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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.

No noteworthy solutions have been received since the contest ended.