趣味题

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趣味题 1～9有9个数字，三个三个一组，可能正好能组成一个加法等式 比如：124＋659＝783 给出所有的结果，使用工具不限制

northwolves

124+659=783 125+739=864 127+359=486 127+368=495 128+367=495 128+439=567 129+357=486 129+438=567 129+654=783 129+735=864 134+658=792 135+729=864 138+429=567 138+654=792 139+428=567 139+725=864 142+596=738 142+695=837 143+586=729 145+692=837 146+583=729 146+592=738 152+487=639 152+784=936 154+629=783 154+638=792 154+782=936 157+329=486 157+482=639 158+634=792 159+327=486 159+624=783 162+387=549 162+783=945 163+782=945 167+328=495 167+382=549 168+327=495 173+286=459 173+295=468 175+293=468 176+283=459 182+367=549 182+394=576 182+457=639 182+493=675 182+754=936 182+763=945 183+276=459 183+492=675 183+546=729 183+762=945 184+392=576 184+752=936 186+273=459 186+543=729 187+362=549 187+452=639 192+384=576 192+483=675 192+546=738 192+645=837 193+275=468 193+482=675 194+382=576 195+273=468 195+642=837 196+542=738 214+569=783 214+659=873 215+478=693 215+748=963 216+378=594 216+738=954 218+349=567 218+376=594 218+439=657 218+475=693 218+736=954 218+745=963 219+348=567 219+438=657 219+564=783 219+654=873 234+657=891 235+746=981 236+718=954 236+745=981 237+654=891 238+419=657 238+716=954 239+418=657 241+596=837 243+576=819 243+675=918 245+673=918 245+718=963 245+736=981 246+573=819 246+591=837 246+735=981 248+319=567 248+715=963 249+318=567 251+397=648 254+619=873 254+637=891 257+391=648 257+634=891 259+614=873 264+519=783 269+514=783 271+593=864 271+683=954 273+186=459 273+195=468 273+546=819 273+591=864 273+645=918 273+681=954 275+193=468 275+418=693 275+643=918 276+183=459 276+318=594 276+543=819 278+316=594 278+415=693 281+394=675 281+673=954 283+176=459 283+671=954 284+391=675 286+173=459 291+357=648 291+384=675 291+546=837 291+573=864 293+175=468 293+571=864 294+381=675 295+173=468 296+541=837 297+351=648 314+658=972 316+278=594 317+529=846 317+628=945 318+249=567 318+276=594 318+627=945 318+654=972 319+248=567 319+527=846 324+567=891 324+657=981 327+159=486 327+168=495 327+519=846 327+564=891 327+618=945 327+654=981 328+167=495 328+617=945 329+157=486 329+517=846 341+586=927 342+576=918 346+572=918 346+581=927 348+219=567 349+218=567 351+297=648 352+467=819 354+618=972 354+627=981 357+129=486 357+291=648 357+462=819 357+624=981 358+614=972 359+127=486 362+187=549 362+457=819 364+527=891 367+128=495 367+182=549 367+452=819 367+524=891 368+127=495 372+546=918 376+218=594 376+542=918 378+216=594 381+294=675 381+546=927 382+167=549 382+194=576 384+192=576 384+291=675 386+541=927 387+162=549 391+257=648 391+284=675 392+184=576 394+182=576 394+281=675 397+251=648 415+278=693 418+239=657 418+275=693 419+238=657 428+139=567 429+138=567 438+129=567 438+219=657 439+128=567 439+218=657 452+187=639 452+367=819 457+182=639 457+362=819 462+357=819 467+352=819 475+218=693 478+215=693 482+157=639 482+193=675 483+192=675 487+152=639 492+183=675 493+182=675 514+269=783 517+329=846 519+264=783 519+327=846 524+367=891 527+319=846 527+364=891 529+317=846 541+296=837 541+386=927 542+196=738 542+376=918 543+186=729 543+276=819 546+183=729 546+192=738 546+273=819 546+291=837 546+372=918 546+381=927 564+219=783 564+327=891 567+324=891 569+214=783 571+293=864 572+346=918 573+246=819 573+291=864 576+243=819 576+342=918 581+346=927 583+146=729 586+143=729 586+341=927 591+246=837 591+273=864 592+146=738 593+271=864 596+142=738 596+241=837 614+259=873 614+358=972 617+328=945 618+327=945 618+354=972 619+254=873 624+159=783 624+357=981 627+318=945 627+354=981 628+317=945 629+154=783 634+158=792 634+257=891 637+254=891 638+154=792 642+195=837 643+275=918 645+192=837 645+273=918 654+129=783 654+138=792 654+219=873 654+237=891 654+318=972 654+327=981 657+234=891 657+324=981 658+134=792 658+314=972 659+124=783 659+214=873 671+283=954 673+245=918 673+281=954 675+243=918 681+273=954 683+271=954 692+145=837 695+142=837 715+248=963 716+238=954 718+236=954 718+245=963 725+139=864 729+135=864 735+129=864 735+246=981 736+218=954 736+245=981 738+216=954 739+125=864 745+218=963 745+236=981 746+235=981 748+215=963 752+184=936 754+182=936 762+183=945 763+182=945 782+154=936 782+163=945 783+162=945 784+152=936

northwolves

336 个解

wayne

有168组： {{124, 659, 783}, {125, 739, 864}, {127, 359, 486}, {127, 368, 495}, {128, 367, 495}, {128, 439, 567}, {129, 357, 486}, {129, 438, 567}, {129, 654, 783}, {129, 735, 864}, {134, 658, 792}, {135, 729, 864}, {138, 429, 567}, {138, 654, 792}, {139, 428, 567}, {139, 725, 864}, {142, 596, 738}, {142, 695, 837}, {143, 586, 729}, {145, 692, 837}, {146, 583, 729}, {146, 592, 738}, {152, 487, 639}, {152, 784, 936}, {154, 629, 783}, {154, 638, 792}, {154, 782, 936}, {157, 329, 486}, {157, 482, 639}, {158, 634, 792}, {159, 327, 486}, {159, 624, 783}, {162, 387, 549}, {162, 783, 945}, {163, 782, 945}, {167, 328, 495}, {167, 382, 549}, {168, 327, 495}, {173, 286, 459}, {173, 295, 468}, {175, 293, 468}, {176, 283, 459}, {182, 367, 549}, {182, 394, 576}, {182, 457, 639}, {182, 493, 675}, {182, 754, 936}, {182, 763, 945}, {183, 276, 459}, {183, 492, 675}, {183, 546, 729}, {183, 762, 945}, {184, 392, 576}, {184, 752, 936}, {186, 273, 459}, {186, 543, 729}, {187, 362, 549}, {187, 452, 639}, {192, 384, 576}, {192, 483, 675}, {192, 546, 738}, {192, 645, 837}, {193, 275, 468}, {193, 482, 675}, {194, 382, 576}, {195, 273, 468}, {195, 642, 837}, {196, 542, 738}, {214, 569, 783}, {214, 659, 873}, {215, 478, 693}, {215, 748, 963}, {216, 378, 594}, {216, 738, 954}, {218, 349, 567}, {218, 376, 594}, {218, 439, 657}, {218, 475, 693}, {218, 736, 954}, {218, 745, 963}, {219, 348, 567}, {219, 438, 657}, {219, 564, 783}, {219, 654, 873}, {234, 657, 891}, {235, 746, 981}, {236, 718, 954}, {236, 745, 981}, {237, 654, 891}, {238, 419, 657}, {238, 716, 954}, {239, 418, 657}, {241, 596, 837}, {243, 576, 819}, {243, 675, 918}, {245, 673, 918}, {245, 718, 963}, {245, 736, 981}, {246, 573, 819}, {246, 591, 837}, {246, 735, 981}, {248, 319, 567}, {248, 715, 963}, {249, 318, 567}, {251, 397, 648}, {254, 619, 873}, {254, 637, 891}, {257, 391, 648}, {257, 634, 891}, {259, 614, 873}, {264, 519, 783}, {269, 514, 783}, {271, 593, 864}, {271, 683, 954}, {273, 546, 819}, {273, 591, 864}, {273, 645, 918}, {273, 681, 954}, {275, 418, 693}, {275, 643, 918}, {276, 318, 594}, {276, 543, 819}, {278, 316, 594}, {278, 415, 693}, {281, 394, 675}, {281, 673, 954}, {283, 671, 954}, {284, 391, 675}, {291, 357, 648}, {291, 384, 675}, {291, 546, 837}, {291, 573, 864}, {293, 571, 864}, {294, 381, 675}, {296, 541, 837}, {297, 351, 648}, {314, 658, 972}, {317, 529, 846}, {317, 628, 945}, {318, 627, 945}, {318, 654, 972}, {319, 527, 846}, {324, 567, 891}, {324, 657, 981}, {327, 519, 846}, {327, 564, 891}, {327, 618, 945}, {327, 654, 981}, {328, 617, 945}, {329, 517, 846}, {341, 586, 927}, {342, 576, 918}, {346, 572, 918}, {346, 581, 927}, {352, 467, 819}, {354, 618, 972}, {354, 627, 981}, {357, 462, 819}, {357, 624, 981}, {358, 614, 972}, {362, 457, 819}, {364, 527, 891}, {367, 452, 819}, {367, 524, 891}, {372, 546, 918}, {376, 542, 918}, {381, 546, 927}, {386, 541, 927}}

数学星空

336 个解 northwolves 发表于 2010-6-10 14:18

有168组： wayne 发表于 2010-6-10 14:22

呵呵,看来northwolves 忽略下一个基本的关系了a+b=b+a....

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用什么语言算出来的?

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我发现有的右值有8组解,有的有16组解 可以通过2个左值的个十百位对调产生 387+162=549 187+362=549 367+182=549 167+382=549 162+387=549 362+187=549 182+367=549 382+167=549 138+429=567 438+129=567 318+249=567 429+138=567 319+248=567 348+219=567 249+318=567 428+139=567 248+319=567 218+349=567 128+439=567 349+218=567 139+428=567 439+128=567 129+438=567 219+348=567

wayne

试求笔算之捷径，未果。 还是贴出Mathematica代码吧：

1. data=Select[Map[FromDigits /@ # &, Union[Sort@Partition[#, 3] & /@ Permutations[Range[9]]]], Total[#] == 2 Max[#] &]

复制代码

统计右值的个数：

1. data[[All, -1]] // Tally // Sort

复制代码

{{459, 4}, {468, 4}, {486, 4}, {495, 4}, {549, 4}, {567, 8}, {576, 4}, {594, 4}, {639, 4}, {648, 4}, {657, 4}, {675, 8}, {693, 4}, {729, 4}, {738, 4}, {783, 8}, {792, 4}, {819, 8}, {837, 8}, {846, 4}, {864, 8}, {873, 4}, {891, 8}, {918, 8}, {927, 4}, {936, 4}, {945, 8}, {954, 8}, {963, 4}, {972, 4}, {981, 8}}

无心人

Mathematica代码颇有些函数式语言的味道

wayne

9# 无心人 函数式只是 Mathematica 编程的一种可选风格。 ============================ 我最近开始尝试使用Haskell， 我发现我开始喜欢上Haskell了