task_id stringlengths 23 52 | subset stringclasses 1
value | family stringclasses 80
values | problem_key stringclasses 75
values | domain stringclasses 8
values | tier stringclasses 2
values | level stringclasses 6
values | source stringclasses 80
values | license stringclasses 3
values | tags listlengths 0 4 | prompt stringlengths 308 37k | instance stringlengths 56 37.8k | direction null | baseline null | best_known null | reference_answer stringlengths 8 198k | reference_reward float64 1 1 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
construct-rlve-antiderivative-l4-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*cos(x - sin(4))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, a... | {"f_prime": "2*cos(x - sin(4))", "max_ops": 36, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*sin(x - sin(4))"} | 1 |
construct-rlve-antiderivative-l4-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*x*log(x)*cos(x**2/3)/3 + (sin(x**2/3) + 2)/x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, ... | {"f_prime": "2*x*log(x)*cos(x**2/3)/3 + (sin(x**2/3) + 2)/x", "max_ops": 44, "max_len": 880, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "(sin(x**2/3) + 2)*log(x)"} | 1 |
construct-rlve-antiderivative-l4-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -2*x*exp(x)*sin(2*x) + x*exp(x)*cos(2*x) + exp(x)*cos(2*x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, intege... | {"f_prime": "-2*x*exp(x)*sin(2*x) + x*exp(x)*cos(2*x) + exp(x)*cos(2*x)", "max_ops": 40, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*exp(x)*cos(2*x)"} | 1 |
construct-rlve-antiderivative-l4-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 4 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -(-sin(x + 1) - 3)*sin(sin(-3*x + cos(x + 1) + 2))*cos(-3*x + cos(x + 1) + 2)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the... | {"f_prime": "-(-sin(x + 1) - 3)*sin(sin(-3*x + cos(x + 1) + 2))*cos(-3*x + cos(x + 1) + 2)", "max_ops": 48, "max_len": 1020, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(sin(-3*x + cos(x + 1) + 2))"} | 1 |
construct-rlve-antiderivative-l5-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x*cos(x)/(2*sin(x)) + x**sin(x)*(log(x)*cos(x) + sin(x)/x)/2 + log(sin(x))/2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the ... | {"f_prime": "x*cos(x)/(2*sin(x)) + x**sin(x)*(log(x)*cos(x) + sin(x)/x)/2 + log(sin(x))/2", "max_ops": 52, "max_len": 980, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*log(sin(x))/2 + x**sin(x)/2"} | 1 |
construct-rlve-antiderivative-l5-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -(x**2 - 3*x)**cos(x)*((2*x - 3)*cos(x)/(x**2 - 3*x) - log(x**2 - 3*x)*sin(x)) + 1
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only... | {"f_prime": "-(x**2 - 3*x)**cos(x)*((2*x - 3)*cos(x)/(x**2 - 3*x) - log(x**2 - 3*x)*sin(x)) + 1", "max_ops": 48, "max_len": 960, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x - (x**2 - 3*x)**cos(x) - 1"} | 1 |
construct-rlve-antiderivative-l5-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -x**(3/2) - 3*sqrt(x)*(x - 1)/2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and ... | {"f_prime": "-x**(3/2) - 3*sqrt(x)*(x - 1)/2", "max_ops": 40, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-x**(3/2)*(x - 1)"} | 1 |
construct-rlve-antiderivative-l5-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 144*sin(4*x - 4)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, an... | {"f_prime": "144*sin(4*x - 4)", "max_ops": 40, "max_len": 720, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-36*cos(4*x - 4)"} | 1 |
construct-rlve-antiderivative-l5-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x**(1/3)*(-12*x**11 - cos(x)*cos(sin(x)))*exp(-x**12 - sin(sin(x))) + exp(-x**12 - sin(sin(x)))/(3*x**(2/3))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string ... | {"f_prime": "x**(1/3)*(-12*x**11 - cos(x)*cos(sin(x)))*exp(-x**12 - sin(sin(x))) + exp(-x**12 - sin(sin(x)))/(3*x**(2/3))", "max_ops": 56, "max_len": 1080, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**(1/3)*exp(-x**12 - sin(sin(x)))"} | 1 |
construct-rlve-antiderivative-l5-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (-x**2*cos(x)/sin(x)**2 + 2*x/sin(x))*cos(x**2/sin(x))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer li... | {"f_prime": "(-x**2*cos(x)/sin(x)**2 + 2*x/sin(x))*cos(x**2/sin(x))", "max_ops": 36, "max_len": 720, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "sin(x**2/sin(x))"} | 1 |
construct-rlve-antiderivative-l5-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -7 + 3*sqrt(x**2)/x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses,... | {"f_prime": "-7 + 3*sqrt(x**2)/x", "max_ops": 48, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-7*x + 3*sqrt(x**2) + 6"} | 1 |
construct-rlve-antiderivative-l5-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -3*x*(4*x*cos(x)/3 + 4*sin(x)/3)*sin(4*x*sin(x)/3)*cos(4*x*sin(x)/3)**2 + cos(4*x*sin(x)/3)**3
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy synta... | {"f_prime": "-3*x*(4*x*cos(x)/3 + 4*sin(x)/3)*sin(4*x*sin(x)/3)*cos(4*x*sin(x)/3)**2 + cos(4*x*sin(x)/3)**3", "max_ops": 48, "max_len": 840, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*cos(4*x*sin(x)/3)**3"} | 1 |
construct-rlve-antiderivative-l5-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*x**3*sin(x)/(log(cos(x))**2*cos(x)) + 6*x**2/log(cos(x))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, intege... | {"f_prime": "2*x**3*sin(x)/(log(cos(x))**2*cos(x)) + 6*x**2/log(cos(x))", "max_ops": 40, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*x**3/log(cos(x))"} | 1 |
construct-rlve-antiderivative-l5-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 5 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = log(x)*sin(x)*sin(2*x)/cos(x)**2 + 2*log(x)*cos(2*x)/cos(x) + sin(2*x)/(x*cos(x))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only:... | {"f_prime": "log(x)*sin(x)*sin(2*x)/cos(x)**2 + 2*log(x)*cos(2*x)/cos(x) + sin(2*x)/(x*cos(x))", "max_ops": 48, "max_len": 920, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "log(x)*sin(2*x)/cos(x) + 1"} | 1 |
construct-rlve-antiderivative-l6-s0 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -(2*x*(2*x**x*(log(x) + 1) + 6) + 12*x + 4*x**x - 8)*sin(2*x*(6*x + 2*x**x - 4))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: ... | {"f_prime": "-(2*x*(2*x**x*(log(x) + 1) + 6) + 12*x + 4*x**x - 8)*sin(2*x*(6*x + 2*x**x - 4))", "max_ops": 52, "max_len": 940, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(2*x*(6*x + 2*x**x - 4))"} | 1 |
construct-rlve-antiderivative-l6-s1 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = x*(20 - 36*x)*sin((2 - 18*x)*(x - 1))*sin(sin(cos((2 - 18*x)*(x - 1))))*cos(cos((2 - 18*x)*(x - 1))) + cos(sin(cos((2 - 18*x)*(x - 1))))
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is acc... | {"f_prime": "x*(20 - 36*x)*sin((2 - 18*x)*(x - 1))*sin(sin(cos((2 - 18*x)*(x - 1))))*cos(cos((2 - 18*x)*(x - 1))) + cos(sin(cos((2 - 18*x)*(x - 1))))", "max_ops": 52, "max_len": 1100, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x*cos(sin(cos((2 - 18*x)*(x - 1))))"} | 1 |
construct-rlve-antiderivative-l6-s2 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 3*x**2 - 1
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the ... | {"f_prime": "3*x**2 - 1", "max_ops": 32, "max_len": 640, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "x**3 - x - 1"} | 1 |
construct-rlve-antiderivative-l6-s3 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*(sqrt(2)*sqrt(x)/8)**x*(log(sqrt(2)*sqrt(x)/8) + 1/2)/3
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer... | {"f_prime": "2*(sqrt(2)*sqrt(x)/8)**x*(log(sqrt(2)*sqrt(x)/8) + 1/2)/3", "max_ops": 64, "max_len": 1040, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*(sqrt(2)*sqrt(x)/8)**x/3 + 8/3"} | 1 |
construct-rlve-antiderivative-l6-s4 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -4*(x**2/2 + x*(x + 1))*sin(x**2*(x + 1)/2)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + -... | {"f_prime": "-4*(x**2/2 + x*(x + 1))*sin(x**2*(x + 1)/2)", "max_ops": 44, "max_len": 820, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "4*cos(x**2*(x + 1)/2)"} | 1 |
construct-rlve-antiderivative-l6-s5 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = (8 - 4*cos(3*x))*log(x)*cos(x) + 12*log(x)*sin(x)*sin(3*x) - 1/2 + (8 - 4*cos(3*x))*sin(x)/x
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax ... | {"f_prime": "(8 - 4*cos(3*x))*log(x)*cos(x) + 12*log(x)*sin(x)*sin(3*x) - 1/2 + (8 - 4*cos(3*x))*sin(x)/x", "max_ops": 60, "max_len": 1140, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-x/2 + (8 - 4*cos(3*x))*log(x)*sin(x)"} | 1 |
construct-rlve-antiderivative-l6-s6 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -2*sin(x - 1/3)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and... | {"f_prime": "-2*sin(x - 1/3)", "max_ops": 40, "max_len": 760, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*cos(x - 1/3) - 1"} | 1 |
construct-rlve-antiderivative-l6-s7 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2 + (2 - 4*E)*exp(-x)/4
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parenthe... | {"f_prime": "2 + (2 - 4*E)*exp(-x)/4", "max_ops": 52, "max_len": 900, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "2*x - (2 - 4*E)*exp(-x)/4"} | 1 |
construct-rlve-antiderivative-l6-s8 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = 2*cos(2*x)/3 - 2
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, an... | {"f_prime": "2*cos(2*x)/3 - 2", "max_ops": 48, "max_len": 860, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "-2*x + sin(2*x)/3 - 4/3"} | 1 |
construct-rlve-antiderivative-l6-s9 | construct | rlve_antiderivative | symbolic_antiderivative | analysis | competition | 6 | RLVE-Gym/integral | MIT | [] | Find an antiderivative F(x) of
f(x) = -(18*x - 6)*sin(9*x**2 - 6*x)
(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and pa... | {"f_prime": "-(18*x - 6)*sin(9*x**2 - 6*x)", "max_ops": 40, "max_len": 740, "family": "rlve_antiderivative", "subset": "construct"} | null | null | null | {"F": "cos(9*x**2 - 6*x)"} | 1 |
construct-rlve-bezout-identity-l1-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-19, 19] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 19.
(19 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `... | {"A": [-19, 19], "target": 19, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 1]} | 1 |
construct-rlve-bezout-identity-l1-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [2, -28] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `/wo... | {"A": [2, -28], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [1, 0]} | 1 |
construct-rlve-bezout-identity-l1-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [26, 13] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 13.
(13 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `/... | {"A": [26, 13], "target": 13, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 1]} | 1 |
construct-rlve-bezout-identity-l1-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [4, 6] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `/work... | {"A": [4, 6], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-1, 1]} | 1 |
construct-rlve-bezout-identity-l1-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-7, -7] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 7.
(7 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `/wo... | {"A": [-7, -7], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, -1]} | 1 |
construct-rlve-bezout-identity-l1-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [10, 10] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 10.
(10 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `/... | {"A": [10, 10], "target": 10, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 1]} | 1 |
construct-rlve-bezout-identity-l1-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-31, 31] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 31.
(31 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `... | {"A": [-31, 31], "target": 31, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 1]} | 1 |
construct-rlve-bezout-identity-l1-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-22, 11] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 11.
(11 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to `... | {"A": [-22, 11], "target": 11, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 1]} | 1 |
construct-rlve-bezout-identity-l1-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-22, -22] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 22.
(22 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to ... | {"A": [-22, -22], "target": 22, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, -1]} | 1 |
construct-rlve-bezout-identity-l1-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 1 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 2 nonzero integers A = [-29, -29] (A[0], ..., A[1]).
Find integers X[0], ..., X[1] (any sign, any size) such that
S = A[0]*X[0] + ... + A[1]*X[1] = 29.
(29 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_1]} (a JSON list of 2 integers)
Write your final answer as JSON to ... | {"A": [-29, -29], "target": 29, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, -1]} | 1 |
construct-rlve-bezout-identity-l2-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [74, -96, -32, 118] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as J... | {"A": [74, -96, -32, 118], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [13, 10, 0, 0]} | 1 |
construct-rlve-bezout-identity-l2-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [72, 96, -108, 96] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 12.
(12 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as ... | {"A": [72, 96, -108, 96], "target": 12, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [4, -4, -1, 0]} | 1 |
construct-rlve-bezout-identity-l2-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [42, 105, 42, 119] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 7.
(7 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JS... | {"A": [42, 105, 42, 119], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-12, 6, 0, -1]} | 1 |
construct-rlve-bezout-identity-l2-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [128, 46, -70, 96] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JS... | {"A": [128, 46, -70, 96], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [9, -25, 0, 0]} | 1 |
construct-rlve-bezout-identity-l2-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [3, -102, 105, 9] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JSO... | {"A": [3, -102, 105, 9], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [1, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l2-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [-25, -120, -65, -100] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 5.
(5 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer a... | {"A": [-25, -120, -65, -100], "target": 5, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-5, 1, 0, 0]} | 1 |
construct-rlve-bezout-identity-l2-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [-128, -66, -10, -4] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as ... | {"A": [-128, -66, -10, -4], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [16, -31, 0, -1]} | 1 |
construct-rlve-bezout-identity-l2-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [-4, -16, -42, 24] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JS... | {"A": [-4, -16, -42, 24], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [10, 0, -1, 0]} | 1 |
construct-rlve-bezout-identity-l2-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [124, -4, 42, -24] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JS... | {"A": [124, -4, 42, -24], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 10, 1, 0]} | 1 |
construct-rlve-bezout-identity-l2-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 2 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 4 nonzero integers A = [66, 99, -123, 45] (A[0], ..., A[3]).
Find integers X[0], ..., X[3] (any sign, any size) such that
S = A[0]*X[0] + ... + A[3]*X[3] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_3]} (a JSON list of 4 integers)
Write your final answer as JS... | {"A": [66, 99, -123, 45], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-15, 15, 4, 0]} | 1 |
construct-rlve-bezout-identity-l3-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [400, 182, 190, -65, 286, -385] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 1.
(1 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your final... | {"A": [400, 182, 190, -65, 286, -385], "target": 1, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [160, -352, 0, -1, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [138, 128, 220, -422, 184, 370] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your final... | {"A": [138, 128, 220, -422, 184, 370], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [13, -14, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [-18, -51, -393, 177, 147, -378] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your fina... | {"A": [-18, -51, -393, 177, 147, -378], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-3, 1, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [346, 118, -2, -428, 222, -418] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your final... | {"A": [346, 118, -2, -428, 222, -418], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 0, -1, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [-206, -254, -480, -280, 208, 402] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your fi... | {"A": [-206, -254, -480, -280, 208, 402], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-37, 30, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [4, 418, -296, 402, -316, -302] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your final... | {"A": [4, 418, -296, 402, -316, -302], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-104, 1, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [411, -150, -222, 267, 468, 312] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your fina... | {"A": [411, -150, -222, 267, 468, 312], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [23, 63, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [-478, 390, -308, -226, -464, -282] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your f... | {"A": [-478, 390, -308, -226, -464, -282], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [31, 38, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [-469, -105, -322, 427, -462, 196] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 7.
(7 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your fi... | {"A": [-469, -105, -322, 427, -462, 196], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [2, -9, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l3-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 3 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 6 nonzero integers A = [-312, -192, 321, 336, -504, 39] (A[0], ..., A[5]).
Find integers X[0], ..., X[5] (any sign, any size) such that
S = A[0]*X[0] + ... + A[5]*X[5] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_5]} (a JSON list of 6 integers)
Write your fina... | {"A": [-312, -192, 321, 336, -504, 39], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-120, 200, 3, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [-1846, -1207, 1349, 1136, 284, -923, 71, -994] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 71.
(71 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)... | {"A": [-1846, -1207, 1349, 1136, 284, -923, 71, -994], "target": 71, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 0, 0, 0, 0, 0, 1, 0]} | 1 |
construct-rlve-bezout-identity-l4-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [20, 2010, -1060, -512, 1922, -1204, -1774, 1450] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)... | {"A": [20, 2010, -1060, -512, 1922, -1204, -1774, 1450], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [5100, -51, 0, -1, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [505, -1919, 950, -1520, -2020, -1919, -606, 202] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 1.
(1 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)... | {"A": [505, -1919, 950, -1520, -2020, -1919, -606, 202], "target": 1, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [1204, 301, -32, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [272, -588, 234, -202, 1586, -1768, 1696, -694] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)
... | {"A": [272, -588, 234, -202, 1586, -1768, 1696, -694], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [3886, 1798, 1, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [1046, 1569, -1046, 1046, -1046, -523, 450, 1569] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 1.
(1 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)... | {"A": [1046, 1569, -1046, 1046, -1046, -523, 450, 1569], "target": 1, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 0, 0, 0, 0, -37, -43, 0]} | 1 |
construct-rlve-bezout-identity-l4-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [448, 1602, -348, -140, 1504, 884, 1034, 2] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)
Writ... | {"A": [448, 1602, -348, -140, 1504, 884, 1034, 2], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [0, 0, 0, 0, 0, 0, 0, 1]} | 1 |
construct-rlve-bezout-identity-l4-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [1704, -639, -1846, -1491, -1136, 994, 1207, -1633] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 71.
(71 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integ... | {"A": [1704, -639, -1846, -1491, -1136, 994, 1207, -1633], "target": 71, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-9, -27, 1, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [-1830, -292, 864, -1288, -1900, -604, -1034, -266] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integer... | {"A": [-1830, -292, 864, -1288, -1900, -604, -1034, -266], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-15, 94, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [1178, 1650, 1340, -388, 1148, -146, -1374, -570] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 integers)... | {"A": [1178, 1650, 1340, -388, 1148, -146, -1374, -570], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [409, -292, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l4-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 4 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 8 nonzero integers A = [-1276, -1954, 1004, -1346, -1690, -1552, 20, -1054] (A[0], ..., A[7]).
Find integers X[0], ..., X[7] (any sign, any size) such that
S = A[0]*X[0] + ... + A[7]*X[7] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_7]} (a JSON list of 8 intege... | {"A": [-1276, -1954, 1004, -1346, -1690, -1552, 20, -1054], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-464, 303, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [7820, 2512, -7314, -3611, 7958, -2990, -4186, 5014, 6486, -2070] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 1.
(1 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON li... | {"A": [7820, 2512, -7314, -3611, 7958, -2990, -4186, 5014, 6486, -2070], "target": 1, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [379447100, -1181235320, 1805, -1, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [2742, -6432, 630, -3748, -4536, -918, -5086, 6414, 7962, -782] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON list... | {"A": [2742, -6432, 630, -3748, -4536, -918, -5086, 6414, 7962, -782], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [275625, 117500, 0, 1, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [6246, -5421, 5973, -1911, -1944, 6735, 7326, -1305, 408, -444] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON list... | {"A": [6246, -5421, 5973, -1911, -1944, 6735, 7326, -1305, 408, -444], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [46, 53, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [-7175, -2795, 2450, -3900, 1330, -1425, 1729, 2375, -3990, -7020] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 1.
(1 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON l... | {"A": [-7175, -2795, 2450, -3900, 1330, -1425, 1729, 2375, -3990, -7020], "target": 1, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-56744, 145666, 0, 0, 0, 0, -1, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [1368, -1347, -7869, -1767, -1335, -4563, -4488, 5508, 7803, 3348] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON l... | {"A": [1368, -1347, -7869, -1767, -1335, -4563, -4488, 5508, 7803, 3348], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-64, -65, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [-4625, 3800, 5765, -960, 15, -4540, -2205, 5725, 8050, -7925] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 5.
(5 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON list ... | {"A": [-4625, 3800, 5765, -960, 15, -4540, -2205, 5725, 8050, -7925], "target": 5, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-10603, -12908, 2, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [5244, -5236, 7566, 8068, 7902, -1058, 5118, 4292, -1614, -214] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON list... | {"A": [5244, -5236, 7566, 8068, 7902, -1058, 5118, 4292, -1614, -214], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [1236714, 1238605, 1, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [-8177, 680, -7208, -3145, 85, 3519, 7157, 1734, -4369, -3689] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 17.
(17 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON lis... | {"A": [-8177, 680, -7208, -3145, 85, 3519, 7157, 1734, -4369, -3689], "target": 17, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-1, -12, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [-4674, -6156, 1977, -4527, 3039, -5499, 5103, 1266, 3225, 1719] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 3.
(3 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON lis... | {"A": [-4674, -6156, 1977, -4527, 3039, -5499, 5103, 1266, 3225, 1719], "target": 3, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-1300, 988, 3, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l5-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 5 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 10 nonzero integers A = [-8108, -5536, 5622, -412, -4698, -6226, -3468, -6662, 4436, -1202] (A[0], ..., A[9]).
Find integers X[0], ..., X[9] (any sign, any size) such that
S = A[0]*X[0] + ... + A[9]*X[9] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, ..., X_9]} (a JSON ... | {"A": [-8108, -5536, 5622, -412, -4698, -6226, -3468, -6662, 4436, -1202], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [813495, -1191440, 1, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s0 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [18004, -28890, -13270, -18442, -15464, 31360, 4466, -4056, 29088, 2734, 15212, 17142] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_... | {"A": [18004, -28890, -13270, -18442, -15464, 31360, 4466, -4056, 29088, 2734, 15212, 17142], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [4838, 3015, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s1 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [-31641, 32489, 3127, 14946, -1643, -23161, 27825, 18391, -17543, -31906, -10176, -21730] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 53.
(53 is the smallest positive value S can take.)
Answer format: {"X"... | {"A": [-31641, 32489, 3127, 14946, -1643, -23161, 27825, 18391, -17543, -31906, -10176, -21730], "target": 53, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [115, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s2 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [22225, 9884, -28021, 20027, 6314, -15148, 11403, -22351, -2660, 19040, 13755, -25613] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 7.
(7 is the smallest positive value S can take.)
Answer format: {"X": [X_... | {"A": [22225, 9884, -28021, 20027, 6314, -15148, 11403, -22351, -2660, 19040, 13755, -25613], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-177, 398, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s3 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [25112, 18022, -25110, 21082, 11580, -25860, -13642, -924, 10358, 11718, 17014, 21086] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_... | {"A": [25112, 18022, -25110, 21082, 11580, -25860, -13642, -924, 10358, 11718, 17014, 21086], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-1426, 1987, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s4 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [11270, 15911, 10549, -2114, -4830, 32165, 5047, -28581, 31801, -7742, 7651, -13741] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 7.
(7 is the smallest positive value S can take.)
Answer format: {"X": [X_0,... | {"A": [11270, 15911, 10549, -2114, -4830, 32165, 5047, -28581, 31801, -7742, 7651, -13741], "target": 7, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-24, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s5 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [90, -30434, -858, -8804, -15114, 20198, 18568, 7604, -11974, -1562, -9286, -1772] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0, .... | {"A": [90, -30434, -858, -8804, -15114, 20198, 18568, 7604, -11974, -1562, -9286, -1772], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-4396, -13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s6 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [-6324, -28806, 26008, 11980, -30996, 5070, 5312, 3830, -27626, -31986, -8584, 6344] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0,... | {"A": [-6324, -28806, 26008, 11980, -30996, 5070, 5312, 3830, -27626, -31986, -8584, 6344], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [4126920, -906015, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s7 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [-16307, 21091, 138, -13179, -23598, -18676, 2829, 29969, 5957, 15065, -25921, -4899] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 23.
(23 is the smallest positive value S can take.)
Answer format: {"X": [X... | {"A": [-16307, 21091, 138, -13179, -23598, -18676, 2829, 29969, 5957, 15065, -25921, -4899], "target": 23, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-410, -317, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s8 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [30144, -20344, -4656, -4710, -23402, -9730, 17630, 27784, 11382, 4532, -29184, 2198] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0... | {"A": [30144, -20344, -4656, -4710, -23402, -9730, 17630, 27784, 11382, 4532, -29184, 2198], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [-467077, -692075, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-bezout-identity-l6-s9 | construct | rlve_bezout_identity | bezout_coefficients | number_theory | competition | 6 | RLVE-Gym/bezout_identity | MIT | [
"agentic_trivial"
] | You are given 12 nonzero integers A = [3396, -23268, 6122, 2866, -16970, -1924, -31354, 31672, -8478, 14886, 2974, -30864] (A[0], ..., A[11]).
Find integers X[0], ..., X[11] (any sign, any size) such that
S = A[0]*X[0] + ... + A[11]*X[11] = 2.
(2 is the smallest positive value S can take.)
Answer format: {"X": [X_0,... | {"A": [3396, -23268, 6122, 2866, -16970, -1924, -31354, 31672, -8478, 14886, 2974, -30864], "target": 2, "family": "rlve_bezout_identity", "subset": "construct"} | null | null | null | {"X": [447270, 65280, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]} | 1 |
construct-rlve-construct-hack-interval-l1-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 520 (that is, 10 * 52) such that
f(L) + f(L+1) + ... + f(R) is divisible by 52.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 52, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 13} | 1 |
construct-rlve-construct-hack-interval-l1-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 180 (that is, 10 * 18) such that
f(L) + f(L+1) + ... + f(R) is divisible by 18.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 18, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 6} | 1 |
construct-rlve-construct-hack-interval-l1-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 770 (that is, 10 * 77) such that
f(L) + f(L+1) + ... + f(R) is divisible by 77.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 77, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 8, "R": 21} | 1 |
construct-rlve-construct-hack-interval-l1-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 270 (that is, 10 * 27) such that
f(L) + f(L+1) + ... + f(R) is divisible by 27.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 27, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 2, "R": 7} | 1 |
construct-rlve-construct-hack-interval-l1-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 370 (that is, 10 * 37) such that
f(L) + f(L+1) + ... + f(R) is divisible by 37.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 37, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 9, "R": 16} | 1 |
construct-rlve-construct-hack-interval-l1-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 310 (that is, 10 * 31) such that
f(L) + f(L+1) + ... + f(R) is divisible by 31.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 31, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 6, "R": 10} | 1 |
construct-rlve-construct-hack-interval-l1-s6 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 450 (that is, 10 * 45) such that
f(L) + f(L+1) + ... + f(R) is divisible by 45.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 45, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 1, "R": 9} | 1 |
construct-rlve-construct-hack-interval-l1-s7 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 300 (that is, 10 * 30) such that
f(L) + f(L+1) + ... + f(R) is divisible by 30.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 30, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 4, "R": 8} | 1 |
construct-rlve-construct-hack-interval-l1-s8 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 660 (that is, 10 * 66) such that
f(L) + f(L+1) + ... + f(R) is divisible by 66.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 66, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 1, "R": 15} | 1 |
construct-rlve-construct-hack-interval-l1-s9 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 1 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 630 (that is, 10 * 63) such that
f(L) + f(L+1) + ... + f(R) is divisible by 63.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance dat... | {"mod": 63, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 15} | 1 |
construct-rlve-construct-hack-interval-l2-s0 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 41000 (that is, 10 * 4100) such that
f(L) + f(L+1) + ... + f(R) is divisible by 4100.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 4100, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 20, "R": 399} | 1 |
construct-rlve-construct-hack-interval-l2-s1 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 7990 (that is, 10 * 799) such that
f(L) + f(L+1) + ... + f(R) is divisible by 799.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instance ... | {"mod": 799, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 7, "R": 94} | 1 |
construct-rlve-construct-hack-interval-l2-s2 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 38570 (that is, 10 * 3857) such that
f(L) + f(L+1) + ... + f(R) is divisible by 3857.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 3857, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 11, "R": 381} | 1 |
construct-rlve-construct-hack-interval-l2-s3 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 24580 (that is, 10 * 2458) such that
f(L) + f(L+1) + ... + f(R) is divisible by 2458.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 2458, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 10, "R": 265} | 1 |
construct-rlve-construct-hack-interval-l2-s4 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 21900 (that is, 10 * 2190) such that
f(L) + f(L+1) + ... + f(R) is divisible by 2190.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 2190, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 237} | 1 |
construct-rlve-construct-hack-interval-l2-s5 | construct | rlve_construct_hack_interval | cf468c_hack_interval | number_theory | competition | 2 | RLVE-Gym/construct_hack_interval | MIT | [] | Let f(x) be the sum of the decimal digits of x (e.g. f(1234) = 10). Construct integers L and R with 1 <= L <= R <= 32520 (that is, 10 * 3252) such that
f(L) + f(L+1) + ... + f(R) is divisible by 3252.
Answer format: {"L": <integer>, "R": <integer>}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"mod": 3252, "family": "rlve_construct_hack_interval", "subset": "construct"} | null | null | null | {"L": 3, "R": 329} | 1 |
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