task_id stringclasses 8
values | seed int64 0 19 | question stringlengths 49 186 | answer stringlengths 1 8 |
|---|---|---|---|
sequences-hard | 0 | A sequence starts with a(1) = 1 and a(2) = 3, and for n >= 3, a(n) = 2*a(n-1) + 2*a(n-2). What is a(14)? | 508992 |
sequences-hard | 1 | A sequence starts with a(1) = 3 and a(2) = 1, and for n >= 3, a(n) = 1*a(n-1) - 2*a(n-2). What is a(13)? | -93 |
sequences-hard | 2 | A sequence starts with a(1) = 1 and a(2) = 3, and for n >= 3, a(n) = 1*a(n-1) - 2*a(n-2). What is a(11)? | 1 |
sequences-hard | 3 | A sequence starts with a(1) = 3 and a(2) = 5, and for n >= 3, a(n) = 1*a(n-1) - 1*a(n-2). What is a(13)? | 3 |
sequences-hard | 4 | A sequence starts with a(1) = 1 and a(2) = 6, and for n >= 3, a(n) = 1*a(n-1) + 1*a(n-2). What is a(13)? | 953 |
sequences-hard | 5 | A sequence starts with a(1) = 3 and a(2) = 7, and for n >= 3, a(n) = 3*a(n-1) + 1*a(n-2). What is a(14)? | 12205087 |
sequences-hard | 6 | A sequence starts with a(1) = 4 and a(2) = 7, and for n >= 3, a(n) = 3*a(n-1) - 2*a(n-2). What is a(12)? | 6145 |
sequences-hard | 7 | A sequence starts with a(1) = 4 and a(2) = 6, and for n >= 3, a(n) = 2*a(n-1) - 1*a(n-2). What is a(10)? | 22 |
sequences-hard | 8 | A sequence starts with a(1) = 4 and a(2) = 2, and for n >= 3, a(n) = 1*a(n-1) + 1*a(n-2). What is a(11)? | 246 |
sequences-hard | 9 | A sequence starts with a(1) = 3 and a(2) = 2, and for n >= 3, a(n) = 2*a(n-1) + 1*a(n-2). What is a(11)? | 7711 |
sequences-hard | 10 | A sequence starts with a(1) = 4 and a(2) = 4, and for n >= 3, a(n) = 3*a(n-1) - 2*a(n-2). What is a(14)? | 4 |
sequences-hard | 11 | A sequence starts with a(1) = 4 and a(2) = 5, and for n >= 3, a(n) = 2*a(n-1) + 2*a(n-2). What is a(14)? | 1081280 |
sequences-hard | 12 | A sequence starts with a(1) = 5 and a(2) = 6, and for n >= 3, a(n) = 2*a(n-1) + 1*a(n-2). What is a(12)? | 46336 |
sequences-hard | 13 | A sequence starts with a(1) = 2 and a(2) = 6, and for n >= 3, a(n) = 2*a(n-1) + 1*a(n-2). What is a(11)? | 16238 |
sequences-hard | 14 | A sequence starts with a(1) = 3 and a(2) = 6, and for n >= 3, a(n) = 1*a(n-1) - 1*a(n-2). What is a(12)? | -3 |
sequences-hard | 15 | A sequence starts with a(1) = 5 and a(2) = 6, and for n >= 3, a(n) = 1*a(n-1) - 2*a(n-2). What is a(10)? | -72 |
sequences-hard | 16 | A sequence starts with a(1) = 4 and a(2) = 3, and for n >= 3, a(n) = 2*a(n-1) + 2*a(n-2). What is a(13)? | 295936 |
sequences-hard | 17 | A sequence starts with a(1) = 3 and a(2) = 3, and for n >= 3, a(n) = 3*a(n-1) + 2*a(n-2). What is a(12)? | 1328883 |
sequences-hard | 18 | A sequence starts with a(1) = 4 and a(2) = 3, and for n >= 3, a(n) = 1*a(n-1) - 2*a(n-2). What is a(11)? | 103 |
sequences-hard | 19 | A sequence starts with a(1) = 5 and a(2) = 1, and for n >= 3, a(n) = 3*a(n-1) - 2*a(n-2). What is a(14)? | -32759 |
probability-medium | 0 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 10? Give a reduced fraction. | 1/6 |
probability-medium | 1 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 2 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 10? Give a reduced fraction. | 1/6 |
probability-medium | 3 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 4 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 5 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 8? Give a reduced fraction. | 5/12 |
probability-medium | 6 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 10? Give a reduced fraction. | 1/6 |
probability-medium | 7 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 6? Give a reduced fraction. | 13/18 |
probability-medium | 8 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 9 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 7? Give a reduced fraction. | 7/12 |
probability-medium | 10 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 8? Give a reduced fraction. | 5/12 |
probability-medium | 11 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 7? Give a reduced fraction. | 7/12 |
probability-medium | 12 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 7? Give a reduced fraction. | 7/12 |
probability-medium | 13 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 6? Give a reduced fraction. | 13/18 |
probability-medium | 14 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 4? Give a reduced fraction. | 11/12 |
probability-medium | 15 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 16 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 6? Give a reduced fraction. | 13/18 |
probability-medium | 17 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 8? Give a reduced fraction. | 5/12 |
probability-medium | 18 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 5? Give a reduced fraction. | 5/6 |
probability-medium | 19 | Two fair six-sided dice are rolled. What is the probability that the sum is at least 9? Give a reduced fraction. | 5/18 |
probability-hard | 0 | A bag has 8 red, 5 blue and 8 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 32/133 |
probability-hard | 1 | A bag has 3 red, 6 blue and 8 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 18/85 |
probability-hard | 2 | A bag has 8 red, 8 blue and 2 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 8/51 |
probability-hard | 3 | A bag has 3 red, 6 blue and 6 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 108/455 |
probability-hard | 4 | A bag has 3 red, 4 blue and 2 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 2/7 |
probability-hard | 5 | A bag has 6 red, 4 blue and 7 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 21/85 |
probability-hard | 6 | A bag has 8 red, 6 blue and 8 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 96/385 |
probability-hard | 7 | A bag has 4 red, 3 blue and 5 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 3/11 |
probability-hard | 8 | A bag has 3 red, 4 blue and 5 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 3/11 |
probability-hard | 9 | A bag has 5 red, 6 blue and 4 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 24/91 |
probability-hard | 10 | A bag has 6 red, 2 blue and 5 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 30/143 |
probability-hard | 11 | A bag has 5 red, 8 blue and 6 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 80/323 |
probability-hard | 12 | A bag has 5 red, 4 blue and 7 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 1/4 |
probability-hard | 13 | A bag has 4 red, 4 blue and 7 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 16/65 |
probability-hard | 14 | A bag has 2 red, 6 blue and 7 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 12/65 |
probability-hard | 15 | A bag has 3 red, 2 blue and 6 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 12/55 |
probability-hard | 16 | A bag has 4 red, 5 blue and 5 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 25/91 |
probability-hard | 17 | A bag has 6 red, 5 blue and 8 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 80/323 |
probability-hard | 18 | A bag has 3 red, 2 blue and 7 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 21/110 |
probability-hard | 19 | A bag has 7 red, 2 blue and 8 green marbles. Three marbles are drawn at random without replacement. What is the probability that all three are different colours? Give a reduced fraction. | 14/85 |
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