趣味题
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 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=936 336 个解 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}} 336 个解
northwolves 发表于 2010-6-10 14:18 http://bbs.emath.ac.cn/images/common/back.gif
有168组：
wayne 发表于 2010-6-10 14:22 http://bbs.emath.ac.cn/images/common/back.gif
呵呵,看来northwolves 忽略下一个基本的关系了a+b=b+a.... 用什么语言算出来的? 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 试求笔算之捷径，未果。
还是贴出Mathematica代码吧：data=Select & /@ Permutations]]], Total[#] == 2 Max[#] &]统计右值的个数：data[] // Tally // Sort{{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}} Mathematica代码颇有些函数式语言的味道 9# 无心人
函数式只是 Mathematica 编程的一种可选风格。
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