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-prefix-sum-permutation-l6-s6 | construct | rlve_prefix_sum_permutation | prefix_sum_mod_distinct_permutation | number_theory | competition | 6 | RLVE-Gym/prefix_sum_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_24684 of the integers 1, 2, ..., 24684 such that the 24684 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_24684 are pairwise distinct modulo 24684.
Answer format: {"perm": [p_1, ..., p_24684]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"n": 24684, "family": "rlve_prefix_sum_permutation", "subset": "construct"} | null | null | null | {"perm": [24684, 1, 24682, 3, 24680, 5, 24678, 7, 24676, 9, 24674, 11, 24672, 13, 24670, 15, 24668, 17, 24666, 19, 24664, 21, 24662, 23, 24660, 25, 24658, 27, 24656, 29, 24654, 31, 24652, 33, 24650, 35, 24648, 37, 24646, 39, 24644, 41, 24642, 43, 24640, 45, 24638, 47, 24636, 49, 24634, 51, 24632, 53, 24630, 55, 24628, ... | 1 |
construct-rlve-prefix-sum-permutation-l6-s7 | construct | rlve_prefix_sum_permutation | prefix_sum_mod_distinct_permutation | number_theory | competition | 6 | RLVE-Gym/prefix_sum_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_16524 of the integers 1, 2, ..., 16524 such that the 16524 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_16524 are pairwise distinct modulo 16524.
Answer format: {"perm": [p_1, ..., p_16524]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"n": 16524, "family": "rlve_prefix_sum_permutation", "subset": "construct"} | null | null | null | {"perm": [16524, 1, 16522, 3, 16520, 5, 16518, 7, 16516, 9, 16514, 11, 16512, 13, 16510, 15, 16508, 17, 16506, 19, 16504, 21, 16502, 23, 16500, 25, 16498, 27, 16496, 29, 16494, 31, 16492, 33, 16490, 35, 16488, 37, 16486, 39, 16484, 41, 16482, 43, 16480, 45, 16478, 47, 16476, 49, 16474, 51, 16472, 53, 16470, 55, 16468, ... | 1 |
construct-rlve-prefix-sum-permutation-l6-s8 | construct | rlve_prefix_sum_permutation | prefix_sum_mod_distinct_permutation | number_theory | competition | 6 | RLVE-Gym/prefix_sum_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_10712 of the integers 1, 2, ..., 10712 such that the 10712 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_10712 are pairwise distinct modulo 10712.
Answer format: {"perm": [p_1, ..., p_10712]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"n": 10712, "family": "rlve_prefix_sum_permutation", "subset": "construct"} | null | null | null | {"perm": [10712, 1, 10710, 3, 10708, 5, 10706, 7, 10704, 9, 10702, 11, 10700, 13, 10698, 15, 10696, 17, 10694, 19, 10692, 21, 10690, 23, 10688, 25, 10686, 27, 10684, 29, 10682, 31, 10680, 33, 10678, 35, 10676, 37, 10674, 39, 10672, 41, 10670, 43, 10668, 45, 10666, 47, 10664, 49, 10662, 51, 10660, 53, 10658, 55, 10656, ... | 1 |
construct-rlve-prefix-sum-permutation-l6-s9 | construct | rlve_prefix_sum_permutation | prefix_sum_mod_distinct_permutation | number_theory | competition | 6 | RLVE-Gym/prefix_sum_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_22966 of the integers 1, 2, ..., 22966 such that the 22966 prefix sums p_1, p_1+p_2, ..., p_1+p_2+...+p_22966 are pairwise distinct modulo 22966.
Answer format: {"perm": [p_1, ..., p_22966]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdi... | {"n": 22966, "family": "rlve_prefix_sum_permutation", "subset": "construct"} | null | null | null | {"perm": [22966, 1, 22964, 3, 22962, 5, 22960, 7, 22958, 9, 22956, 11, 22954, 13, 22952, 15, 22950, 17, 22948, 19, 22946, 21, 22944, 23, 22942, 25, 22940, 27, 22938, 29, 22936, 31, 22934, 33, 22932, 35, 22930, 37, 22928, 39, 22926, 41, 22924, 43, 22922, 45, 22920, 47, 22918, 49, 22916, 51, 22914, 53, 22912, 55, 22910, ... | 1 |
construct-rlve-prime-graph-coloring-l1-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 8 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_8]} (the i-th entry is the colo... | {"n": 8, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0]} | 1 |
construct-rlve-prime-graph-coloring-l1-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 6 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 3. Give a proper colouring using only colours 0..2 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_6]} (the i-th entry is the colo... | {"n": 6, "k": 3, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 2, 2]} | 1 |
construct-rlve-prime-graph-coloring-l1-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 7 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_7]} (the i-th entry is the colo... | {"n": 7, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l1-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 11 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_11]} (the i-th entry is the co... | {"n": 11, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l1-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 5 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 3. Give a proper colouring using only colours 0..2 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_5]} (the i-th entry is the colo... | {"n": 5, "k": 3, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l1-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 12 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_12]} (the i-th entry is the co... | {"n": 12, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0]} | 1 |
construct-rlve-prime-graph-coloring-l1-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 3 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 2. Give a proper colouring using only colours 0..1 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_3]} (the i-th entry is the colo... | {"n": 3, "k": 2, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1]} | 1 |
construct-rlve-prime-graph-coloring-l1-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 4 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 2. Give a proper colouring using only colours 0..1 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_4]} (the i-th entry is the colo... | {"n": 4, "k": 2, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [0, 0, 1, 1]} | 1 |
construct-rlve-prime-graph-coloring-l1-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 10 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_10]} (the i-th entry is the co... | {"n": 10, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l1-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 1 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 9 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_9]} (the i-th entry is the colo... | {"n": 9, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1]} | 1 |
construct-rlve-prime-graph-coloring-l2-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 36 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_36]} (the i-th entry is the co... | {"n": 36, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0]} | 1 |
construct-rlve-prime-graph-coloring-l2-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 30 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_30]} (the i-th entry is the co... | {"n": 30, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l2-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 18 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_18]} (the i-th entry is the co... | {"n": 18, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l2-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 35 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_35]} (the i-th entry is the co... | {"n": 35, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l2-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 23 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_23]} (the i-th entry is the co... | {"n": 23, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l2-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 13 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_13]} (the i-th entry is the co... | {"n": 13, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1]} | 1 |
construct-rlve-prime-graph-coloring-l2-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 21 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_21]} (the i-th entry is the co... | {"n": 21, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1]} | 1 |
construct-rlve-prime-graph-coloring-l2-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 15 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_15]} (the i-th entry is the co... | {"n": 15, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l2-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 28 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_28]} (the i-th entry is the co... | {"n": 28, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0]} | 1 |
construct-rlve-prime-graph-coloring-l2-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 2 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 31 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_31]} (the i-th entry is the co... | {"n": 31, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 43 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_43]} (the i-th entry is the co... | {"n": 43, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 91 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_91]} (the i-th entry is the co... | {"n": 91, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 82 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_82]} (the i-th entry is the co... | {"n": 82, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l3-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 63 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_63]} (the i-th entry is the co... | {"n": 63, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 68 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_68]} (the i-th entry is the co... | {"n": 68, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0]} | 1 |
construct-rlve-prime-graph-coloring-l3-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 46 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_46]} (the i-th entry is the co... | {"n": 46, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l3-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 59 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_59]} (the i-th entry is the co... | {"n": 59, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 67 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_67]} (the i-th entry is the co... | {"n": 67, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]} | 1 |
construct-rlve-prime-graph-coloring-l3-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 45 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_45]} (the i-th entry is the co... | {"n": 45, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1]} | 1 |
construct-rlve-prime-graph-coloring-l3-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 3 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 42 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_42]} (the i-th entry is the co... | {"n": 42, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2]} | 1 |
construct-rlve-prime-graph-coloring-l4-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 199 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_199]} (the i-th entry is the ... | {"n": 199, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 282 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_282]} (the i-th entry is the ... | {"n": 282, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 214 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_214]} (the i-th entry is the ... | {"n": 214, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 267 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_267]} (the i-th entry is the ... | {"n": 267, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 272 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_272]} (the i-th entry is the ... | {"n": 272, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 245 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_245]} (the i-th entry is the ... | {"n": 245, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 120 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_120]} (the i-th entry is the ... | {"n": 120, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 268 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_268]} (the i-th entry is the ... | {"n": 268, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 107 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_107]} (the i-th entry is the ... | {"n": 107, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l4-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 4 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 274 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_274]} (the i-th entry is the ... | {"n": 274, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 516 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_516]} (the i-th entry is the ... | {"n": 516, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 531 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_531]} (the i-th entry is the ... | {"n": 531, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 530 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_530]} (the i-th entry is the ... | {"n": 530, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 430 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_430]} (the i-th entry is the ... | {"n": 430, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 498 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_498]} (the i-th entry is the ... | {"n": 498, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 544 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_544]} (the i-th entry is the ... | {"n": 544, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 735 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_735]} (the i-th entry is the ... | {"n": 735, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 558 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_558]} (the i-th entry is the ... | {"n": 558, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 495 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_495]} (the i-th entry is the ... | {"n": 495, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l5-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 5 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 734 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_734]} (the i-th entry is the ... | {"n": 734, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s0 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 866 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_866]} (the i-th entry is the ... | {"n": 866, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s1 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1258 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1258]} (the i-th entry is th... | {"n": 1258, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s2 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 912 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_912]} (the i-th entry is the ... | {"n": 912, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s3 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1516 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1516]} (the i-th entry is th... | {"n": 1516, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s4 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1402 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1402]} (the i-th entry is th... | {"n": 1402, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s5 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1148 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1148]} (the i-th entry is th... | {"n": 1148, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s6 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1470 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1470]} (the i-th entry is th... | {"n": 1470, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s7 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1053 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1053]} (the i-th entry is th... | {"n": 1053, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s8 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1658 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1658]} (the i-th entry is th... | {"n": 1658, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-prime-graph-coloring-l6-s9 | construct | rlve_prime_graph_coloring | prime_distance_graph_coloring | graph_theory | competition | 6 | RLVE-Gym/prime_graph_minimum_chromatic_number | MIT | [
"agentic_trivial"
] | Consider the graph on vertices 1, 2, ..., 1884 in which u and v are adjacent if and only if |u - v| is a prime number. Its chromatic number is 4. Give a proper colouring using only colours 0..3 (adjacent vertices must receive different colours).
Answer format: {"colors": [c_1, c_2, ..., c_1884]} (the i-th entry is th... | {"n": 1884, "k": 4, "family": "rlve_prime_graph_coloring", "subset": "construct"} | null | null | null | {"colors": [1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,... | 1 |
construct-rlve-recursive-sequence-sum-l1-s0 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 81 and F(n) = 1 * F(n - 1) + 15807 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 126699.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answ... | {"F0": 81, "A": 1, "B": 15807, "S": 126699, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 3, 4]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s1 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 69 and F(n) = 1 * F(n - 1) + 12991 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 130186.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answ... | {"F0": 69, "A": 1, "B": 12991, "S": 130186, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 4]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s2 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 110 and F(n) = 8 * F(n - 1) + 2247 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 27263.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answe... | {"F0": 110, "A": 8, "B": 2247, "S": 27263, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s3 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 116 and F(n) = 12 * F(n - 1) + 8992 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 10384.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answ... | {"F0": 116, "A": 12, "B": 8992, "S": 10384, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s4 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 74 and F(n) = 4 * F(n - 1) + 12677 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 348495.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answ... | {"F0": 74, "A": 4, "B": 12677, "S": 348495, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s5 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 2 and F(n) = 10 * F(n - 1) + 4625 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 51075.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer... | {"F0": 2, "A": 10, "B": 4625, "S": 51075, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s6 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 122 and F(n) = 12 * F(n - 1) + 13480 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 30474520.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/... | {"F0": 122, "A": 12, "B": 13480, "S": 30474520, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 4]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s7 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 12 and F(n) = 16 * F(n - 1) + 16232 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 279016.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/ans... | {"F0": 12, "A": 16, "B": 16232, "S": 279016, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s8 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 75 and F(n) = 16 * F(n - 1) + 367 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 434397.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answe... | {"F0": 75, "A": 16, "B": 367, "S": 434397, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3]} | 1 |
construct-rlve-recursive-sequence-sum-l1-s9 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 1 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 36 and F(n) = 12 * F(n - 1) + 959 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 17651.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer... | {"F0": 36, "A": 12, "B": 959, "S": 17651, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s0 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 13 and F(n) = 4 * F(n - 1) + 8102 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 8154.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer.... | {"F0": 13, "A": 4, "B": 8102, "S": 8154, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s1 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 95 and F(n) = 6 * F(n - 1) + 5264 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 55330174.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/ans... | {"F0": 95, "A": 6, "B": 5264, "S": 55330174, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 4, 6]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s2 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 68 and F(n) = 11 * F(n - 1) + 12781 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 26468337650.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdi... | {"F0": 68, "A": 11, "B": 12781, "S": 26468337650, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2, 4, 5, 7]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s3 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 7 and F(n) = 1 * F(n - 1) + 15292 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 152941.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answe... | {"F0": 7, "A": 1, "B": 15292, "S": 152941, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 4, 5]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s4 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 15 and F(n) = 7 * F(n - 1) + 1754 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 290116595.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/an... | {"F0": 15, "A": 7, "B": 1754, "S": 290116595, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2, 3, 4, 6, 7]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s5 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 79 and F(n) = 1 * F(n - 1) + 7874 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 31654.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer... | {"F0": 79, "A": 1, "B": 7874, "S": 31654, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 3]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s6 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 119 and F(n) = 1 * F(n - 1) + 410 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 3518.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer.... | {"F0": 119, "A": 1, "B": 410, "S": 3518, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 7]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s7 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 19 and F(n) = 10 * F(n - 1) + 9981 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 12533324317.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir... | {"F0": 19, "A": 10, "B": 9981, "S": 12533324317, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 4, 5, 6, 7]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s8 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 83 and F(n) = 7 * F(n - 1) + 11023 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 1844224573.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/... | {"F0": 83, "A": 7, "B": 11023, "S": 1844224573, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 4, 5, 6, 7]} | 1 |
construct-rlve-recursive-sequence-sum-l2-s9 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 2 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 92 and F(n) = 4 * F(n - 1) + 4128 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 22112.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answer... | {"F0": 92, "A": 4, "B": 4128, "S": 22112, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s0 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 13 and F(n) = 9 * F(n - 1) + 14282 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 63476251456707.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/work... | {"F0": 13, "A": 9, "B": 14282, "S": 63476251456707, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 5, 6, 8, 9, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s1 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 80 and F(n) = 16 * F(n - 1) + 3847 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 6289138856459747.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/wo... | {"F0": 80, "A": 16, "B": 3847, "S": 6289138856459747, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 3, 6, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s2 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 55 and F(n) = 16 * F(n - 1) + 5969 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 529130839929766.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/wor... | {"F0": 55, "A": 16, "B": 5969, "S": 529130839929766, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 4, 9, 10]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s3 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 49 and F(n) = 10 * F(n - 1) + 4169 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 56861845230554.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/work... | {"F0": 49, "A": 10, "B": 4169, "S": 56861845230554, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [4, 5, 7, 9, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s4 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 128 and F(n) = 1 * F(n - 1) + 13209 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 238146.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/ans... | {"F0": 128, "A": 1, "B": 13209, "S": 238146, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [4, 5, 9]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s5 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 107 and F(n) = 16 * F(n - 1) + 5128 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 8421046432173616.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/w... | {"F0": 107, "A": 16, "B": 5128, "S": 8421046432173616, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2, 4, 7, 9, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s6 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 24 and F(n) = 12 * F(n - 1) + 5463 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 32236431435261.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/work... | {"F0": 24, "A": 12, "B": 5463, "S": 32236431435261, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 10]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s7 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 64 and F(n) = 16 * F(n - 1) + 2036 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 3733355291160988.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/wo... | {"F0": 64, "A": 16, "B": 2036, "S": 3733355291160988, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [5, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s8 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 7 and F(n) = 15 * F(n - 1) + 1944 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 1346111077753815.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/wor... | {"F0": 7, "A": 15, "B": 1944, "S": 1346111077753815, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 4, 8, 10, 11]} | 1 |
construct-rlve-recursive-sequence-sum-l3-s9 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 3 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 14 and F(n) = 1 * F(n - 1) + 10300 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 679940.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answ... | {"F0": 14, "A": 1, "B": 10300, "S": 679940, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 3, 4, 5, 6, 7, 8, 9, 11, 12]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s0 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 31 and F(n) = 1 * F(n - 1) + 3523 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 204520.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answe... | {"F0": 31, "A": 1, "B": 3523, "S": 204520, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2, 4, 7, 11, 14, 20]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s1 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 60 and F(n) = 7 * F(n - 1) + 6050 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 1780264396922637880.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/... | {"F0": 60, "A": 7, "B": 6050, "S": 1780264396922637880, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 6, 7, 9, 15, 16, 18]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s2 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 128 and F(n) = 7 * F(n - 1) + 7023 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 15110584069633972810.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to ... | {"F0": 128, "A": 7, "B": 7023, "S": 15110584069633972810, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [3, 5, 6, 11, 14, 15, 17, 19]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s3 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 31 and F(n) = 1 * F(n - 1) + 13366 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 1951839.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/ans... | {"F0": 31, "A": 1, "B": 13366, "S": 1951839, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [2, 4, 5, 6, 8, 9, 10, 14, 15, 16, 18, 19, 20]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s4 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 47 and F(n) = 11 * F(n - 1) + 3006 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 257231235942684582725647.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON... | {"F0": 47, "A": 11, "B": 3006, "S": 257231235942684582725647, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 7, 9, 12, 13, 14, 16, 17, 18, 19, 20]} | 1 |
construct-rlve-recursive-sequence-sum-l4-s5 | construct | rlve_recursive_sequence_sum | linear_recurrence_subset_sum | number_theory | competition | 4 | RLVE-Gym/recursive_sequence_sum_construction | MIT | [
"agentic_trivial"
] | Define the sequence F by F(0) = 54 and F(n) = 1 * F(n - 1) + 1695 for every integer n >= 1.
Find a non-empty set of distinct positive indices n_1, ..., n_k (index 0 is not allowed) such that F(n_1) + ... + F(n_k) = 131001.
Answer format: {"indices": [n_1, ..., n_k]}
Write your final answer as JSON to `/workdir/answe... | {"F0": 54, "A": 1, "B": 1695, "S": 131001, "family": "rlve_recursive_sequence_sum", "subset": "construct"} | null | null | null | {"indices": [1, 2, 3, 5, 9, 11, 13, 16, 17]} | 1 |
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