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Sums of Powers


The Sums of Powers contest has ended. Congratulations to our winners:

Position Winner Prize
1st Martin Piotte Montreal, Quebec, Canada Choice of a crystal plaque or any item from Bathsheba Sculpture.
2nd Rafaël Bocquet Paris, France Choice of a crystal plaque or almost any item from Bathsheba Sculpture.


These are the contestants who submitted the best solution for each problem. (Problems for which the best solution was found during the first 48 hours of the contest are omitted.)

Problem Score Solver Date Achieved
^16 0.993827160 Jeremy Sawicki Menlo Park, California, United States 10 Jul 2020 13:24
^17 0.991869919 Jeremy Sawicki Menlo Park, California, United States 3 Jul 2020 16:35
^18 0.995000000 Jeremy Sawicki Menlo Park, California, United States 16 Jul 2020 23:55
^19 0.995726496 Jeremy Sawicki Menlo Park, California, United States 12 Apr 2020 08:25
^20 0.995867769 Jeremy Sawicki Menlo Park, California, United States 13 Apr 2020 23:20
^21 0.997916667 Jeremy Sawicki Menlo Park, California, United States 17 Jul 2020 02:52
^22 0.998058252 Jeremy Sawicki Menlo Park, California, United States 10 May 2020 04:21
^23 0.998956159 Martin Piotte Montreal, Quebec, Canada 5 Jul 2020 14:50
^24 0.999056604 Jeremy Sawicki Menlo Park, California, United States 13 May 2020 22:22
^25 0.999536178 Martin Piotte Montreal, Quebec, Canada 5 Jul 2020 14:50
^26 0.999749812 Martin Piotte Montreal, Quebec, Canada 10 Jul 2020 10:55
^27 0.999868508 Martin Piotte Montreal, Quebec, Canada 13 Jul 2020 23:22
^28 0.999949495 Jeremy Sawicki Menlo Park, California, United States 27 May 2020 07:03
^29 0.999991983 Jarek Wroblewski Wroclaw, Poland 21 May 2020 22:38
^30 0.999994869 Rafaël Bocquet Paris, France 8 Jul 2020 04:06


These are the best solutions received for each problem in the contest:

Problem Score Solution
^16 0.993827160 162^16 => {1, 4, 5, 6, 7, 9, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 25, 27, 29, 30, 31, 33, 34, 37, 38, 39, 41, 43, 44, 46, 47, 49, 51, 53, 54, 55, 57, 59, 61, 62, 63, 64, 65, 67, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 83, 84, 85, 89, 90, 91, 92, 95, 96, 97, 99, 101, 102, 103, 105, 106, 107, 108, 109, 111, 113, 116, 117, 119, 123, 125, 128, 129, 131, 133, 134, 135, 139, 141, 143, 145, 147}
^17 0.991869919 123^17 => {3, 5, 7, 8, 9, 11, 13, 16, 17, 19, 30, 33, 34, 35, 38, 40, 41, 43, 51, 52, 54, 55, 58, 59, 60, 63, 66, 69, 70, 71, 72, 73, 75, 76, 81, 86, 87, 88, 89, 90, 92, 95, 98, 106, 107, 108, 120}
^18 0.995000000 200^18 => {1, 6, 7, 10, 11, 13, 14, 16, 25, 26, 29, 30, 31, 32, 35, 36, 37, 41, 43, 45, 46, 47, 50, 52, 54, 55, 57, 58, 62, 66, 69, 70, 73, 76, 77, 80, 81, 84, 87, 90, 95, 96, 97, 98, 102, 104, 107, 109, 112, 113, 114, 115, 116, 117, 120, 125, 126, 127, 128, 130, 134, 137, 139, 141, 142, 143, 144, 150, 155, 158, 159, 160, 161, 162, 168, 171, 172, 173, 176, 177, 183, 184}
^19 0.995726496 234^19 => {1, 3, 4, 8, 9, 12, 16, 18, 20, 21, 22, 24, 27, 28, 32, 35, 38, 39, 40, 44, 45, 46, 47, 50, 52, 59, 61, 63, 65, 66, 67, 69, 70, 71, 72, 73, 75, 78, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 94, 96, 99, 101, 102, 104, 105, 108, 109, 110, 115, 116, 118, 120, 123, 124, 125, 126, 132, 141, 144, 145, 147, 149, 158, 159, 160, 162, 163, 164, 165, 166, 171, 174, 177, 181, 182, 184, 185, 186, 190, 192, 194, 195, 196, 197, 203, 208, 209, 210, 212, 214}
^20 0.995867769 242^20 => {1, 2, 4, 9, 10, 11, 13, 17, 18, 22, 25, 26, 27, 30, 35, 38, 39, 40, 41, 42, 43, 47, 48, 49, 55, 57, 58, 60, 61, 65, 66, 67, 68, 70, 76, 77, 79, 80, 83, 89, 90, 91, 93, 97, 98, 101, 102, 103, 104, 108, 111, 113, 114, 117, 127, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140, 141, 144, 146, 148, 149, 151, 154, 158, 160, 162, 167, 171, 172, 174, 176, 179, 180, 188, 193, 195, 200, 204, 206, 210, 211, 212, 213, 215, 218, 222, 223}
^21 0.997916667 480^21 => {2, 3, 4, 5, 7, 11, 12, 13, 14, 15, 17, 19, 20, 21, 23, 25, 30, 33, 34, 38, 39, 40, 41, 44, 45, 46, 47, 48, 49, 50, 51, 53, 56, 57, 59, 60, 62, 63, 66, 67, 72, 77, 78, 79, 81, 85, 91, 93, 94, 97, 99, 105, 108, 109, 110, 111, 116, 120, 122, 123, 124, 128, 130, 133, 134, 136, 138, 139, 140, 145, 146, 151, 153, 154, 156, 157, 159, 162, 164, 165, 168, 171, 177, 180, 181, 183, 184, 188, 189, 190, 191, 192, 193, 194, 196, 200, 202, 206, 214, 219, 220, 221, 224, 226, 227, 228, 229, 230, 231, 232, 235, 238, 239, 240, 241, 242, 244, 247, 250, 252, 253, 257, 262, 263, 264, 265, 268, 269, 271, 275, 276, 278, 280, 281, 282, 284, 288, 289, 290, 292, 294, 296, 297, 300, 301, 303, 304, 307, 308, 310, 311, 312, 313, 315, 319, 326, 328, 331, 332, 333, 334, 338, 340, 341, 342, 343, 348, 349, 350, 352, 353, 356, 359, 361, 362, 364, 368, 369, 371, 372, 378, 381, 382, 385, 389, 390, 391, 392, 394, 398, 403, 404, 407, 410, 411, 412, 413, 414, 415, 417, 420, 427, 428, 430, 433}
^22 0.998058252 515^22 => {1, 5, 6, 9, 11, 16, 17, 18, 20, 24, 25, 28, 29, 31, 32, 34, 36, 38, 41, 44, 49, 50, 51, 52, 53, 56, 58, 59, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 79, 81, 82, 83, 87, 89, 90, 91, 92, 93, 95, 96, 97, 99, 100, 103, 105, 106, 107, 110, 113, 114, 115, 116, 117, 118, 121, 122, 127, 132, 134, 136, 137, 140, 143, 144, 145, 147, 148, 149, 150, 151, 152, 155, 156, 158, 160, 162, 164, 165, 166, 170, 174, 175, 176, 180, 182, 185, 186, 188, 189, 190, 192, 193, 198, 200, 202, 203, 205, 206, 207, 208, 211, 212, 214, 218, 220, 225, 227, 228, 230, 232, 234, 241, 242, 246, 249, 253, 254, 255, 258, 259, 261, 264, 267, 269, 271, 273, 274, 279, 280, 283, 286, 287, 288, 290, 291, 292, 293, 295, 298, 299, 300, 302, 303, 304, 305, 306, 309, 310, 311, 312, 313, 314, 316, 317, 319, 321, 322, 323, 324, 325, 327, 328, 329, 330, 331, 332, 333, 335, 337, 339, 343, 345, 346, 349, 352, 353, 354, 356, 357, 358, 363, 366, 371, 374, 378, 379, 380, 381, 382, 383, 385, 388, 391, 392, 393, 395, 396, 398, 401, 402, 403, 404, 406, 407, 408, 409, 411, 413, 414, 417, 419, 421, 423, 426, 427, 430, 431, 436, 437, 439, 445, 448, 449, 450, 451, 452, 454, 458, 459, 461, 464}
^23 0.998956159 958^23 => {2, 3, 5, 9, 14, 16, 17, 18, 19, 21, 22, 25, 26, 29, 31, 32, 38, 40, 42, 44, 45, 47, 49, 52, 53, 54, 55, 57, 58, 60, 64, 65, 66, 67, 72, 74, 75, 76, 77, 78, 83, 84, 85, 87, 91, 93, 103, 104, 106, 108, 109, 111, 113, 115, 117, 120, 121, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 140, 144, 148, 149, 151, 152, 153, 155, 157, 159, 161, 162, 164, 165, 168, 169, 170, 171, 173, 174, 175, 176, 180, 181, 183, 186, 187, 190, 192, 193, 194, 195, 198, 200, 201, 206, 207, 214, 218, 219, 221, 222, 223, 227, 230, 232, 236, 240, 244, 246, 247, 249, 252, 255, 257, 259, 262, 265, 267, 270, 273, 275, 277, 281, 283, 284, 285, 287, 289, 290, 291, 293, 295, 301, 304, 305, 307, 313, 318, 319, 321, 323, 324, 326, 328, 329, 334, 335, 336, 337, 339, 340, 341, 342, 346, 349, 350, 351, 352, 354, 356, 357, 358, 359, 360, 363, 364, 366, 368, 369, 370, 371, 372, 374, 376, 377, 378, 379, 383, 385, 387, 389, 391, 392, 393, 395, 399, 401, 402, 403, 404, 407, 408, 409, 411, 412, 414, 416, 418, 419, 421, 426, 428, 430, 431, 432, 438, 439, 440, 441, 442, 446, 447, 449, 450, 451, 452, 456, 457, 458, 464, 465, 466, 468, 473, 474, 477, 478, 479, 480, 482, 483, 485, 486, 489, 493, 494, 496, 497, 498, 501, 504, 508, 509, 510, 512, 513, 515, 517, 518, 521, 523, 526, 528, 530, 531, 533, 534, 536, 540, 541, 542, 544, 545, 549, 550, 551, 553, 555, 556, 560, 561, 562, 565, 566, 568, 570, 571, 575, 576, 577, 583, 585, 589, 590, 591, 592, 593, 595, 596, 599, 600, 601, 602, 605, 610, 612, 613, 615, 616, 618, 619, 622, 623, 628, 629, 630, 632, 640, 642, 643, 645, 646, 647, 648, 649, 650, 652, 653, 655, 656, 657, 658, 659, 661, 662, 664, 665, 669, 671, 672, 673, 676, 677, 678, 684, 686, 687, 689, 690, 692, 693, 694, 695, 698, 699, 703, 705, 707, 709, 713, 714, 715, 716, 724, 726, 727, 738, 744, 750, 756, 758, 760, 764, 766, 768, 770, 774, 776, 778, 782, 784, 786, 790, 792, 796, 800, 802, 806, 809, 812, 818, 822, 826, 830, 832, 834, 836, 842, 844, 846, 850, 852, 862, 870}
^24 0.999056604 1060^24 => {3, 4, 5, 7, 9, 13, 20, 21, 23, 27, 31, 32, 33, 36, 39, 41, 42, 43, 48, 51, 53, 54, 55, 56, 57, 59, 61, 65, 67, 68, 69, 71, 73, 77, 81, 83, 84, 86, 87, 90, 92, 96, 97, 99, 101, 105, 106, 108, 109, 115, 116, 120, 121, 122, 124, 126, 127, 130, 132, 135, 136, 137, 139, 140, 141, 142, 144, 151, 153, 155, 157, 158, 159, 165, 168, 170, 174, 178, 181, 184, 187, 191, 193, 194, 195, 196, 201, 202, 203, 206, 207, 210, 212, 213, 214, 218, 219, 221, 224, 227, 228, 232, 236, 241, 242, 243, 244, 249, 254, 255, 256, 258, 261, 263, 264, 265, 268, 269, 272, 273, 275, 277, 278, 280, 281, 284, 286, 287, 289, 291, 293, 296, 298, 299, 303, 305, 306, 307, 308, 310, 313, 314, 316, 319, 320, 321, 326, 329, 333, 334, 336, 337, 338, 341, 342, 343, 344, 345, 347, 350, 354, 357, 358, 363, 364, 366, 368, 369, 371, 373, 374, 378, 379, 380, 382, 384, 386, 392, 395, 396, 402, 403, 405, 408, 409, 412, 420, 421, 423, 424, 425, 429, 430, 432, 433, 434, 438, 440, 441, 445, 448, 451, 452, 455, 458, 460, 463, 464, 466, 468, 471, 472, 476, 480, 481, 482, 483, 484, 486, 490, 495, 496, 499, 500, 501, 504, 505, 506, 507, 508, 511, 513, 514, 515, 516, 517, 519, 520, 522, 524, 525, 526, 529, 531, 533, 535, 536, 537, 538, 539, 540, 541, 542, 543, 545, 547, 548, 550, 553, 554, 555, 560, 561, 563, 568, 569, 570, 572, 573, 576, 579, 581, 582, 586, 589, 591, 592, 594, 595, 598, 601, 604, 606, 610, 611, 613, 615, 616, 618, 620, 621, 625, 626, 628, 630, 632, 635, 637, 638, 639, 642, 643, 647, 653, 654, 655, 656, 657, 658, 662, 664, 665, 666, 668, 669, 674, 675, 679, 682, 686, 688, 689, 691, 693, 697, 698, 700, 701, 702, 703, 706, 707, 708, 709, 710, 711, 713, 714, 715, 716, 717, 724, 725, 728, 729, 736, 739, 740, 741, 744, 747, 750, 754, 755, 756, 759, 761, 762, 763, 765, 767, 768, 770, 771, 775, 777, 778, 779, 781, 782, 783, 784, 785, 789, 791, 792, 794, 797, 798, 800, 802, 803, 809, 810, 811, 814, 817, 819, 822, 825, 828, 829, 830, 832, 834, 838, 839, 843, 846, 847, 850, 851, 855, 864, 866, 869, 871, 872, 874, 876, 879, 880, 883, 886, 890, 891, 892, 893, 895, 896, 897, 900, 902, 903, 904, 905, 909, 910, 916, 917, 921, 922, 923, 925, 929, 930, 931, 932, 934, 935, 936}
^25 0.999536178 2156^25 => {1, 2, 3, 5, 8, 11, 12, 13, 15, 16, 23, 24, 25, 26, 29, 30, 34, 37, 38, 41, 42, 46, 47, 49, 53, 54, 55, 56, 57, 58, 59, 61, 63, 68, 69, 71, 72, 73, 74, 76, 78, 79, 80, 81, 82, 83, 85, 87, 89, 90, 91, 93, 95, 96, 97, 98, 99, 101, 103, 104, 105, 108, 111, 112, 113, 117, 119, 120, 127, 128, 131, 132, 135, 136, 137, 140, 141, 144, 147, 150, 151, 153, 155, 156, 158, 159, 165, 167, 169, 170, 171, 174, 176, 177, 179, 181, 182, 183, 185, 186, 188, 192, 194, 195, 196, 198, 199, 200, 201, 204, 206, 209, 210, 211, 212, 213, 214, 215, 216, 217, 221, 224, 227, 228, 229, 234, 235, 236, 237, 240, 241, 242, 243, 244, 249, 250, 251, 252, 258, 260, 262, 264, 265, 266, 267, 268, 269, 271, 273, 274, 276, 278, 279, 280, 282, 283, 284, 286, 288, 289, 292, 296, 299, 301, 302, 303, 307, 308, 309, 311, 312, 314, 319, 320, 323, 325, 327, 329, 336, 339, 340, 341, 343, 351, 353, 355, 359, 362, 364, 368, 370, 372, 373, 374, 376, 377, 379, 381, 386, 391, 392, 395, 396, 397, 398, 399, 402, 408, 409, 410, 412, 414, 417, 418, 421, 422, 424, 425, 426, 429, 436, 439, 440, 442, 444, 445, 446, 447, 448, 449, 451, 452, 454, 456, 462, 463, 464, 465, 466, 468, 472, 474, 477, 478, 481, 482, 483, 485, 488, 489, 490, 493, 499, 500, 504, 507, 508, 512, 513, 515, 517, 524, 525, 526, 529, 531, 532, 533, 534, 540, 541, 543, 544, 546, 547, 551, 552, 553, 554, 558, 560, 563, 566, 567, 568, 571, 572, 573, 574, 575, 576, 578, 580, 582, 583, 584, 585, 586, 589, 590, 591, 592, 593, 596, 600, 601, 603, 613, 615, 616, 617, 618, 621, 623, 624, 625, 627, 629, 631, 633, 634, 635, 637, 642, 645, 650, 651, 655, 656, 658, 660, 661, 665, 666, 673, 674, 675, 676, 677, 679, 680, 681, 682, 684, 685, 686, 687, 688, 691, 693, 695, 698, 699, 700, 702, 704, 705, 706, 710, 711, 717, 719, 722, 724, 725, 726, 728, 730, 733, 739, 740, 741, 744, 745, 748, 749, 751, 754, 758, 759, 760, 762, 764, 765, 768, 769, 772, 773, 775, 776, 780, 781, 783, 786, 787, 788, 789, 790, 793, 794, 798, 801, 802, 803, 805, 806, 807, 811, 813, 818, 819, 820, 823, 826, 827, 829, 832, 834, 835, 840, 845, 846, 847, 851, 852, 854, 855, 858, 859, 865, 867, 868, 869, 873, 874, 875, 877, 878, 879, 884, 888, 889, 893, 894, 898, 900, 902, 903, 907, 908, 909, 911, 912, 913, 917, 918, 919, 920, 921, 923, 925, 926, 927, 930, 931, 934, 936, 943, 945, 947, 950, 954, 956, 957, 958, 964, 966, 968, 970, 971, 972, 975, 978, 980, 981, 984, 985, 986, 987, 988, 991, 992, 994, 995, 997, 998, 1000, 1001, 1002, 1005, 1006, 1009, 1010, 1012, 1013, 1014, 1016, 1017, 1021, 1024, 1025, 1026, 1027, 1032, 1035, 1036, 1037, 1040, 1041, 1048, 1049, 1050, 1051, 1052, 1054, 1055, 1056, 1057, 1058, 1060, 1063, 1065, 1067, 1071, 1081, 1082, 1083, 1085, 1089, 1091, 1092, 1096, 1097, 1103, 1104, 1105, 1108, 1112, 1114, 1115, 1118, 1121, 1127, 1128, 1129, 1131, 1133, 1135, 1138, 1143, 1145, 1146, 1149, 1151, 1159, 1161, 1163, 1164, 1166, 1168, 1169, 1172, 1174, 1175, 1176, 1178, 1179, 1180, 1181, 1184, 1188, 1189, 1190, 1193, 1194, 1198, 1199, 1200, 1201, 1204, 1205, 1206, 1210, 1211, 1212, 1218, 1219, 1220, 1221, 1222, 1225, 1226, 1227, 1228, 1229, 1231, 1232, 1233, 1237, 1240, 1242, 1245, 1247, 1249, 1250, 1251, 1252, 1253, 1254, 1256, 1257, 1260, 1262, 1265, 1268, 1270, 1273, 1275, 1276, 1277, 1278, 1279, 1281, 1283, 1284, 1289, 1291, 1293, 1303, 1304, 1306, 1308, 1310, 1313, 1314, 1315, 1316, 1317, 1318, 1319, 1320, 1321, 1322, 1325, 1326, 1327, 1328, 1329, 1330, 1331, 1334, 1336, 1337, 1341, 1344, 1346, 1348, 1351, 1352, 1353, 1354, 1355, 1356, 1357, 1358, 1362, 1365, 1366, 1369, 1372, 1373, 1376, 1377, 1379, 1380, 1381, 1383, 1387, 1388, 1390, 1391, 1394, 1395, 1397, 1399, 1400, 1402, 1403, 1405, 1406, 1407, 1410, 1415, 1417, 1421, 1423, 1425, 1428, 1430, 1431, 1432, 1437, 1441, 1444, 1446, 1450, 1452, 1453, 1455, 1458, 1459, 1462, 1464, 1465, 1467, 1470, 1471, 1472, 1473, 1475, 1477, 1478, 1480, 1481, 1485, 1487, 1488, 1490, 1492, 1493, 1494, 1495, 1498, 1501, 1504, 1505, 1506, 1507, 1508, 1509, 1514, 1515, 1518, 1519, 1521, 1525, 1531, 1532, 1535, 1536, 1537, 1538, 1544, 1545, 1548, 1549, 1550, 1551, 1553, 1554, 1556, 1557, 1558, 1560, 1561, 1565, 1569, 1570, 1572, 1573, 1576, 1578, 1581, 1582, 1584, 1585, 1586, 1589, 1590, 1591, 1595, 1601, 1604, 1605, 1608, 1610, 1613, 1615, 1617, 1621, 1623, 1626, 1628, 1630, 1633, 1637, 1638, 1640, 1643, 1644, 1647, 1649, 1651, 1652, 1654, 1655, 1657, 1658, 1660, 1662, 1663, 1664, 1667, 1668, 1670, 1672, 1679, 1687, 1688, 1691, 1693, 1699, 1700, 1704, 1705, 1707, 1711, 1712, 1715, 1716, 1717, 1719, 1720, 1721, 1723, 1724, 1727, 1728, 1732, 1733, 1735, 1736, 1737, 1739, 1740, 1741, 1744, 1747, 1748, 1749, 1750, 1752, 1755, 1757, 1760, 1761, 1763, 1764, 1765, 1775, 1777, 1779, 1780, 1787, 1789, 1791, 1792, 1800, 1801, 1805, 1807, 1808, 1809, 1812, 1815, 1825, 1827, 1828, 1831, 1832, 1835, 1839, 1840, 1841, 1843, 1848, 1849, 1851, 1855, 1856, 1861, 1863, 1865, 1869, 1872, 1875, 1888, 1896, 1936}
^26 0.999749812 3997^26 => {3, 5, 6, 8, 9, 11, 15, 16, 17, 18, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 36, 40, 42, 43, 44, 47, 49, 51, 55, 56, 57, 59, 61, 62, 64, 67, 69, 70, 71, 72, 73, 75, 76, 77, 80, 81, 86, 87, 88, 91, 92, 93, 95, 97, 101, 103, 104, 106, 108, 112, 115, 118, 120, 122, 123, 124, 125, 126, 128, 131, 132, 134, 135, 136, 137, 138, 143, 145, 147, 148, 150, 151, 153, 154, 155, 156, 158, 160, 163, 164, 165, 166, 168, 169, 170, 172, 177, 178, 181, 182, 186, 188, 189, 190, 195, 196, 198, 201, 202, 208, 210, 211, 213, 214, 216, 218, 222, 223, 225, 226, 227, 228, 229, 231, 235, 236, 238, 239, 243, 244, 245, 246, 247, 249, 251, 258, 259, 261, 265, 268, 269, 270, 271, 274, 277, 281, 282, 284, 286, 287, 290, 291, 292, 299, 300, 301, 303, 307, 308, 309, 310, 311, 312, 314, 315, 317, 320, 325, 327, 329, 330, 333, 334, 339, 341, 342, 344, 346, 347, 348, 349, 350, 353, 354, 355, 356, 357, 359, 360, 361, 365, 366, 369, 370, 375, 381, 383, 384, 386, 388, 390, 391, 393, 395, 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^31 35.056977472 3^31 => {1, 2}
^32 36.155590920 3^32 => {1, 2}
^33 37.254203981 3^33 => {1, 2}
^34 38.352816785 3^34 => {1, 2}
^35 39.451429417 3^35 => {1, 2}
^36 40.550041934 3^36 => {1, 2}
^37 41.648654375 3^37 => {1, 2}
^38 42.747266766 3^38 => {1, 2}
^39 43.845879122 3^39 => {1, 2}
^40 44.944491456 3^40 => {1, 2}


The following noteworthy solutions were received after the contest ended.

Problem Solver / Score / Date
(Solution)
^21 Hans-Werner Paulsen 0.997716895 10 Sep 2021 09:33
438^21 => {2, 5, 6, 7, 8, 10, 12, 13, 14, 15, 17, 18, 19, 20, 22, 25, 27, 29, 30, 32, 33, 38, 41, 43, 44, 50, 53, 54, 56, 57, 58, 59, 60, 61, 63, 67, 70, 74, 76, 77, 79, 82, 85, 87, 91, 95, 99, 100, 101, 102, 106, 110, 111, 112, 115, 116, 119, 120, 124, 125, 126, 129, 130, 135, 137, 138, 140, 141, 146, 147, 148, 151, 153, 154, 155, 157, 158, 164, 165, 168, 169, 170, 172, 173, 176, 177, 181, 182, 184, 188, 189, 191, 194, 195, 196, 198, 199, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 212, 213, 216, 217, 219, 227, 228, 229, 233, 234, 236, 238, 239, 240, 241, 244, 245, 246, 247, 249, 250, 253, 255, 256, 258, 259, 260, 262, 263, 264, 271, 272, 273, 276, 280, 281, 282, 284, 285, 286, 288, 290, 292, 293, 298, 299, 301, 304, 306, 309, 311, 312, 313, 314, 319, 322, 323, 325, 326, 327, 328, 329, 331, 332, 333, 334, 335, 337, 338, 343, 346, 349, 351, 352, 354, 355, 356, 359, 363, 364, 365, 368, 369, 370, 372, 376, 378, 381, 384, 388, 394, 396, 403}
^23 Hans-Werner Paulsen 0.998931624 10 Sep 2021 09:35
936^23 => {2, 3, 4, 5, 6, 9, 10, 11, 12, 17, 19, 24, 25, 26, 33, 34, 35, 36, 37, 41, 44, 45, 46, 47, 49, 50, 52, 57, 61, 62, 63, 64, 66, 69, 75, 76, 78, 82, 83, 88, 89, 91, 92, 95, 96, 97, 98, 100, 107, 111, 113, 114, 119, 122, 123, 126, 127, 128, 130, 131, 133, 137, 138, 139, 142, 144, 146, 147, 149, 151, 152, 154, 156, 159, 161, 164, 169, 171, 172, 175, 176, 177, 180, 184, 185, 187, 188, 189, 191, 192, 193, 196, 200, 201, 203, 205, 206, 207, 213, 214, 215, 218, 219, 221, 223, 225, 227, 230, 232, 234, 235, 236, 239, 241, 243, 244, 245, 247, 248, 249, 251, 257, 259, 261, 262, 268, 269, 270, 272, 273, 276, 278, 279, 281, 283, 284, 285, 286, 289, 291, 292, 293, 294, 295, 297, 301, 302, 304, 305, 308, 312, 314, 316, 318, 320, 321, 323, 324, 325, 326, 327, 328, 329, 331, 334, 335, 336, 338, 341, 342, 344, 345, 346, 348, 349, 351, 353, 354, 355, 359, 360, 365, 367, 368, 370, 371, 373, 375, 378, 382, 384, 386, 388, 390, 392, 393, 398, 399, 400, 401, 402, 404, 409, 410, 411, 417, 419, 422, 423, 424, 425, 429, 433, 440, 441, 444, 445, 452, 454, 455, 456, 457, 458, 459, 461, 464, 465, 471, 475, 478, 480, 482, 483, 488, 489, 491, 492, 493, 495, 496, 500, 502, 503, 506, 507, 508, 511, 513, 515, 517, 518, 522, 524, 526, 527, 528, 529, 530, 533, 534, 535, 538, 539, 546, 550, 552, 554, 557, 558, 559, 560, 561, 564, 565, 569, 571, 572, 574, 577, 578, 579, 582, 584, 585, 586, 588, 589, 591, 592, 595, 597, 600, 601, 602, 605, 610, 612, 613, 615, 617, 619, 620, 622, 624, 632, 634, 636, 643, 644, 645, 647, 652, 653, 655, 656, 657, 661, 662, 663, 664, 665, 666, 667, 668, 669, 670, 671, 672, 673, 675, 680, 684, 687, 689, 690, 692, 693, 697, 700, 703, 705, 706, 708, 710, 711, 713, 714, 716, 720, 721, 722, 726, 729, 730, 733, 737, 743, 744, 746, 747, 748, 750, 751, 752, 753, 757, 759, 763, 764, 765, 766, 767, 769, 770, 772, 773, 774, 776, 782, 785, 786, 789, 790, 791, 798, 799, 800, 801, 802, 803, 804, 806, 810, 812, 813, 815, 816, 821, 824, 826, 827}