have b... | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-5d09de14cead6701037d09425466d0cdc04b79aca10270d1a3e686acf9b8623a | A man has $5000$ coins in a safe, all of which are either dimes or nickels. He repeatedly transfers 5 coins into his bank account. After $n$ transfers, he has more money (in value) in his bank account than in his safe. Compute the number of possible values of $n$. | [
"667"
] | [
"A man has $5000$ coins in a safe, all of which are either dimes or nickels. He repeatedly transfers 5 coins into his bank account. After $n$ transfers, he has more money (in value) in his bank account than in his safe. Compute the number of possible values of $n$."
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 7,
"genselect": 6,
"tir": 1
} | 14 | 0 | 0 |
omr-ws-c88ef14600873f7783dfe97bb5d79c90dcd7b072f237778727937be815bdbbcf | A man has 1044 candles. After burning a candle, he can make a new candle from 9 stubs left behind. What is the maximum number of candles he can make in total? | [
"129"
] | [
"A man has 1044 candles. After burning a candle, he can make a new candle from 9 stubs left behind. What is the maximum number of candles he can make in total?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-3ba61e63704cc2f0bd4ba616955c16111b37b71710d55df9b75f8d463438e06e | A man has 20 animals and must kill all of them in 5 days. Each day, he must kill at least 1 animal, and the number of animals killed each day must be an odd number. How can he achieve this? | [
"\\text{Impossible}"
] | [
"A man has 20 animals and must kill all of them in 5 days. Each day, he must kill at least 1 animal, and the number of animals killed each day must be an odd number. How can he achieve this?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-5a648f7225ddd455400c373d8b0a2989e5a22e60c0d8843cc10e4c3867b4f06e | A man has 3 coins, \(A\), \(B\), and \(C\). Coin \(A\) is fair, while the probabilities of getting heads for coins \(B\) and \(C\) are \(\frac{2}{3}\) and \(\frac{1}{3}\) respectively. One of these coins is chosen at random and tossed 3 times, resulting in 2 heads and 1 tail. If the probability that the chosen coin was... | [
"9"
] | [
"A man has 3 coins, \\(A\\), \\(B\\), and \\(C\\). Coin \\(A\\) is fair, while the probabilities of getting heads for coins \\(B\\) and \\(C\\) are \\(\\frac{2}{3}\\) and \\(\\frac{1}{3}\\) respectively. One of these coins is chosen at random and tossed 3 times, resulting in 2 heads and 1 tail. If the probability t... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 7
} | 23 | 0 | 0 |
omr-ws-009b4c798da22b383c671c70066d01a0b82a8b3cddbe1a872c77ef9e168de693 | A man has 3 favorite fishing seats with probabilities of catching a fish of 0.6, 0.7, and 0.8 respectively. Given that he dropped the line three times at one seat and caught exactly one fish, find the probability that the fish was caught at the first seat. | [
"\\(\\frac{9}{47}\\)"
] | [
"A man has 3 favorite fishing seats with probabilities of catching a fish of 0.6, 0.7, and 0.8 respectively. Given that he dropped the line three times at one seat and caught exactly one fish, find the probability that the fish was caught at the first seat."
] | [
"aops_c7_college_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-41e7102e3edbf700c87532eae9607a5d869097a8281df0bb72cb5b66b88e266b | A man has 3 sons of ages 5, 10, and 15. He puts $80,250 in the bank at the time of his death, paying 5% simple interest. If each son gets the same amount at the age of 20, find their shares at the time of their father's death. | [
"22,500, 26,250, and 31,500"
] | [
"A man has 3 sons of ages 5, 10, and 15. He puts $80,250 in the bank at the time of his death, paying 5% simple interest. If each son gets the same amount at the age of 20, find their shares at the time of their father's death."
] | [
"aops_c4_high_school_math"
] | [
"tir"
] | {
"tir": 31
} | 31 | 0 | 0 |
omr-ws-794f2111b451ff5ce66385af2607f14ba50c91611513b5c7399bdf4f18c008b2 | A man has 42 cucumbers. Each day he eats at least 1 cucumber. On the 28th day, he finishes all the cucumbers. Let $S$ be the sum of the starting and ending day numbers of a consecutive sequence during which the total number of cucumbers eaten is exactly 15. Find the minimum possible value of $S$. | [
"2"
] | [
"A man has 42 cucumbers. Each day he eats at least 1 cucumber. On the 28th day, he finishes all the cucumbers. Let $S$ be the sum of the starting and ending day numbers of a consecutive sequence during which the total number of cucumbers eaten is exactly 15. Find the minimum possible value of $S$."
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 7,
"genselect": 8
} | 15 | 0 | 0 |
omr-ws-d6736b174c8f609319f9ca8c72280bded0d694ddc0c963643940136f7c35c328 | A man has 6 friends. He met with each of them 11 times, every 2 of them 6 times, every 3 of them 4 times, all 4 of them 3 times, all 5 of them 3 times, and all 6 of them 10 times. He ate out 9 times without meeting any of them. How many times did he eat at the restaurant in total? | [
"28"
] | [
"A man has 6 friends. He met with each of them 11 times, every 2 of them 6 times, every 3 of them 4 times, all 4 of them 3 times, all 5 of them 3 times, and all 6 of them 10 times. He ate out 9 times without meeting any of them. How many times did he eat at the restaurant in total?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 10,
"genselect": 4
} | 14 | 0 | 0 |
omr-ws-40ba63c47bf0e5459b1f449df54aeefdf1e48619bf012f38faed3f0099f48134 | A man has 6 friends. He met with each of them 11 times, every 2 of them 6 times, every 3 of them 4 times, every 4 of them 3 times, every 5 of them 3 times, and all of them 10 times. He eats out 9 times without meeting them. How many times did he eat at the restaurant in total? | [
"28"
] | [
"A man has 6 friends. He met with each of them 11 times, every 2 of them 6 times, every 3 of them 4 times, every 4 of them 3 times, every 5 of them 3 times, and all of them 10 times. He eats out 9 times without meeting them. How many times did he eat at the restaurant in total?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 12,
"genselect": 6
} | 18 | 0 | 0 |
omr-ws-9c7d2afc1a967f8fcb21ceb61038abe7135028db3ea9e81c2912dd8a6165d34f | A man has a bag of sweets. He gave his son one sweet and 1/7 of the remaining sweets. From what was left, he gave his daughter two sweets and 1/7 of the remainder. The two children found that they had the same number of sweets. How many sweets were there initially in the bag? | [
"36"
] | [
"A man has a bag of sweets. He gave his son one sweet and 1/7 of the remaining sweets. From what was left, he gave his daughter two sweets and 1/7 of the remainder. The two children found that they had the same number of sweets. How many sweets were there initially in the bag?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 32
} | 32 | 0 | 0 |
omr-ws-984c537f132b25c41eb7f2090f1519bdff1184f9a5e540c328e815982aafb241 | A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing? | [
"\\( 2500 \\pi \\)"
] | [
"A man has a barn that is 20 ft by 10 ft. He tethers a cow to one corner of the outside of the barn using a 50-ft rope. What is the total area that the cow is capable of grazing?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-8467ac815b21aa30db8b3efddace2c570e8fad11c7b3b0023aebe6daf8ef4f3d | A man has a job requiring him to spend 30 minutes of his free time doing work each day. Each day, he has a 50% chance of having something planned, in which case he'll do a random amount of work from 0 to 30 minutes. The day after he has something planned, if he doesn't have another thing planned, he'll try to make it s... | [
"\\dfrac{343}{729}"
] | [
"A man has a job requiring him to spend 30 minutes of his free time doing work each day. Each day, he has a 50% chance of having something planned, in which case he'll do a random amount of work from 0 to 30 minutes. The day after he has something planned, if he doesn't have another thing planned, he'll try to make... | [
"aops_c4_high_school_math"
] | [
"cot",
"genselect"
] | {
"cot": 4,
"genselect": 1
} | 5 | 0 | 0 |
omr-ws-b474f7e7d733fa3e59cb235024637fce9591b8ac4cf9e8f0514afeffbcf77889 | A man has an infinite amount of money and distributes it among \( n \) people such that each person receives no more than \( 4n-1 \) rupees. The total amount of money distributed is a multiple of 4. In how many ways can he distribute the money? | [
"4^{n-1}n^n"
] | [
"A man has an infinite amount of money and distributes it among \\( n \\) people such that each person receives no more than \\( 4n-1 \\) rupees. The total amount of money distributed is a multiple of 4. In how many ways can he distribute the money?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-514d56cb2a688af9c76497683c5d6d4167fd3538930d4a01fd56fd4295b7b9d2 | A man has an infinite amount of money and wants to distribute it among \( n \) people such that each person receives a multiple of 4 rupees and no more than \( 4n-1 \) rupees. In how many ways can he do this? | [
"n^n"
] | [
"A man has an infinite amount of money and wants to distribute it among \\( n \\) people such that each person receives a multiple of 4 rupees and no more than \\( 4n-1 \\) rupees. In how many ways can he do this?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 31
} | 31 | 0 | 0 |
omr-ws-33e8a6cd524c99b15e5a5750f902c337a0234f7020a41655433e35ece25741e7 | A man has initially $\$S$ in his piggy bank. The first month he takes out half of his money, and the second month he adds $\$D$. The third month he takes out half his money, and the fourth month he adds $\$D$. This continues, every other month taking out half his money, and every other month adding $\$D$. In terms of $... | [
"2D"
] | [
"A man has initially $\\$S$ in his piggy bank. The first month he takes out half of his money, and the second month he adds $\\$D$. The third month he takes out half his money, and the fourth month he adds $\\$D$. This continues, every other month taking out half his money, and every other month adding $\\$D$. In t... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-7c7a80d28326c6930198e36cc771b60a0e88c9427f49a6f3901c5de299953d7b | A man has one white, two red, and three green flags. How many different signals can he make by arranging five flags one above the other? | [
"60"
] | [
"A man has one white, two red, and three green flags. How many different signals can he make by arranging five flags one above the other?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 18
} | 34 | 0 | 0 |
omr-ws-bf61dbaabc7b810a65adf9dd665cfc5e8b7ff07581e08ca246ab94084d27c0c4 | A man has six friends that he must collect money from. Each friend must give between $2$ to $7$ dollars, inclusive, using $1, 2,$ and/or $5$ dollar bills. How many different total numbers of bills could the man have after collecting all the money from his six friends? | [
"31"
] | [
"A man has six friends that he must collect money from. Each friend must give between $2$ to $7$ dollars, inclusive, using $1, 2,$ and/or $5$ dollar bills. How many different total numbers of bills could the man have after collecting all the money from his six friends?"
] | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-1d68d9959ddf4187dd2407fb6037a2647968ab4e47c112955c0175a685686a61 | A man has six partners. He had dinner with each of his partners 11 times, with every 2 of them 6 times, with every 3 of them 4 times, with every 5 of them 3 times, and with all of his partners 10 times. He also had dinner without meeting any of his partners 12 times. How many times did he have dinner in that restaurant... | [
"276"
] | [
"A man has six partners. He had dinner with each of his partners 11 times, with every 2 of them 6 times, with every 3 of them 4 times, with every 5 of them 3 times, and with all of his partners 10 times. He also had dinner without meeting any of his partners 12 times. How many times did he have dinner in that resta... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 6
} | 6 | 0 | 0 |
omr-ws-f6d485179595a3edfcb2c80e7910179af398c79dcfd6b2c9bbe2b3b9b033bfe7 | A man has sufficiently many metal bars of length $2$ and wants to construct an $n \times n$ unit net grill. He can fold up two bars at an endpoint or cut a bar into two equal pieces, but bars may not overlap or intersect. What is the minimum number of pieces he must use? | [
"n(n + 1)"
] | [
"A man has sufficiently many metal bars of length $2$ and wants to construct an $n \\times n$ unit net grill. He can fold up two bars at an endpoint or cut a bar into two equal pieces, but bars may not overlap or intersect. What is the minimum number of pieces he must use?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 14,
"genselect": 7
} | 21 | 0 | 0 |
omr-ws-6841371c54c83d44a9e240e81efab655b31ce062b8e7d496d4eb5c339bf50c25 | A man has sufficiently many metal bars of length 2 and wants to construct a grill of the shape of a $2n \times 2n$ unit net. He is allowed to fold up two bars at an endpoint or to cut a bar into two equal pieces, but two bars may not overlap or intersect. What is the minimum number of pieces he must use? | [
"2n(2n + 1)"
] | [
"A man has sufficiently many metal bars of length 2 and wants to construct a grill of the shape of a $2n \\times 2n$ unit net. He is allowed to fold up two bars at an endpoint or to cut a bar into two equal pieces, but two bars may not overlap or intersect. What is the minimum number of pieces he must use?"
] | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 13,
"genselect": 8
} | 21 | 0 | 0 |
omr-ws-577b8cfb3f91bc5843d0a639e220fabf3918af02e983bd7808b44091392374e4 | A man has three daughters. He knows that the product of their ages is 168 and that the sum of their ages is his street number. However, he cannot determine any of their ages. What are the possible ages of his oldest daughter? | [
"12 and 14"
] | [
"A man has three daughters. He knows that the product of their ages is 168 and that the sum of their ages is his street number. However, he cannot determine any of their ages. What are the possible ages of his oldest daughter?"
] | [
"aops_c5_contests_amp_programs"
] | [
"tir"
] | {
"tir": 1
} | 1 | 0 | 0 |
omr-ws-5ac8e93d3ed10b1944534998299ed5947673f2e730564802146aa305f4f2d60c | A man has three sons. The product of their ages is 36, and the sum of their ages equals the number of letters in the name of their former Dean. Additionally, the oldest son can play the guitar. Determine the ages of the three sons. | [
"2, 2, 9"
] | [
"A man has three sons. The product of their ages is 36, and the sum of their ages equals the number of letters in the name of their former Dean. Additionally, the oldest son can play the guitar. Determine the ages of the three sons."
] | [
"aops_c4_high_school_math",
"c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 10,
"tir": 31
} | 41 | 0 | 0 |
omr-ws-0befcdd71fe4aafcc8b0ed1333750f9c6cf30479d183a652be1119a5d40eee0d | A man has to take 10 steps, moving in 4 directions: left, right, forward, and backward. In how many ways can he take those 10 steps if he has to take at least one step in each direction? | [
"84"
] | [
"A man has to take 10 steps, moving in 4 directions: left, right, forward, and backward. In how many ways can he take those 10 steps if he has to take at least one step in each direction?"
] | [
"aops_c6_high_school_olympiads"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-00c16e7f2a62851a13299a75f707faf8c9f44391672f1650f5a1855d61dc822c | A man in a speed boat traveling at 50 km/h dropped his spare life jacket into a river flowing at a constant speed. Twenty minutes later, he turned back and found the jacket 3 km downstream from where he lost it. What is the speed of the river's flow? | [
"4.5 km/h"
] | [
"A man in a speed boat traveling at 50 km/h dropped his spare life jacket into a river flowing at a constant speed. Twenty minutes later, he turned back and found the jacket 3 km downstream from where he lost it. What is the speed of the river's flow?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 16
} | 32 | 0 | 0 |
omr-ws-e0172050fd3142ba1039d10bc31719ae9bc8bf2a1e9cbdcce306b2289c561016 | A man invested ₹64000 in 12% ₹60 shares quoted at a premium of ₹20. The market value of these shares rose to ₹95 when shares were sold to raise enough to get ₹57000 to invest in ₹12 shares at ₹19 which provides a dividend of 18%. So, at the end of the year, find: (i) the number of shares sold, (ii) the number of shares... | [
"(i) 600, (ii) 200, (iii) 7920, (iv) 12.375%"
] | [
"A man invested ₹64000 in 12% ₹60 shares quoted at a premium of ₹20. The market value of these shares rose to ₹95 when shares were sold to raise enough to get ₹57000 to invest in ₹12 shares at ₹19 which provides a dividend of 18%. So, at the end of the year, find:\n(i) the number of shares sold,\n(ii) the number of... | [
"aops_c4_high_school_math"
] | [
"tir"
] | {
"tir": 1
} | 1 | 0 | 0 |
omr-ws-e8cc4d45f7b125a383bf7e57f97c330080e1640189a96bdb226be9f2bc5320b0 | A man is $\frac{3}{8}$ of the way across a narrow railway bridge when he hears a train approaching at 60 miles per hour. No matter which way he runs, he can just escape being hit by the train. How fast can he run? | [
"15"
] | [
"A man is $\\frac{3}{8}$ of the way across a narrow railway bridge when he hears a train approaching at 60 miles per hour. No matter which way he runs, he can just escape being hit by the train. How fast can he run?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-b1f46bd50981542b3c1f512f7cbef29b0b73f04a3f4cdc758c53290cf0493c51 | A man is 6 miles east and 5 miles south of his home. He is also 3 miles north of a river which is 8 miles south of his home. What is the least number of miles he may travel if he must fetch water from the river and then return home? | [
"\\(\\sqrt{157}\\)"
] | [
"A man is 6 miles east and 5 miles south of his home. He is also 3 miles north of a river which is 8 miles south of his home. What is the least number of miles he may travel if he must fetch water from the river and then return home?"
] | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 28
} | 44 | 0 | 0 |
omr-ws-2cae594a61b26437ec703f1c25bbc0bb228776efe21e7bd78aa076582ae78b24 | A man is 6 miles east and 5 miles south of his home. He is also 3 miles north of a river which is 8 miles south of his home. What is the least number of miles he may travel if he must fetch water from the river, then return home? Express your answer in simplest radical form. | [
"\\sqrt{157}"
] | [
"A man is 6 miles east and 5 miles south of his home. He is also 3 miles north of a river which is 8 miles south of his home. What is the least number of miles he may travel if he must fetch water from the river, then return home? Express your answer in simplest radical form."
] | [
"aops_c5_contests_amp_programs"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-0fab9dfb441815a2dc251956671c6bde0a57d8d4cca419bccc87b4ee3fa1df65 | A man is \( x \) years old in the year \( x^2 \). Given that he was born in the 18th century, how old was he in 1776? | [
"54"
] | [
"A man is \\( x \\) years old in the year \\( x^2 \\). Given that he was born in the 18th century, how old was he in 1776?"
] | [
"aops_c5_contests_amp_programs"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 11
} | 27 | 0 | 0 |
omr-ws-b6e2cc0772179d871ab672398d2090db46f8bdf8de1e7c01220765e5ef16d6ed | A man is at an integral point on the x-axis between the origin and the point 3. He takes a unit step to the right with probability $\frac{1}{3}$ or to the left with probability $\frac{2}{3}$, unless he is at the origin, where he takes a step to the right to reach the point 1, or at the point 3, where he takes a step to... | [
"\\(\\frac{23}{54}\\)"
] | [
"A man is at an integral point on the x-axis between the origin and the point 3. He takes a unit step to the right with probability $\\frac{1}{3}$ or to the left with probability $\\frac{2}{3}$, unless he is at the origin, where he takes a step to the right to reach the point 1, or at the point 3, where he takes a ... | [
"aops_c7_college_math",
"c7_college_math"
] | [
"tir"
] | {
"tir": 15
} | 15 | 0 | 0 |
omr-ws-c60cf01c9398b2fd89e7d2ba70af3f349d145e9eda44f7ec9813d0197d517784 | A man is at one corner of a square pool. He can run at a constant rate $r$ and swim at a constant rate $s$. If he wants to move to the opposite corner of the pool, what path should he take to minimize his travel time? | [
"Run the entire way if \\( \\frac{r}{s} \\geq \\sqrt{2} \\); otherwise, the exact path is not specified."
] | [
"A man is at one corner of a square pool. He can run at a constant rate $r$ and swim at a constant rate $s$. If he wants to move to the opposite corner of the pool, what path should he take to minimize his travel time?"
] | [
"aops_c7_college_math"
] | [
"tir"
] | {
"tir": 3
} | 3 | 0 | 0 |
omr-ws-d5d01778483d9070542e8b7c3fe7f9555cf3290e5203e57d5dfec1124542d17a | A man is at the base of a tree 10 miles due south of a water well. His home is located 20 miles southeast of the tree. What is the total distance he must travel from his starting location to go the shortest distance to the water well and then the shortest distance to return home? Assume all paths are coplanar. Round to... | [
"27.98"
] | [
"A man is at the base of a tree 10 miles due south of a water well. His home is located 20 miles southeast of the tree. What is the total distance he must travel from his starting location to go the shortest distance to the water well and then the shortest distance to return home? Assume all paths are coplanar. Rou... | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-848d1ef9e941e89afbeb712359a939962a24f29a0ca3ccb6d9e8d511ca19de14 | A man is crossing a river to a point downstream on the shore in the shortest amount of time. He first crosses the river at an angle to the shores and then walks along the shore to the destination. Given the width of the river $a$, the distance downstream $b$, the distance laterally he should travel while crossing $c$, ... | [
"\\( c = \\frac{ad}{\\sqrt{e^2 - d^2}} \\)"
] | [
"A man is crossing a river to a point downstream on the shore in the shortest amount of time. He first crosses the river at an angle to the shores and then walks along the shore to the destination. Given the width of the river $a$, the distance downstream $b$, the distance laterally he should travel while crossing ... | [
"aops_c7_college_math"
] | [
"cot",
"tir"
] | {
"cot": 12,
"tir": 2
} | 14 | 0 | 0 |
omr-ws-7b7ce2d14e1353d79eb2ece1d298da321a04e39238a6dc10abd650c448656b82 | A man is in a boat 2 miles from the nearest point on the coast. He needs to go to a point Q, which is 3 miles down the coast and 1 mile inland. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach point Q in the least amount of time? | [
"1 mile below B."
] | [
"A man is in a boat 2 miles from the nearest point on the coast. He needs to go to a point Q, which is 3 miles down the coast and 1 mile inland. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach point Q in the least amount of time?"
] | [
"aops_c7_college_math"
] | [
"cot",
"genselect",
"tir"
] | {
"cot": 8,
"genselect": 3,
"tir": 16
} | 27 | 0 | 0 |
omr-ws-15aee94bc5bdf1fd865f73ef0eced37723d46c9f092e984ba62c8330b89cd07a | A man is in a boat 2 miles from the nearest point on the coast. He needs to go to a point Q, which is 3 miles down the coast and 1 mile inland. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach point Q in the least time? | [
"1"
] | [
"A man is in a boat 2 miles from the nearest point on the coast. He needs to go to a point Q, which is 3 miles down the coast and 1 mile inland. If he can row at 2 miles per hour and walk at 4 miles per hour, toward what point on the coast should he row in order to reach point Q in the least time?"
] | [
"aops_c7_college_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 16
} | 32 | 0 | 0 |
omr-ws-eb666eaf54e64564845dadc499e96cf85b7ddbd49085a04cb7d54aa2852dfdcf | A man is in a muddy field, 300 feet from the nearest point A of a straight road bordering the field. He wants to walk to a point B on the road, 600 feet away from A. He can walk at 3 feet per second in the muddy field and 5 feet per second on the road. Find the least time in which he can walk to B. | [
"\\( 20(4+3\\sqrt{3}) \\) seconds."
] | [
"A man is in a muddy field, 300 feet from the nearest point A of a straight road bordering the field. He wants to walk to a point B on the road, 600 feet away from A. He can walk at 3 feet per second in the muddy field and 5 feet per second on the road. Find the least time in which he can walk to B."
] | [
"aops_c6_high_school_olympiads"
] | [
"tir"
] | {
"tir": 1
} | 1 | 0 | 0 |
omr-ws-29b154863d129060b100697aaf84e174a8284650dc3c3c5a9977d0815f5a1af6 | A man is lost in a forest whose boundary is a straight line. The distance from the man to the forest boundary does not exceed 2 km. Find a path along which he will certainly be able to get out of the forest after walking no more than 13 km. The man does not know the direction of the forest boundary but can move along a... | [
"13"
] | [
"A man is lost in a forest whose boundary is a straight line. The distance from the man to the forest boundary does not exceed 2 km. Find a path along which he will certainly be able to get out of the forest after walking no more than 13 km. The man does not know the direction of the forest boundary but can move al... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"genselect"
] | {
"cot": 13,
"genselect": 3
} | 16 | 0 | 0 |
omr-ws-54fe881f2b6b7a9489cdaf4b3add6eb1cfcbbf1877ab112fb3743b4bd720b3ee | A man is lost in a forest whose boundary is a straight line. The distance from the man to the forest boundary does not exceed 2 km. Suggest a path along which he will certainly be able to get out of the forest after walking no more than 14 km. The man does not know the direction of the forest boundary but can move alon... | [
"14"
] | [
"A man is lost in a forest whose boundary is a straight line. The distance from the man to the forest boundary does not exceed 2 km. Suggest a path along which he will certainly be able to get out of the forest after walking no more than 14 km. The man does not know the direction of the forest boundary but can move... | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 11
} | 11 | 0 | 0 |
omr-ws-a367df9f809ce62fe555e11b5ea7e34b8557f95aaed66bcb361fbd08ee061d4a | A man is on the bank of a river that is 1 mile wide. He wants to travel to a town on the opposite bank, but 1 mile upstream. He intends to row on a straight line to some point P on the opposite bank and then walk the remaining distance along the bank. If he can walk at 5 mi/hr and row at 4 mi/hr, what is the optimal po... | [
"\\( \\frac{7}{20} \\) hrs or 21 minutes"
] | [
"A man is on the bank of a river that is 1 mile wide. He wants to travel to a town on the opposite bank, but 1 mile upstream. He intends to row on a straight line to some point P on the opposite bank and then walk the remaining distance along the bank. If he can walk at 5 mi/hr and row at 4 mi/hr, what is the optim... | [
"aops_c7_college_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-3c3e80b772ee801035d3f56f91e5bbc95dcdd29eba096026f16672ae77cbb3b0 | A man is participating in a television program where he has to complete tasks at 4 points. If he fails a task, he must return to point 1. The probabilities of success at each point are as follows: 85% at point 1, 65% at point 2, 45% at point 3, and 25% at point 4. Once he succeeds at point 4, he wins. On average, how m... | [
"42.65"
] | [
"A man is participating in a television program where he has to complete tasks at 4 points. If he fails a task, he must return to point 1. The probabilities of success at each point are as follows: 85% at point 1, 65% at point 2, 45% at point 3, and 25% at point 4. Once he succeeds at point 4, he wins. On average, ... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 29,
"tir": 24
} | 53 | 0 | 0 |
omr-ws-95bde5e873b3561e73e2bd3fa00520eca9ecfc7440b6878f3078f476a7ddaaab | A man is participating in a television program where he has to complete tasks at 4 points. The probabilities of success at each point are as follows: 85% at the first point, 65% at the second point, 45% at the third point, and 25% at the fourth point. If he fails any task, he must return to the first point. How many ta... | [
"42.65"
] | [
"A man is participating in a television program where he has to complete tasks at 4 points. The probabilities of success at each point are as follows: 85% at the first point, 65% at the second point, 45% at the third point, and 25% at the fourth point. If he fails any task, he must return to the first point. How ma... | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 22
} | 38 | 0 | 0 |
omr-ws-8ae06542c0dc73529a4a606d5ccdb750aeb1861c065a7195990fb6d6f9b9e0ad | A man is running through a train tunnel. When he is 2/5 of the way through, he hears a train approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (Assume... | [
"12 mph"
] | [
"A man is running through a train tunnel. When he is 2/5 of the way through, he hears a train approaching the tunnel from behind him at a speed of 60 mph. Whether he runs ahead or back, he will reach an end of the tunnel at the same time the train reaches that end. At what rate, in miles per hour, is he running? (A... | [
"aops_c4_high_school_math"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 2
} | 18 | 0 | 0 |
omr-ws-01eccde7811266542c4b48a83311db420edd5bfa2aff268e203936f0fe3a56ed | A man is standing at $\frac{3\pi}{2}$ radians on the southernmost edge of the outer ring (radius 4 units). He begins walking due north at $0.05$ units per second and continues walking straight. At what point on the outermost circle (in radians) will he eventually land? How long will it take him to reach that point? | [
"\\(\\frac{\\pi}{6}\\) radians, 160 seconds"
] | [
"A man is standing at $\\frac{3\\pi}{2}$ radians on the southernmost edge of the outer ring (radius 4 units). He begins walking due north at $0.05$ units per second and continues walking straight. At what point on the outermost circle (in radians) will he eventually land? How long will it take him to reach that poi... | [
"aops_c4_high_school_math"
] | [
"additional_problems"
] | {
"additional_problems": 1
} | 1 | 0 | 0 |
omr-ws-5608bb9e23c76d051e6bef83468280e6f7c485fbe4d304ca35fefcfd7e4a41e8 | A man is standing on the real number line at the number $n$. He can move to the right one unit with probability $p$ or to the left one unit with probability $1-p$. If his house is at the number $N$ ($n < N$) and there is a cliff at the number $0$, what is the probability that he will reach his house before falling off ... | [
"\\dfrac{1 - \\left( \\dfrac{1 - p}{p} \\right)^n}{1 - \\left( \\dfrac{1 - p}{p} \\right)^N}"
] | [
"A man is standing on the real number line at the number $n$. He can move to the right one unit with probability $p$ or to the left one unit with probability $1-p$. If his house is at the number $N$ ($n < N$) and there is a cliff at the number $0$, what is the probability that he will reach his house before falling... | [
"aops_c6_high_school_olympiads"
] | [
"cot"
] | {
"cot": 5
} | 5 | 0 | 0 |
omr-ws-9586107683355062182ad410144cd8737a913d9daed67523a4055f571e642191 | A man is tasked with nailing signs at 10 signposts, each a mile apart in a straight line, numbered 1 to 10. He cannot nail a sign at the same signpost twice. Determine the longest possible path he can take to nail all the signs. Hint: The most common route is 1, 10, 2, 9, 3, 8, 4, 7, 5, 6, which covers 45 miles. Anothe... | [
"49"
] | [
"A man is tasked with nailing signs at 10 signposts, each a mile apart in a straight line, numbered 1 to 10. He cannot nail a sign at the same signpost twice. Determine the longest possible path he can take to nail all the signs.\n\nHint: The most common route is 1, 10, 2, 9, 3, 8, 4, 7, 5, 6, which covers 45 miles... | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-c0b66595ba93f5f53d07fca95185e4ef0c593a9fe501b24b3c0a0aac36d4e148 | A man is walking due east at 2 m.p.h. and to him, the wind appears to be blowing from the north. On doubling his speed to 4 m.p.h. and still walking due east, the wind appears to be blowing from the northeast. What is the speed of the wind (assumed to have a constant velocity)? | [
"2\\sqrt{2}"
] | [
"A man is walking due east at 2 m.p.h. and to him, the wind appears to be blowing from the north. On doubling his speed to 4 m.p.h. and still walking due east, the wind appears to be blowing from the northeast. What is the speed of the wind (assumed to have a constant velocity)?"
] | [
"aops_c4_high_school_math"
] | [
"cot"
] | {
"cot": 16
} | 16 | 0 | 0 |
omr-ws-0d626c4920c18fc500ad2e848caaefbd1a8169a20671c5ff0388786a25815653 | A man is walking on a bridge and is $\frac{2}{5}$ of the way across when he sees a train coming at $40$ miles per hour. He realizes that if he runs towards the train, he can reach the end of the bridge just as the train reaches him. Similarly, if he runs away from the train, he can reach the other end of the bridge jus... | [
"8 miles per hour"
] | [
"A man is walking on a bridge and is $\\frac{2}{5}$ of the way across when he sees a train coming at $40$ miles per hour. He realizes that if he runs towards the train, he can reach the end of the bridge just as the train reaches him. Similarly, if he runs away from the train, he can reach the other end of the brid... | [
"aops_c6_high_school_olympiads"
] | [
"cot",
"tir"
] | {
"cot": 16,
"tir": 1
} | 17 | 0 | 0 |
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