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-polynomial-integer-roots-l4-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (33949238400)*x^0 + (-14402707200)*x^1 + (-1205414136)*x^2 + (1301471388)*x^3 + (-96715566)*x^4 + (-36882099)*x^5 + (5735409)*x^6 + (245353)*x^7 + (-95735)*x^8 + (3799)*x^9 + (427)*x^10 + (-41)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12... | {"coeffs": [33949238400, -14402707200, -1205414136, 1301471388, -96715566, -36882099, 5735409, 245353, -95735, 3799, 427, -41, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-9, -7, -6, -5, 5, 6, 6, 7, 9, 11, 12, 12]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-3870720000)*x^0 + (-1778688000)*x^1 + (628339200)*x^2 + (272110720)*x^3 + (-31070816)*x^4 + (-15547528)*x^5 + (364316)*x^6 + (401010)*x^7 + (9711)*x^8 + (-4426)*x^9 + (-220)*x^10 + (16)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not ... | {"coeffs": [-3870720000, -1778688000, 628339200, 272110720, -31070816, -15547528, 364316, 401010, 9711, -4426, -220, 16, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-12, -10, -8, -7, -6, -5, -2, 4, 5, 5, 8, 12]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (1128960000)*x^0 + (-162624000)*x^1 + (-1231740800)*x^2 + (174284640)*x^3 + (106063912)*x^4 + (-11936684)*x^5 + (-3332294)*x^6 + (278701)*x^7 + (49537)*x^8 + (-2666)*x^9 + (-356)*x^10 + (9)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (no... | {"coeffs": [1128960000, -162624000, -1231740800, 174284640, 106063912, -11936684, -3332294, 278701, 49537, -2666, -356, 9, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-12, -12, -10, -8, -5, -1, 1, 4, 7, 7, 10, 10]} | 1 |
construct-rlve-polynomial-integer-roots-l4-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 4 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-12 polynomial
P(x) = (-1152000)*x^2 + (2697600)*x^3 + (-2134880)*x^4 + (564624)*x^5 + (76064)*x^6 + (-56016)*x^7 + (3354)*x^8 + (1401)*x^9 + (-139)*x^10 + (-9)*x^11 + (1)*x^12
can be written as (x - a_1)(x - a_2)...(x - a_12) with integers a_1, ..., a_12 (not necessarily distinct). Find such integers.
Answe... | {"coeffs": [0, 0, -1152000, 2697600, -2134880, 564624, 76064, -56016, 3354, 1401, -139, -9, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-10, -6, -5, 0, 0, 1, 2, 2, 3, 4, 8, 10]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-1565650944000)*x^0 + (-1009613721600)*x^1 + (1285219128960)*x^2 + (521911678464)*x^3 + (-320491747448)*x^4 + (-94618547484)*x^5 + (26729556402)*x^6 + (7765018167)*x^7 + (-604310943)*x^8 + (-248952012)*x^9 + (-3717344)*x^10 + (2615154)*x^11 + (114990)*x^12 + (-10704)*x^13 + (-618)*x^14 ... | {"coeffs": [-1565650944000, -1009613721600, 1285219128960, 521911678464, -320491747448, -94618547484, 26729556402, 7765018167, -604310943, -248952012, -3717344, 2615154, 114990, -10704, -618, 15, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-15, -13, -11, -11, -9, -5, -4, -2, -1, 2, 2, 3, 5, 12, 16, 16]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (12332512051200)*x^1 + (-3064442388480)*x^2 + (-2058156048384)*x^3 + (529215823872)*x^4 + (126769520640)*x^5 + (-34967668736)*x^6 + (-3527664640)*x^7 + (1128722400)*x^8 + (41133040)*x^9 + (-18731680)*x^10 + (-78120)*x^11 + (155750)*x^12 + (-1241)*x^13 + (-627)*x^14 + (5)*x^15 + (1)*x^16
... | {"coeffs": [0, 12332512051200, -3064442388480, -2058156048384, 529215823872, 126769520640, -34967668736, -3527664640, 1128722400, 41133040, -18731680, -78120, 155750, -1241, -627, 5, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-16, -16, -12, -6, -6, -5, -4, 0, 4, 4, 6, 6, 8, 10, 11, 11]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (226663557120000)*x^0 + (324065798784000)*x^1 + (89491910947200)*x^2 + (-16351303539840)*x^3 + (-8986501876184)*x^4 + (-305552970180)*x^5 + (270912904410)*x^6 + (28498183857)*x^7 + (-2973198603)*x^8 + (-532044096)*x^9 + (6655012)*x^10 + (4241682)*x^11 + (88746)*x^12 + (-15444)*x^13 + (-5... | {"coeffs": [226663557120000, 324065798784000, 89491910947200, -16351303539840, -8986501876184, -305552970180, 270912904410, 28498183857, -2973198603, -532044096, 6655012, 4241682, 88746, -15444, -582, 21, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-15, -12, -11, -10, -9, -8, -7, -7, -4, -1, 5, 6, 10, 13, 13, 16]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-187342848000)*x^1 + (172339200)*x^2 + (172308088320)*x^3 + (45623493632)*x^4 + (-25618001376)*x^5 + (-7069926288)*x^6 + (1603594256)*x^7 + (378817032)*x^8 + (-47236038)*x^9 + (-9043269)*x^10 + (622218)*x^11 + (104235)*x^12 + (-3386)*x^13 + (-543)*x^14 + (6)*x^15 + (1)*x^16
can be writt... | {"coeffs": [0, -187342848000, 172339200, 172308088320, 45623493632, -25618001376, -7069926288, 1603594256, 378817032, -47236038, -9043269, 622218, 104235, -3386, -543, 6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-14, -11, -11, -10, -5, -3, -2, -2, 0, 1, 4, 5, 6, 8, 12, 16]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-2421619200000)*x^0 + (2376034080000)*x^1 + (2740686472000)*x^2 + (-2651876902400)*x^3 + (-327815915600)*x^4 + (287240744016)*x^5 + (8672913228)*x^6 + (-11618643384)*x^7 + (81489589)*x^8 + (222898876)*x^9 + (-5840936)*x^10 + (-2187684)*x^11 + (82194)*x^12 + (10596)*x^13 + (-476)*x^14 + ... | {"coeffs": [-2421619200000, 2376034080000, 2740686472000, -2651876902400, -327815915600, 287240744016, 8672913228, -11618643384, 81489589, 222898876, -5840936, -2187684, 82194, 10596, -476, -20, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-13, -11, -10, -9, -6, -4, -1, 1, 1, 5, 7, 10, 10, 10, 14, 16]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-63685440000000)*x^0 + (99845784000000)*x^1 + (-30833805600000)*x^2 + (-9324970740000)*x^3 + (3798035394000)*x^4 + (367781615600)*x^5 + (-162116078040)*x^6 + (-8700978866)*x^7 + (3348027901)*x^8 + (122630940)*x^9 + (-37541800)*x^10 + (-966728)*x^11 + (233898)*x^12 + (3860)*x^13 + (-760)... | {"coeffs": [-63685440000000, 99845784000000, -30833805600000, -9324970740000, 3798035394000, 367781615600, -162116078040, -8700978866, 3348027901, 122630940, -37541800, -966728, 233898, 3860, -760, -6, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-15, -12, -10, -9, -9, -8, -5, 1, 2, 4, 5, 10, 10, 13, 14, 15]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-10327274496)*x^3 + (20459888064)*x^4 + (-11362201200)*x^5 + (150454560)*x^6 + (1215526688)*x^7 + (-82855152)*x^8 + (-55772925)*x^9 + (1133255)*x^10 + (1090287)*x^11 + (19587)*x^12 + (-8375)*x^13 + (-315)*x^14 + (21)*x^15 + (1)*x^16
can be written as (x - a_1)(x - a_2)...(x - a_16) with... | {"coeffs": [0, 0, 0, -10327274496, 20459888064, -11362201200, 150454560, 1215526688, -82855152, -55772925, 1133255, 1090287, 19587, -8375, -315, 21, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-16, -12, -11, -9, -7, -6, 0, 0, 0, 1, 2, 2, 3, 7, 11, 14]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-3662382366720)*x^0 + (4873861988352)*x^1 + (-1126426411008)*x^2 + (-1012991840256)*x^3 + (497829860864)*x^4 + (18500979712)*x^5 + (-46987583456)*x^6 + (6840202672)*x^7 + (972794944)*x^8 + (-350882696)*x^9 + (26985762)*x^10 + (1373423)*x^11 + (-314179)*x^12 + (12122)*x^13 + (512)*x^14 +... | {"coeffs": [-3662382366720, 4873861988352, -1126426411008, -1012991840256, 497829860864, 18500979712, -46987583456, 6840202672, 972794944, -350882696, 26985762, 1373423, -314179, 12122, 512, -49, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-16, -12, -4, -3, -3, 2, 2, 2, 6, 7, 7, 8, 10, 11, 16, 16]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-316141056000)*x^1 + (928413446400)*x^2 + (-1066883883840)*x^3 + (605048463936)*x^4 + (-163166481456)*x^5 + (7523211616)*x^6 + (6534060644)*x^7 + (-1358819676)*x^8 + (11023387)*x^9 + (21787643)*x^10 + (-1676673)*x^11 + (-89761)*x^12 + (13969)*x^13 + (-159)*x^14 + (-31)*x^15 + (1)*x^16
c... | {"coeffs": [0, -316141056000, 928413446400, -1066883883840, 605048463936, -163166481456, 7523211616, 6534060644, -1358819676, 11023387, 21787643, -1676673, -89761, 13969, -159, -31, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-16, -11, -10, -6, 0, 1, 2, 2, 3, 3, 4, 9, 10, 11, 14, 15]} | 1 |
construct-rlve-polynomial-integer-roots-l5-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 5 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-16 polynomial
P(x) = (-768592281600000)*x^0 + (752654592000000)*x^1 + (-152350626816000)*x^2 + (-61959249388800)*x^3 + (30607940473920)*x^4 + (-3395661872112)*x^5 + (-415182717876)*x^6 + (122036613848)*x^7 + (-5357232657)*x^8 + (-964839954)*x^9 + (109445834)*x^10 + (43686)*x^11 + (-527184)*x^12 + (21946)*x^1... | {"coeffs": [-768592281600000, 752654592000000, -152350626816000, -61959249388800, 30607940473920, -3395661872112, -415182717876, 122036613848, -5357232657, -964839954, 109445834, 43686, -527184, 21946, 522, -54, 1], "family": "rlve_polynomial_integer_roots", "subset": "construct"} | null | null | null | {"roots": [-16, -13, -12, -8, -3, 2, 4, 5, 8, 9, 10, 11, 12, 15, 15, 15]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s0 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (39046947400581120)*x^0 + (18305450790617088)*x^1 + (-70709098325188608)*x^2 + (-21290079982491648)*x^3 + (39715032787637760)*x^4 + (2321955476341632)*x^5 + (-8762688795400128)*x^6 + (764149280711904)*x^7 + (737673598403856)*x^8 + (-106065431697240)*x^9 + (-28486741314564)*x^10 + (468486... | {"coeffs": [39046947400581120, 18305450790617088, -70709098325188608, -21290079982491648, 39715032787637760, 2321955476341632, -8762688795400128, 764149280711904, 737673598403856, -106065431697240, -28486741314564, 4684860931266, 629771958317, -95987700892, -9804238155, 997485548, 108257258, -4190664, -698546, -7070, 1... | null | null | null | {"roots": [-22, -21, -16, -16, -15, -13, -12, -6, -4, -2, -1, -1, 1, 3, 3, 3, 6, 6, 6, 6, 7, 12]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s1 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (-43454015064082022400000)*x^0 + (48583438108007362560000)*x^1 + (-12728394974587009536000)*x^2 + (-2394302119453602892800)*x^3 + (1132652789900160537600)*x^4 + (5896968400082057472)*x^5 + (-35799295518195718400)*x^6 + (1675695232641012352)*x^7 + (575023731079474560)*x^8 + (-437562772907... | {"coeffs": [-43454015064082022400000, 48583438108007362560000, -12728394974587009536000, -2394302119453602892800, 1132652789900160537600, 5896968400082057472, -35799295518195718400, 1675695232641012352, 575023731079474560, -43756277290776800, -5195788349561456, 534882140654820, 26264931296884, -3775235255075, -60477875... | null | null | null | {"roots": [-20, -18, -15, -15, -13, -13, -10, -8, -6, 2, 2, 6, 10, 11, 11, 13, 14, 14, 14, 16, 19, 21]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s2 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (1100346962130763776)*x^3 + (253322713481084928)*x^4 + (-822212505988927488)*x^5 + (195176757108722688)*x^6 + (99242600563789056)*x^7 + (-59181806638425024)*x^8 + (11452229991963648)*x^9 + (-613774875685968)*x^10 + (-107600209349232)*x^11 + (17581190495516)*x^12 + (-327217647784)*x^13 + ... | {"coeffs": [0, 0, 0, 1100346962130763776, 253322713481084928, -822212505988927488, 195176757108722688, 99242600563789056, -59181806638425024, 11452229991963648, -613774875685968, -107600209349232, 17581190495516, -327217647784, -104487980847, 6726899672, 190873508, -28235544, 221926, 49528, -1128, -32, 1], "family": "r... | null | null | null | {"roots": [-22, -19, -18, -18, -13, -2, -1, 0, 0, 0, 3, 4, 6, 8, 8, 9, 9, 12, 12, 17, 18, 19]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s3 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (62666254744289280000)*x^0 + (-49256056556421120000)*x^1 + (-29751691812426547200)*x^2 + (14258051873144340480)*x^3 + (3961117568963506176)*x^4 + (-1807720838398126080)*x^5 + (-185793005855690496)*x^6 + (120479086953698688)*x^7 + (-872801128006704)*x^8 + (-4176859492086192)*x^9 + (356660... | {"coeffs": [62666254744289280000, -49256056556421120000, -29751691812426547200, 14258051873144340480, 3961117568963506176, -1807720838398126080, -185793005855690496, 120479086953698688, -872801128006704, -4176859492086192, 356660407507536, 62982008174964, -11167823499433, 17718589368, 116889209597, -8786590752, -819211... | null | null | null | {"roots": [-21, -15, -6, -6, -5, -4, -3, -3, 1, 4, 6, 7, 8, 9, 9, 12, 12, 16, 17, 18, 20, 20]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s4 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (-2849205705091200000)*x^0 + (-532735561932480000)*x^1 + (3753649073002680000)*x^2 + (561074806099036800)*x^3 + (-1014641055548433360)*x^4 + (-19466985832250688)*x^5 + (115819669332460980)*x^6 + (-9809132420214792)*x^7 + (-5717329707781251)*x^8 + (967788215743770)*x^9 + (94708192709183)*... | {"coeffs": [-2849205705091200000, -532735561932480000, 3753649073002680000, 561074806099036800, -1014641055548433360, -19466985832250688, 115819669332460980, -9809132420214792, -5717329707781251, 967788215743770, 94708192709183, -31305839604276, 671605858389, 393155502070, -32062248105, -1440046272, 276698415, -5726298... | null | null | null | {"roots": [-19, -19, -10, -9, -6, -4, -3, -2, -1, 1, 5, 5, 6, 6, 9, 9, 12, 13, 14, 15, 15, 17]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s5 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (-555412321345609728000)*x^1 + (297272139313379328000)*x^2 + (272637298505517603840)*x^3 + (7216570079314500096)*x^4 + (-20358885382098700608)*x^5 + (-2064343441920168384)*x^6 + (629219182940651376)*x^7 + (91501934888253168)*x^8 + (-9353944716872076)*x^9 + (-1902624360093684)*x^10 + (559... | {"coeffs": [0, -555412321345609728000, 297272139313379328000, 272637298505517603840, 7216570079314500096, -20358885382098700608, -2064343441920168384, 629219182940651376, 91501934888253168, -9353944716872076, -1902624360093684, 55966954518377, 21723194550455, 176225682731, -139694144179, -4516865542, 476650502, 2556389... | null | null | null | {"roots": [-20, -18, -18, -17, -17, -14, -13, -9, -7, -6, -6, -4, 0, 1, 6, 8, 8, 9, 11, 15, 15, 21]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s6 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (779492764774563840000)*x^1 + (-1253636608598212608000)*x^2 + (746676271158593126400)*x^3 + (-175811736103993221120)*x^4 + (-5308448228754075648)*x^5 + (10214646704142300672)*x^6 + (-1391098805896421120)*x^7 + (-114256743894895872)*x^8 + (40564799668308480)*x^9 + (-1495646368872896)*x^10... | {"coeffs": [0, 779492764774563840000, -1253636608598212608000, 746676271158593126400, -175811736103993221120, -5308448228754075648, 10214646704142300672, -1391098805896421120, -114256743894895872, 40564799668308480, -1495646368872896, -397390825486752, 37370558234976, 1115867364640, -265165560090, 4479924417, 814837717... | null | null | null | {"roots": [-22, -18, -18, -16, -10, -7, -7, 0, 2, 3, 3, 4, 7, 8, 10, 13, 14, 15, 16, 18, 20, 22]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s7 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (-44749048878755020800)*x^1 + (15949006336864972800)*x^2 + (52352242939548744192)*x^3 + (-20742496031367652224)*x^4 + (-6910071544332905312)*x^5 + (4847041226049601128)*x^6 + (-715428355440016756)*x^7 + (-52532728949551270)*x^8 + (22529163551062419)*x^9 + (-1042085612162327)*x^10 + (-223... | {"coeffs": [0, -44749048878755020800, 15949006336864972800, 52352242939548744192, -20742496031367652224, -6910071544332905312, 4847041226049601128, -715428355440016756, -52532728949551270, 22529163551062419, -1042085612162327, -223997664018170, 23458575611316, 670249276961, -176169609769, 2868316320, 609639514, -255036... | null | null | null | {"roots": [-19, -17, -17, -13, -11, -11, -2, -1, 0, 1, 4, 5, 6, 8, 11, 12, 13, 13, 16, 18, 20, 21]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s8 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (139036548357907200000)*x^0 + (302438195784869760000)*x^1 + (167855258090798964000)*x^2 + (-17750634180630980400)*x^3 + (-23369454851396960160)*x^4 + (56831609121195288)*x^5 + (1282203847892904194)*x^6 + (23599123647943305)*x^7 + (-38161657612239271)*x^8 + (-934008544350455)*x^9 + (69008... | {"coeffs": [139036548357907200000, 302438195784869760000, 167855258090798964000, -17750634180630980400, -23369454851396960160, 56831609121195288, 1282203847892904194, 23599123647943305, -38161657612239271, -934008544350455, 690083669868737, 17839650851245, -7959089592387, -198062210963, 59481471945, 1319831195, -285550... | null | null | null | {"roots": [-19, -15, -13, -11, -10, -10, -10, -8, -7, -3, -1, -1, 6, 7, 7, 8, 9, 11, 15, 17, 18, 19]} | 1 |
construct-rlve-polynomial-integer-roots-l6-s9 | construct | rlve_polynomial_integer_roots | integer_root_factorization | algebra | competition | 6 | RLVE-Gym/polynomial_factorization | MIT | [
"agentic_trivial",
"unique_answer"
] | The degree-22 polynomial
P(x) = (1852877437931520000)*x^0 + (1870256519239680000)*x^1 + (-2396717772750144000)*x^2 + (-2392063778290348800)*x^3 + (630235687185930528)*x^4 + (565387120895442064)*x^5 + (-91604824366524608)*x^6 + (-45284714102086664)*x^7 + (5348888846648050)*x^8 + (1741609881434413)*x^9 + (-14126485279381... | {"coeffs": [1852877437931520000, 1870256519239680000, -2396717772750144000, -2392063778290348800, 630235687185930528, 565387120895442064, -91604824366524608, -45284714102086664, 5348888846648050, 1741609881434413, -141264852793811, -37224452533118, 1859812536496, 470380099915, -11829167657, -3567493676, 21865642, 15843... | null | null | null | {"roots": [-22, -18, -17, -15, -13, -11, -10, -8, -5, -2, -1, -1, 1, 3, 4, 5, 8, 9, 12, 13, 14, 17]} | 1 |
construct-rlve-polynomial-interpolation-l1-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(-1) = 3
f(2) = -3
f(-2) = 13
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/w... | {"X": [-1, 2, -2], "Y": [3, -3, 13], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, -4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l1-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(1) = 10
f(-2) = 4
f(-1) = 0
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"X": [1, -2, -1], "Y": [10, 4, 0], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [2, 5, 3]} | 1 |
construct-rlve-polynomial-interpolation-l1-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(-2) = 19
f(1) = 1
f(-1) = 3
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"X": [-2, 1, -1], "Y": [19, 1, 3], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, -1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l1-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(-2) = 11
f(1) = -1
f(0) = 1
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"X": [-2, 1, 0], "Y": [11, -1, 1], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, -3, 1]} | 1 |
construct-rlve-polynomial-interpolation-l1-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(0) = -3
f(1) = -5
f(-1) = 5
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"X": [0, 1, -1], "Y": [-3, -5, 5], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, -5, 3]} | 1 |
construct-rlve-polynomial-interpolation-l1-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(1) = -5
f(0) = -5
f(-1) = -1
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/w... | {"X": [1, 0, -1], "Y": [-5, -5, -1], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, -2, 2]} | 1 |
construct-rlve-polynomial-interpolation-l1-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(0) = -2
f(-1) = -5
f(2) = 10
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/w... | {"X": [0, -1, 2], "Y": [-2, -5, 10], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-2, 4, 1]} | 1 |
construct-rlve-polynomial-interpolation-l1-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(2) = 31
f(-2) = 11
f(-1) = 1
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/w... | {"X": [2, -2, -1], "Y": [31, 11, 1], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, 5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l1-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(-1) = 5
f(-2) = 15
f(0) = 5
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/wo... | {"X": [-1, -2, 0], "Y": [5, 15, 5], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [5, 5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l1-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 1 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
f(-2) = 0
f(-1) = -2
f(0) = -2
Find a_0, ..., a_2.
Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/w... | {"X": [-2, -1, 0], "Y": [0, -2, -2], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-2, 1, 1]} | 1 |
construct-rlve-polynomial-interpolation-l2-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(2) = 42
f(-1) = 6
f(1) = 2
f(-4) = 492
f(3) = 198
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/ins... | {"X": [2, -1, 1, -4, 3], "Y": [42, 6, 2, 492, 198], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [0, -3, 2, 1, 2]} | 1 |
construct-rlve-polynomial-interpolation-l2-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(4) = 309
f(1) = 3
f(-4) = 853
f(-1) = 19
f(0) = 5
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/ins... | {"X": [4, 1, -4, -1, 0], "Y": [309, 3, 853, 19, 5], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [5, -4, 4, -4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l2-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(-1) = 5
f(0) = -4
f(-3) = 407
f(-2) = 88
f(1) = -5
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/in... | {"X": [-1, 0, -3, -2, 1], "Y": [5, -4, 407, 88, -5], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, -2, 0, -3, 4]} | 1 |
construct-rlve-polynomial-interpolation-l2-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(2) = 73
f(3) = 397
f(-2) = 37
f(1) = 1
f(-4) = 1111
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/i... | {"X": [2, 3, -2, 1, -4], "Y": [73, 397, 37, 1, 1111], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, 5, -5, 1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l2-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(-1) = 6
f(-3) = 108
f(0) = 3
f(4) = 731
f(-2) = 23
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/in... | {"X": [-1, -3, 0, 4, -2], "Y": [6, 108, 3, 731, 23], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [3, -2, 2, 3, 2]} | 1 |
construct-rlve-polynomial-interpolation-l2-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(4) = 1012
f(3) = 344
f(1) = 4
f(-3) = 116
f(2) = 76
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/i... | {"X": [4, 3, 1, -3, 2], "Y": [1012, 344, 4, 116, 76], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, 2, -1, 4, 3]} | 1 |
construct-rlve-polynomial-interpolation-l2-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(-3) = 403
f(2) = 103
f(-2) = 79
f(0) = -5
f(-1) = 1
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/i... | {"X": [-3, 2, -2, 0, -1], "Y": [403, 103, 79, -5, 1], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, 2, 4, 1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l2-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(4) = 1661
f(2) = 137
f(-2) = 65
f(-4) = 1037
f(3) = 575
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workd... | {"X": [4, 2, -2, -4, 3], "Y": [1661, 137, 65, 1037, 575], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [5, -2, 4, 5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l2-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(-2) = 87
f(-3) = 357
f(0) = 3
f(-1) = 13
f(3) = 117
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/i... | {"X": [-2, -3, 0, -1, 3], "Y": [87, 357, 3, 13, 117], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [3, -4, -1, -4, 3]} | 1 |
construct-rlve-polynomial-interpolation-l2-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 2 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_4 x^4 of degree 4 with integer coefficients satisfies
f(4) = 1327
f(0) = 3
f(-3) = 375
f(-4) = 1207
f(-1) = 7
Find a_0, ..., a_4.
Answer format: {"coeffs": [a_0, a_1, ..., a_4]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir... | {"X": [4, 0, -3, -4, -1], "Y": [1327, 3, 375, 1207, 7], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [3, -1, -1, 1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l3-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(3) = 658
f(-2) = 273
f(1) = -6
f(0) = 1
f(2) = 1
f(5) = 21826
f(-3) = 2386
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data... | {"X": [3, -2, 1, 0, 2, 5, -3], "Y": [658, 273, -6, 1, 1, 21826, 2386], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, 0, -2, -5, 1, -3, 2]} | 1 |
construct-rlve-polynomial-interpolation-l3-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(0) = 0
f(-4) = 11392
f(-5) = 44275
f(6) = 151272
f(-2) = 136
f(1) = 7
f(3) = 2691
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"X": [0, -4, -5, 6, -2, 1, 3], "Y": [0, 11392, 44275, 151272, 136, 7, 2691], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [0, 0, -4, 5, 2, 1, 3]} | 1 |
construct-rlve-polynomial-interpolation-l3-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(0) = -4
f(2) = 86
f(-2) = 450
f(-3) = 3821
f(3) = 1265
f(6) = 105962
f(-4) = 18632
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The insta... | {"X": [0, 2, -2, -3, 3, 6, -4], "Y": [-4, 86, 450, 3821, 1265, 105962, 18632], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, -3, 4, -2, 4, -5, 3]} | 1 |
construct-rlve-polynomial-interpolation-l3-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(4) = 6197
f(-3) = 415
f(3) = 1207
f(6) = 62839
f(-5) = 10391
f(-6) = 33067
f(2) = 115
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The in... | {"X": [4, -3, 3, 6, -5, -6, 2], "Y": [6197, 415, 1207, 62839, 10391, 33067, 115], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, -3, 0, -3, 1, 2, 1]} | 1 |
construct-rlve-polynomial-interpolation-l3-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(2) = 208
f(-3) = 4343
f(4) = 16236
f(6) = 200768
f(-4) = 23788
f(5) = 65071
f(-5) = 88821
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. Th... | {"X": [2, -3, 4, 6, -4, 5, -5], "Y": [208, 4343, 16236, 200768, 23788, 65071, 88821], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, 0, 3, 5, -2, -4, 5]} | 1 |
construct-rlve-polynomial-interpolation-l3-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(-3) = -4
f(-5) = 15292
f(4) = 11098
f(0) = 2
f(2) = 186
f(-2) = -110
f(5) = 40812
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The instan... | {"X": [-3, -5, 4, 0, 2, -2, 5], "Y": [-4, 15292, 11098, 2, 186, -110, 40812], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [2, 2, -3, 2, -5, 4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l3-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(-1) = -6
f(4) = 13294
f(1) = 10
f(-2) = -26
f(5) = 46818
f(-3) = 274
f(2) = 294
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The instance... | {"X": [-1, 4, 1, -2, 5, -3, 2], "Y": [-6, 13294, 10, -26, 46818, 274, 294], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-2, 4, 2, -1, 0, 5, 2]} | 1 |
construct-rlve-polynomial-interpolation-l3-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(-2) = 249
f(-1) = -1
f(-6) = 132249
f(1) = -9
f(-3) = 2583
f(-5) = 46767
f(4) = 3549
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The ins... | {"X": [-2, -1, -6, 1, -3, -5, 4], "Y": [249, -1, 132249, -9, 2583, 46767, 3549], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, -4, -5, 5, 1, -5, 2]} | 1 |
construct-rlve-polynomial-interpolation-l3-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(2) = 139
f(-5) = 93120
f(-1) = 4
f(-2) = 459
f(-4) = 25339
f(-6) = 270859
f(4) = 15099
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The i... | {"X": [2, -5, -1, -2, -4, -6, 4], "Y": [139, 93120, 4, 459, 25339, 270859, 15099], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, 0, 0, 0, -1, -5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l3-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 3 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_6 x^6 of degree 6 with integer coefficients satisfies
f(-1) = -5
f(0) = -3
f(6) = 249195
f(5) = 83827
f(-5) = 66067
f(-6) = 204255
f(-4) = 16345
Find a_0, ..., a_6.
Answer format: {"coeffs": [a_0, a_1, ..., a_6]}
Write your final answer as JSON to `/workdir/answer.json`. The... | {"X": [-1, 0, 6, 5, -5, -6, -4], "Y": [-5, -3, 249195, 83827, 66067, 204255, 16345], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, 1, -2, -4, -5, 3, 5]} | 1 |
construct-rlve-polynomial-interpolation-l4-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(-5) = -7731801
f(-1) = -9
f(-2) = -2073
f(7) = 159192375
f(5) = 7581699
f(1) = 3
f(2) = 1575
f(-3) = -77725
f(-7) = -160345053
f(6) = 39524903
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9]}
Write yo... | {"X": [-5, -1, -2, 7, 5, 1, 2, -3, -7, 6], "Y": [-7731801, -9, -2073, 159192375, 7581699, 3, 1575, -77725, -160345053, 39524903], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-1, 0, -2, 4, 5, 0, -5, -2, 0, 4]} | 1 |
construct-rlve-polynomial-interpolation-l4-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(-9) = -2142224657
f(-5) = -11545449
f(1) = 3
f(9) = 1712846899
f(0) = 1
f(7) = 171419151
f(8) = 583278209
f(-6) = -58177151
f(-7) = -228822061
f(-8) = -750509439
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, .... | {"X": [-9, -5, 1, 9, 0, 7, 8, -6, -7, -8], "Y": [-2142224657, -11545449, 3, 1712846899, 1, 171419151, 583278209, -58177151, -228822061, -750509439], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, 0, 2, -1, 2, 0, 1, -2, -5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l4-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(9) = 953685014
f(-3) = -93166
f(-4) = -1123672
f(-1) = -16
f(5) = 4045226
f(8) = 321804740
f(-6) = -38812006
f(7) = 93491464
f(3) = 31580
f(-5) = -7860284
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9... | {"X": [9, -3, -4, -1, 5, 8, -6, 7, 3, -5], "Y": [953685014, -93166, -1123672, -16, 4045226, 321804740, -38812006, 93491464, 31580, -7860284], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, 1, -1, -3, -2, 5, 3, 1, -5, 3]} | 1 |
construct-rlve-polynomial-interpolation-l4-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(5) = 5612247
f(8) = 339520293
f(3) = 69303
f(-9) = -612899913
f(2) = 2223
f(-7) = -59457177
f(7) = 105316663
f(-6) = -14064729
f(-4) = -302103
f(-5) = -2524553
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ...... | {"X": [5, 8, 3, -9, 2, -7, 7, -6, -4, -5], "Y": [5612247, 339520293, 69303, -612899913, 2223, -59457177, 105316663, -14064729, -302103, -2524553], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, 5, 4, -3, -5, 2, -1, 2, 4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l4-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(-9) = -1815681664
f(9) = 2078252882
f(-5) = -8701876
f(-1) = -8
f(0) = -1
f(6) = 56217671
f(-3) = -81298
f(2) = 4087
f(-7) = -185728670
f(-8) = -624056833
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9... | {"X": [-9, 9, -5, -1, 0, 6, -3, 2, -7, -8], "Y": [-1815681664, 2078252882, -8701876, -8, -1, 56217671, -81298, 4087, -185728670, -624056833], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-1, 0, 0, 5, 3, 5, 4, 2, 3, 5]} | 1 |
construct-rlve-polynomial-interpolation-l4-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(8) = 384677117
f(-8) = -416175859
f(-9) = -1198198561
f(3) = 51887
f(2) = 1211
f(0) = 5
f(-6) = -31422301
f(-7) = -125477473
f(-2) = -1393
f(-5) = -6100465
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_... | {"X": [8, -8, -9, 3, 2, 0, -6, -7, -2, -5], "Y": [384677117, -416175859, -1198198561, 51887, 1211, 5, -31422301, -125477473, -1393, -6100465], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [5, -1, -4, 3, -5, -4, 4, -1, -1, 3]} | 1 |
construct-rlve-polynomial-interpolation-l4-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(-6) = -13869293
f(9) = 957343612
f(0) = -5
f(-3) = -15188
f(-2) = -61
f(7) = 105558392
f(-9) = -610884104
f(4) = 821627
f(-8) = -204846853
f(6) = 27484771
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9... | {"X": [-6, 9, 0, -3, -2, 7, -9, 4, -8, 6], "Y": [-13869293, 957343612, -5, -15188, -61, 105558392, -610884104, 821627, -204846853, 27484771], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, 0, -4, 3, -3, -5, 2, 2, 4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l4-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(7) = 112096775
f(4) = 658472
f(-4) = -778856
f(6) = 27470604
f(-9) = -1185491961
f(1) = -1
f(3) = 44295
f(-2) = -1060
f(-5) = -5912185
f(8) = 377702800
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9]}
... | {"X": [7, 4, -4, 6, -9, 1, 3, -2, -5, 8], "Y": [112096775, 658472, -778856, 27470604, -1185491961, -1, 44295, -1060, -5912185, 377702800], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [0, 2, -2, -3, 5, -2, 1, -4, -1, 3]} | 1 |
construct-rlve-polynomial-interpolation-l4-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(9) = 1983630263
f(6) = 52222817
f(0) = 5
f(-6) = -49050127
f(-9) = -1899662413
f(1) = 7
f(-5) = -9471365
f(-7) = -196993449
f(4) = 1380133
f(2) = 2673
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9]}
... | {"X": [9, 6, 0, -6, -9, 1, -5, -7, 4, 2], "Y": [1983630263, 52222817, 5, -49050127, -1899662413, 7, -9471365, -196993449, 1380133, 2673], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [5, 4, 1, -4, 0, -4, -2, 1, 1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l4-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 4 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_9 x^9 of degree 9 with integer coefficients satisfies
f(-2) = -495
f(6) = 23683633
f(0) = 1
f(1) = 18
f(7) = 92653002
f(-7) = -68897310
f(3) = 55570
f(-3) = -25238
f(-5) = -3092094
f(-4) = -385647
Find a_0, ..., a_9.
Answer format: {"coeffs": [a_0, a_1, ..., a_9]}
Write your... | {"X": [-2, 6, 0, 1, 7, -7, 3, -3, -5, -4], "Y": [-495, 23683633, 1, 18, 92653002, -68897310, 55570, -25238, -3092094, -385647], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, 4, 2, 2, -2, 4, 3, 0, 2, 2]} | 1 |
construct-rlve-polynomial-interpolation-l5-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(-3) = -2953921
f(12) = 201224484984194
f(11) = 64425309883629
f(-6) = -26601149386
f(-1) = 9
f(2) = -1866
f(1) = -21
f(-7) = -198278559309
f(6) = 21992363654
f(7) = 169420177089
f(-12) = -219307789425694
f(8) = 98548968... | {"X": [-3, 12, 11, -6, -1, 2, 1, -7, 6, 7, -12, 8, 4, 10], "Y": [-2953921, 201224484984194, 64425309883629, -26601149386, 9, -1866, -21, -198278559309, 21992363654, 169420177089, -219307789425694, 985489680546, 93816354, 18478580846262], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [2, -4, 3, -4, -5, -1, 1, -2, -4, -1, -2, -5, -1, 2]} | 1 |
construct-rlve-polynomial-interpolation-l5-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(0) = 3
f(6) = 20423572461
f(4) = 117571991
f(-3) = 640827
f(-4) = 5767311
f(-1) = -9
f(5) = 2010860283
f(10) = 13654740012113
f(8) = 794124358731
f(-12) = -69436597451769
f(12) = 140143647547167
f(-9) = -1337523794889
f... | {"X": [0, 6, 4, -3, -4, -1, 5, 10, 8, -12, 12, -9, 11, -11], "Y": [3, 20423572461, 117571991, 640827, 5767311, -9, 2010860283, 13654740012113, 794124358731, -69436597451769, 140143647547167, -1337523794889, 46102028143911, -21255261499909], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [3, 1, 1, 2, 1, 0, 0, 4, -3, 5, -5, -3, 4, 1]} | 1 |
construct-rlve-polynomial-interpolation-l5-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(-6) = -75167619731
f(-5) = -7189467825
f(-10) = -54710450987295
f(-1) = -21
f(-7) = -548029274343
f(4) = 237842439
f(11) = 156038784638655
f(-13) = -1625630917341033
f(-12) = -577381323435113
f(7) = 409005102627
f(9) = ... | {"X": [-6, -5, -10, -1, -7, 4, 11, -13, -12, 7, 9, -9, 1, 6], "Y": [-75167619731, -7189467825, -54710450987295, -21, -548029274343, 237842439, 156038784638655, -1625630917341033, -577381323435113, 409005102627, 11199402696649, -14031017054285, -15, 53265336145], "family": "rlve_polynomial_interpolation", "subset": "con... | null | null | null | {"coeffs": [-5, -1, -3, -3, 1, 0, -1, 5, -4, 0, -1, -3, -5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l5-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(8) = 2866286024281
f(-6) = -60452914661
f(-2) = -35209
f(-4) = -298075067
f(1) = 8
f(-5) = -5556311614
f(12) = 551145370132981
f(9) = 13202341861744
f(6) = 68783522383
f(-1) = -26
f(-12) = -515855930418899
f(10) = 51773... | {"X": [8, -6, -2, -4, 1, -5, 12, 9, 6, -1, -12, 10, 3, 4], "Y": [2866286024281, -60452914661, -35209, -298075067, 8, -5556311614, 551145370132981, 13202341861744, 68783522383, -26, -515855930418899, 51773597373131, 8554186, 358342109], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [1, 3, 1, 3, -3, 4, -3, 0, -4, 4, -3, -2, 2, 5]} | 1 |
construct-rlve-polynomial-interpolation-l5-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(-2) = -4890
f(11) = 77507000033071
f(-6) = -18783042518
f(-4) = -76610024
f(-8) = -872363813076
f(7) = 228330928599
f(-3) = -1391201
f(12) = 238271298958024
f(5) = 2992044079
f(-11) = -58886086900593
f(13) = 66974420584... | {"X": [-2, 11, -6, -4, -8, 7, -3, 12, 5, -11, 13, 1, -5, -9], "Y": [-4890, 77507000033071, -18783042518, -76610024, -872363813076, 228330928599, -1391201, 238271298958024, 2992044079, -58886086900593, 669744205842495, -9, -1609355121, -4157621775689], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [4, -5, 4, -3, 1, -1, -4, -1, -5, 3, -4, -3, 3, 2]} | 1 |
construct-rlve-polynomial-interpolation-l5-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(6) = 51070916857
f(-10) = -25164222454135
f(-7) = -224460247597
f(0) = -5
f(-8) = -1319130249309
f(12) = 367313650781071
f(11) = 119943690742937
f(2) = 55181
f(-2) = -7167
f(-5) = -2508794295
f(-6) = -28826256299
f(7) =... | {"X": [6, -10, -7, 0, -8, 12, 11, 2, -2, -5, -6, 7, 10, 1], "Y": [51070916857, -25164222454135, -224460247597, -5, -1319130249309, 367313650781071, 119943690742937, 55181, -7167, -2508794295, -28826256299, 365109415701, 35243818553925, 27], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-5, 3, -1, 4, 5, 5, -2, 2, -2, 4, 4, 2, 5, 3]} | 1 |
construct-rlve-polynomial-interpolation-l5-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(-6) = -31640648116
f(4) = 277998204
f(-9) = -6595360798270
f(2) = 43404
f(7) = 351249186354
f(8) = 1947264050172
f(-12) = -287646577881988
f(12) = 358729425883004
f(-2) = -13908
f(-5) = -2842982754
f(6) = 48819662060
f(... | {"X": [-6, 4, -9, 2, 7, 8, -12, 12, -2, -5, 6, 5, 1, -8], "Y": [-31640648116, 277998204, -6595360798270, 43404, 351249186354, 1947264050172, -287646577881988, 358729425883004, -13908, -2842982754, 48819662060, 4758573996, 0, -1401736635396], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-4, 0, 0, 2, -2, -1, -1, 0, 2, -4, -2, 3, 4, 3]} | 1 |
construct-rlve-polynomial-interpolation-l5-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(11) = 33356660476559
f(-1) = -1
f(-11) = -33406388340961
f(13) = 295572879225119
f(9) = 2413085064959
f(-9) = -2419627169761
f(-5) = -1033434673
f(0) = 2
f(5) = 1017834527
f(-7) = -89235770881
f(1) = -1
f(2) = 716
f(3) ... | {"X": [11, -1, -11, 13, 9, -9, -5, 0, 5, -7, 1, 2, 3, 7], "Y": [33356660476559, -1, -33406388340961, 295572879225119, 2413085064959, -2419627169761, -1033434673, 2, 1017834527, -89235770881, -1, 716, 867119, 88728679391], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [2, -5, -3, 2, -5, 3, 1, 3, 5, 0, -1, -4, 0, 1]} | 1 |
construct-rlve-polynomial-interpolation-l5-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(4) = 252410183
f(1) = -1
f(-1) = -7
f(10) = 45014920470953
f(0) = 3
f(-5) = -7295439547
f(-8) = -3089578439269
f(-7) = -552891987337
f(11) = 156961329485909
f(7) = 415597707521
f(-13) = -1630538153725699
f(13) = 1398107... | {"X": [4, 1, -1, 10, 0, -5, -8, -7, 11, 7, -13, 13, -2, -12], "Y": [252410183, -1, -7, 45014920470953, 3, -7295439547, -3089578439269, -552891987337, 156961329485909, 415597707521, -1630538153725699, 1398107114488763, -57187, -579397392985737], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [3, 5, -1, 1, -3, -5, 1, 2, -1, -5, 2, 0, -5, 5]} | 1 |
construct-rlve-polynomial-interpolation-l5-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 5 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_13 x^13 of degree 13 with integer coefficients satisfies
f(-3) = -9565731
f(11) = 166766738921769
f(5) = 5655935757
f(-6) = -70628564535
f(10) = 48145415471017
f(12) = 518286235359189
f(9) = 12188040476325
f(-12) = -554566394953179
f(1) = -11
f(3) = 6895641
f(13) = 147062473572... | {"X": [-3, 11, 5, -6, 10, 12, 9, -12, 1, 3, 13, -4, -1, -2], "Y": [-9565731, 166766738921769, 5655935757, -70628564535, 48145415471017, 518286235359189, 12188040476325, -554566394953179, -11, 6895641, 1470624735721021, -381202251, -15, -55199], "family": "rlve_polynomial_interpolation", "subset": "construct"} | null | null | null | {"coeffs": [-3, 2, 0, 1, -3, -5, -4, 2, 4, -5, -5, 2, -2, 5]} | 1 |
construct-rlve-polynomial-interpolation-l6-s0 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-9) = 490095908584812309
f(3) = 645413013
f(4) = 139275148779
f(12) = 72370464609083069691
f(-7) = 5395520131508713
f(-16) = 14954771365259916738019
f(10) = 2655285250807319823
f(-2) = 761463
f(7) = 4046837053058901
f(-... | {"X": [-9, 3, 4, 12, -7, -16, 10, -2, 7, -15, -13, -5, -6, -4, 9, 0, 6, -11, 5], "Y": [490095908584812309, 645413013, 139275148779, 72370464609083069691, 5395520131508713, 14954771365259916738019, 2655285250807319823, 761463, 4046837053058901, 4694314595906418963273, 359746984394737846741, 12839157288693, 3392740670715... | null | null | null | {"coeffs": [3, 2, -2, 0, 2, 3, -3, 1, -2, 1, -5, 3, 5, -2, 3, 5, -5, -3, 3]} | 1 |
construct-rlve-polynomial-interpolation-l6-s1 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(0) = 3
f(-13) = 485513006071948042958
f(3) = 1215189630
f(-5) = 18483476208358
f(-18) = 166339859780774143440813
f(12) = 98071143210280824183
f(-2) = 1570525
f(13) = 416823369214381662640
f(17) = 53055714045136763278028... | {"X": [0, -13, 3, -5, -18, 12, -2, 13, 17, 18, 9, -7, -1, 7, 16, 11, -10, 14, -17], "Y": [3, 485513006071948042958, 1215189630, 18483476208358, 166339859780774143440813, 98071143210280824183, 1570525, 416823369214381662640, 53055714045136763278028, 148920159160575235375545, 538504296172885812, 7489305830982020, 2, 5676... | null | null | null | {"coeffs": [3, -1, 4, -1, -2, 3, 3, 5, -5, -1, 3, 4, -1, 3, 4, 5, 2, -4, 4]} | 1 |
construct-rlve-polynomial-interpolation-l6-s2 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(16) = 22984652334144338783230
f(-15) = 7573371106088914393723
f(2) = 929990
f(5) = 17244921778523
f(-9) = 780116823665180755
f(8) = 85006576829218046
f(12) = 128309895603341528830
f(6) = 468331090999990
f(-12) = 1371839... | {"X": [16, -15, 2, 5, -9, 8, 12, 6, -12, 1, 11, -17, -11, 14, -13, 3, 13, 7, 17], "Y": [22984652334144338783230, 7573371106088914393723, 929990, 17244921778523, 780116823665180755, 85006576829218046, 128309895603341528830, 468331090999990, 137183918001259586686, -5, 26696864093202199235, 71872561310905048577971, 287185... | null | null | null | {"coeffs": [-2, 0, -4, -1, -4, 5, -2, 4, -1, 0, 0, -4, 1, 2, 0, 0, -2, -2, 5]} | 1 |
construct-rlve-polynomial-interpolation-l6-s3 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-12) = 74698078822391405235
f(17) = 43649794214300099405319
f(9) = 476326279877929167
f(-15) = 4210461041507507211303
f(-11) = 15486482568262947827
f(12) = 83573171142477652659
f(2) = 893439
f(3) = 1274336985
f(1) = 23
... | {"X": [-12, 17, 9, -15, -11, 12, 2, 3, 1, 4, 13, -10, 6, -14, -16, -5, -1, 15, -17], "Y": [74698078822391405235, 43649794214300099405319, 476326279877929167, 4210461041507507211303, 15486482568262947827, 83573171142477652659, 893439, 1274336985, 23, 224676198707, 352022120891395654235, 2760372561182670303, 327609121674... | null | null | null | {"coeffs": [3, 0, 3, 0, -3, 3, 3, 2, 2, -1, -4, 4, 3, 3, 4, 0, -4, 2, 3]} | 1 |
construct-rlve-polynomial-interpolation-l6-s4 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-6) = 514888084817072
f(-9) = 761056249466439875
f(0) = 2
f(-7) = 8261787103435007
f(-8) = 91385118295515402
f(4) = 314707973502
f(-3) = 1880010887
f(-10) = 5067464597180780612
f(18) = 194193518771557643040632
f(-2) = 1... | {"X": [-6, -9, 0, -7, -8, 4, -3, -10, 18, -2, 3, 15, -14, -4, -16, -12, 10, -1, 5], "Y": [514888084817072, 761056249466439875, 2, 8261787103435007, 91385118295515402, 314707973502, 1880010887, 5067464597180780612, 194193518771557643040632, 1075932, 1693425707, 7271966341156601397587, 2157982153896815552280, 34420067687... | null | null | null | {"coeffs": [2, -1, -4, -1, -2, 2, 1, 2, 2, 3, 0, 4, 5, 4, -5, 2, -3, -1, 5]} | 1 |
construct-rlve-polynomial-interpolation-l6-s5 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-11) = 29019317985182945227
f(-13) = 582648787508798617703
f(-8) = 95806704210852493
f(18) = 193001172415606291797347
f(-14) = 2205488267735449709059
f(5) = 18465102485675
f(-10) = 5244993023345535215
f(2) = 1561523
f(-... | {"X": [-11, -13, -8, 18, -14, 5, -10, 2, -3, 13, -12, -16, -4, 8, -5, 9, 6, -7, 16], "Y": [29019317985182945227, 582648787508798617703, 95806704210852493, 193001172415606291797347, 2205488267735449709059, 18465102485675, 5244993023345535215, 1561523, 2339082683, 548559588447494638747, 138401194700368896497, 24288593680... | null | null | null | {"coeffs": [5, -1, 2, -5, 3, -5, 5, -4, 3, -3, 2, 0, 3, 1, 0, 5, 5, -2, 5]} | 1 |
construct-rlve-polynomial-interpolation-l6-s6 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(12) = 128850990831703782512
f(-12) = 137757317747849775848
f(-18) = 201232907979463747385762
f(-8) = 94904064881322212
f(5) = 17676827354546
f(6) = 476398010158922
f(4) = 312733797656
f(-13) = 580303949907394010762
f(-1... | {"X": [12, -12, -18, -8, 5, 6, 4, -13, -15, 8, -5, 17, 1, 3, -6, -3, 16, -14, 14], "Y": [128850990831703782512, 137757317747849775848, 201232907979463747385762, 94904064881322212, 17676827354546, 476398010158922, 312733797656, 580303949907394010762, 7593586581418457031746, 85821016504391828, 20801729674346, 68707030106... | null | null | null | {"coeffs": [-4, -5, 3, -4, -2, 4, 0, 0, 3, 0, 2, 1, 4, -5, 2, -1, 1, -2, 5]} | 1 |
construct-rlve-polynomial-interpolation-l6-s7 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-18) = 87711549808266854587115
f(16) = 8294985403764561882079
f(4) = 70871288695
f(18) = 70156832827194647442899
f(-5) = 11112168913909
f(9) = 236067082389277685
f(1) = -11
f(15) = 2572511276491084736069
f(17) = 2489955... | {"X": [-18, 16, 4, 18, -5, 9, 1, 15, 17, -14, -12, 14, 5, 13, 6, -3, -10, 8, -15], "Y": [87711549808266854587115, 8294985403764561882079, 70871288695, 70156832827194647442899, 11112168913909, 236067082389277685, -11, 2572511276491084736069, 24899552248360210268405, 980811364721227946899, 62562634550154953879, 735326513... | null | null | null | {"coeffs": [-1, -2, -4, 3, 3, -2, 5, -1, 2, 0, -4, 2, -4, 1, -4, -5, 2, -4, 2]} | 1 |
construct-rlve-polynomial-interpolation-l6-s8 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(1) = 13
f(10) = 3393016632331515346
f(-16) = 12964592541221740762188
f(16) = 15332711185621724541868
f(-4) = 129757757328
f(12) = 88605965538995490368
f(3) = 1679952599
f(17) = 45458158411536500623773
f(-5) = 8145241173... | {"X": [1, 10, -16, 16, -4, 12, 3, 17, -5, -15, -8, -11, 14, -6, -9, 0, -18, 4, -17], "Y": [13, 3393016632331515346, 12964592541221740762188, 15332711185621724541868, 129757757328, 88605965538995490368, 1679952599, 45458158411536500623773, 8145241173871, 4031684803366693572221, 44647699867347748, 14599405106326960993, 1... | null | null | null | {"coeffs": [-4, -5, 4, -5, 2, 5, 1, 3, 3, 2, 3, -4, -3, 2, 0, 3, -1, 4, 3]} | 1 |
construct-rlve-polynomial-interpolation-l6-s9 | construct | rlve_polynomial_interpolation | lagrange_interpolation_integer | algebra | competition | 6 | RLVE-Gym/polynomial_interpolation | MIT | [
"agentic_trivial",
"unique_answer"
] | A polynomial f(x) = a_0 + a_1 x + ... + a_18 x^18 of degree 18 with integer coefficients satisfies
f(-11) = 29652735032500234651
f(-5) = 21611696975191
f(-18) = 205015396275682600634960
f(12) = 123436035876485392220
f(13) = 524793534757440267835
f(3) = 1173911735
f(7) = 7057019155066135
f(-13) = 594405750568482866295
f... | {"X": [-11, -5, -18, 12, 13, 3, 7, -13, 17, -1, 8, -15, 0, -16, -7, -2, 2, 15, 5], "Y": [29652735032500234651, 21611696975191, 205015396275682600634960, 123436035876485392220, 524793534757440267835, 1173911735, 7057019155066135, 594405750568482866295, 66799703669058541261755, -9, 79781169898034460, 77589232749060343711... | null | null | null | {"coeffs": [-4, -4, -3, 3, 1, 3, 2, 4, -5, 5, 4, -2, 1, 1, -4, -4, -4, -4, 5]} | 1 |
construct-rlve-prefix-product-permutation-l1-s0 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_3 of the integers 1, 2, ..., 3 such that the 3 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_3 are pairwise distinct modulo 3.
Answer format: {"perm": [p_1, ..., p_3]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. On... | {"n": 3, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 3]} | 1 |
construct-rlve-prefix-product-permutation-l1-s1 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_13 of the integers 1, 2, ..., 13 such that the 13 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_13 are pairwise distinct modulo 13.
Answer format: {"perm": [p_1, ..., p_13]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 13, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 8, 10, 11, 9, 12, 3, 6, 4, 5, 7, 13]} | 1 |
construct-rlve-prefix-product-permutation-l1-s2 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_11 of the integers 1, 2, ..., 11 such that the 11 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_11 are pairwise distinct modulo 11.
Answer format: {"perm": [p_1, ..., p_11]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 11, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 7, 5, 4, 10, 3, 9, 8, 6, 11]} | 1 |
construct-rlve-prefix-product-permutation-l1-s3 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_37 of the integers 1, 2, ..., 37 such that the 37 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_37 are pairwise distinct modulo 37.
Answer format: {"perm": [p_1, ..., p_37]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 37, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 20, 26, 29, 16, 32, 17, 15, 34, 27, 28, 35, 21, 9, 6, 8, 25, 36, 3, 14, 31, 33, 30, 18, 4, 11, 12, 5, 24, 22, 7, 23, 10, 13, 19, 37]} | 1 |
construct-rlve-prefix-product-permutation-l1-s4 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_29 of the integers 1, 2, ..., 29 such that the 29 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_29 are pairwise distinct modulo 29.
Answer format: {"perm": [p_1, ..., p_29]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 29, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 16, 11, 23, 7, 6, 26, 12, 14, 4, 9, 18, 10, 28, 3, 21, 13, 22, 27, 17, 19, 5, 25, 24, 8, 20, 15, 29]} | 1 |
construct-rlve-prefix-product-permutation-l1-s5 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_7 of the integers 1, 2, ..., 7 such that the 7 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_7 are pairwise distinct modulo 7.
Answer format: {"perm": [p_1, ..., p_7]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. On... | {"n": 7, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 5, 6, 3, 4, 7]} | 1 |
construct-rlve-prefix-product-permutation-l1-s6 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_23 of the integers 1, 2, ..., 23 such that the 23 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_23 are pairwise distinct modulo 23.
Answer format: {"perm": [p_1, ..., p_23]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 23, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 13, 9, 7, 15, 5, 11, 4, 19, 8, 22, 3, 17, 6, 21, 14, 20, 10, 18, 16, 12, 23]} | 1 |
construct-rlve-prefix-product-permutation-l1-s7 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_19 of the integers 1, 2, ..., 19 such that the 19 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_19 are pairwise distinct modulo 19.
Answer format: {"perm": [p_1, ..., p_19]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 19, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 11, 14, 6, 5, 17, 12, 13, 18, 3, 8, 9, 4, 16, 15, 7, 10, 19]} | 1 |
construct-rlve-prefix-product-permutation-l1-s8 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_31 of the integers 1, 2, ..., 31 such that the 31 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_31 are pairwise distinct modulo 31.
Answer format: {"perm": [p_1, ..., p_31]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 31, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 17, 22, 9, 26, 27, 10, 5, 8, 29, 18, 14, 13, 21, 30, 3, 12, 20, 19, 15, 4, 25, 28, 23, 6, 7, 24, 11, 16, 31]} | 1 |
construct-rlve-prefix-product-permutation-l1-s9 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 1 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_5 of the integers 1, 2, ..., 5 such that the 5 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_5 are pairwise distinct modulo 5.
Answer format: {"perm": [p_1, ..., p_5]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. On... | {"n": 5, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 4, 3, 5]} | 1 |
construct-rlve-prefix-product-permutation-l2-s0 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_83 of the integers 1, 2, ..., 83 such that the 83 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_83 are pairwise distinct modulo 83.
Answer format: {"perm": [p_1, ..., p_83]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 83, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 43, 29, 22, 51, 15, 13, 53, 38, 26, 69, 8, 33, 7, 73, 27, 45, 61, 36, 55, 5, 35, 66, 46, 11, 17, 41, 4, 64, 37, 76, 14, 79, 23, 20, 31, 10, 60, 67, 28, 82, 3, 57, 18, 25, 75, 54, 65, 62, 6, 71, 9, 48, 21, 81, 44, 68, 74, 39, 19, 50, 80, 30, 49, 24, 40, 58, 12, 78, 52, 77, 16, 59, 47, 32, 72, 70, 34, 63,... | 1 |
construct-rlve-prefix-product-permutation-l2-s1 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_41 of the integers 1, 2, ..., 41 such that the 41 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_41 are pairwise distinct modulo 41.
Answer format: {"perm": [p_1, ..., p_41]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 41, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 22, 15, 32, 34, 8, 7, 37, 33, 38, 16, 25, 20, 4, 12, 19, 30, 17, 14, 40, 3, 29, 26, 13, 24, 31, 39, 23, 18, 27, 5, 10, 6, 36, 35, 9, 11, 28, 21, 41]} | 1 |
construct-rlve-prefix-product-permutation-l2-s2 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_97 of the integers 1, 2, ..., 97 such that the 97 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_97 are pairwise distinct modulo 97.
Answer format: {"perm": [p_1, ..., p_97]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 97, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 50, 66, 74, 40, 82, 15, 86, 55, 69, 54, 90, 16, 8, 14, 92, 41, 28, 47, 35, 38, 76, 39, 94, 67, 57, 19, 53, 88, 56, 73, 95, 51, 21, 62, 63, 22, 24, 6, 18, 72, 68, 89, 87, 70, 20, 65, 96, 3, 34, 79, 29, 12, 10, 31, 27, 81, 93, 75, 77, 36, 37, 78, 48, 4, 26, 43, 11, 46, 80, 42, 32, 5, 60, 23, 61, 64, 52, 7... | 1 |
construct-rlve-prefix-product-permutation-l2-s3 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_43 of the integers 1, 2, ..., 43 such that the 43 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_43 are pairwise distinct modulo 43.
Answer format: {"perm": [p_1, ..., p_43]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 43, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 23, 30, 12, 27, 37, 38, 28, 25, 14, 5, 19, 11, 41, 24, 36, 39, 13, 35, 29, 42, 3, 16, 10, 32, 6, 9, 21, 4, 34, 26, 40, 31, 20, 17, 7, 8, 18, 33, 15, 22, 43]} | 1 |
construct-rlve-prefix-product-permutation-l2-s4 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_89 of the integers 1, 2, ..., 89 such that the 89 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_89 are pairwise distinct modulo 89.
Answer format: {"perm": [p_1, ..., p_89]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 89, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 46, 31, 68, 19, 16, 52, 79, 11, 10, 82, 53, 49, 71, 7, 40, 22, 6, 76, 50, 18, 86, 32, 27, 58, 25, 34, 36, 44, 4, 24, 65, 28, 56, 29, 48, 78, 83, 17, 70, 77, 54, 30, 88, 3, 61, 37, 14, 21, 74, 8, 13, 43, 62, 35, 63, 26, 67, 87, 47, 55, 57, 66, 33, 64, 59, 5, 73, 41, 15, 85, 69, 51, 84, 20, 42, 38, 9, 81,... | 1 |
construct-rlve-prefix-product-permutation-l2-s5 | construct | rlve_prefix_product_permutation | cf487c_prefix_product_sequence | number_theory | competition | 2 | RLVE-Gym/prefix_product_mod_distinct_permutation | MIT | [] | Find a permutation p_1, ..., p_73 of the integers 1, 2, ..., 73 such that the 73 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_73 are pairwise distinct modulo 73.
Answer format: {"perm": [p_1, ..., p_73]}
Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.jso... | {"n": 73, "family": "rlve_prefix_product_permutation", "subset": "construct"} | null | null | null | {"perm": [1, 2, 38, 50, 56, 45, 62, 22, 65, 66, 23, 21, 68, 46, 48, 40, 33, 44, 70, 51, 12, 8, 11, 55, 71, 39, 60, 47, 61, 69, 57, 34, 17, 32, 59, 49, 72, 3, 26, 16, 43, 58, 41, 18, 6, 14, 28, 15, 36, 4, 20, 64, 67, 63, 24, 5, 31, 42, 35, 27, 29, 7, 54, 52, 9, 10, 53, 13, 30, 19, 25, 37, 73]} | 1 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.