Question

谁还能再写几道这样的等式?(少年谜组问)

谁还能再写几道这样的等式?(少年谜组问)

括号里填入数字1、2、3、4、5、6、7、8、9各一次,得数为整数.这样的等式成立吗?

()()()()()()()()÷()=整数

()()()()()()()÷()()=整数

()()()()()()÷()()()=整数

()()()()()÷()()()()=整数

Answer 1

每种型式都有很多算式，下面只列举一些：

1、()()()()()()()()÷()=整数，1132312个【除数大于1】：
902514376/8=112814297，902514378/6=150419063
902514678/3=300838226，902514683/7=128930669
902514687/3=300838229，902514736/8=112814342
902514738/6=150419123，902514768/3=300838256
902514786/3=300838262，902514867/3=300838289
902514876/3=300838292，902516384/7=128930912
902516478/3=300838826，902516487/3=300838829
902516748/3=300838916，902516784/3=300838928
902516847/3=300838949，902516874/3=300838958
902517348/6=150419558，902517368/4=225629342
902517384/6=150419564，902517438/6=150419573
902517468/3=300839156，902517486/3=300839162
902517648/3=300839216，902517684/3=300839228
902517834/6=150419639，902517836/4=225629459
902517846/3=300839282，902517864/3=300839288
902518374/6=150419729，902518376/4=225629594
902518463/7=128931209，902518467/3=300839489
902518476/3=300839492，902518647/3=300839549
902518674/3=300839558，902518734/6=150419789
902518736/4=225629684，902518746/3=300839582
902518764/3=300839588，902531478/6=150421913
902531748/6=150421958，902531768/4=225632942
902531784/6=150421964，902531874/6=150421979
902531876/4=225632969，902534176/8=112816772
902534178/6=150422363，902534718/6=150422453
902536418/7=128933774，902536481/7=128933783
902537148/6=150422858，902537168/4=225634292
902537184/6=150422864，902537416/8=112817177
902537418/6=150422903，902537814/6=150422969
902537816/4=225634454，902538174/6=150423029
902538176/4=225634544，902538714/6=150423119
902538716/4=225634679，902541376/8=112817672
902541378/6=150423563，902541678/3=300847226

2、()()()()()()()÷()()=整数，138263个：
41056392/78=526364，41056782/39=1052738
41056837/29=1415753，41056978/23=1785086
41056983/27=1520629，41057268/93=441476
41057289/63=651703，41057826/93=441482
41057892/36=1140497，41057928/36=1140498
41057982/63=651714，41058297/63=651719
41058392/76=540242，41058792/36=1140522
41058927/63=651729，41058936/72=570263
41058972/36=1140527，41058976/32=1283093
41059368/72=570269，41059386/27=1520718
41059683/27=1520729，41059728/36=1140548
41059862/37=1109726，41059872/36=1140552
41059872/63=651744，41059876/23=1785212
41062375/89=461375，41062859/37=1109807
41063598/27=1520874，41063895/27=1520885
41065392/87=472016，41065823/97=423359
41065839/27=1520957，41065879/23=1785473
41065893/27=1520959，41067538/29=1416122

3、()()()()()()÷()()()=整数，13803个：
5489370/162=33885，5489712/603=9104，5490728/136=40373
5490816/237=23168，5491206/378=14527，5491782/306=17947
5493670/182=30185，5493680/172=31940，5493760/128=42920
5496120/378=14540，5496870/123=44690，5497032/681=8072
5497230/186=29555，5497263/801=6863，5497306/218=25217
5497308/162=33934，5497380/126=43630，5497608/123=44696
5497632/108=50904，5498072/136=40427，5498160/372=14780
5498623/107=51389，5601483/279=20077，5601732/948=5909
5601789/423=13243，5601792/384=14588，5601879/243=23053
5601948/372=15059，5602483/197=28439，5602914/873=6418
5603287/419=13373，5603472/189=29648，5603472/918=6104
5603472/981=5712，5603821/479=11699，5604712/389=14408
5604831/279=20089，5604893/217=25829，5604921/387=14483
5604987/123=45569，5607294/318=17633，5607418/239=23462
5607492/138=40634，5608132/479=11708，5608197/243=23079
5608317/429=13073，5608734/291=19274，5608793/241=23273
5608932/147=38156，5608972/134=41858，5609142/378=14839
5609238/174=32237，5609412/783=7164，5609784/123=45608
5610384/729=7696，5610384/972=5772，5612490/738=7605
5612970/438=12815，5613480/279=20120，5613492/807=6956
5613720/489=11480，5613720/984=5705，5613894/702=7997

4、()()()()()÷()()()()=整数，1382个：
694278/5031=138，694320/1578=440，697034/2158=323
697410/2583=270，697410/2835=246，697452/1083=644
698054/7123=98，698105/3247=215，698420/3715=188
702534/8169=86，703296/1584=444，704358/1962=359
704685/1293=545，704691/2853=247，704835/6129=115
704862/1539=458，704916/3852=183，705128/4639=152
705618/3942=179，706182/9543=74，706248/5193=136
706398/2541=278，708124/3956=179，708136/4952=143
708294/3651=194，708412/3596=197，708564/1293=548
709254/1638=433，709326/4518=157，709536/1824=389
709632/1584=448，712065/3849=185，712380/4596=155
713496/5208=137，713508/9642=74，713904/2568=278
714086/5329=134，714560/8932=80，714582/3609=198
715360/8942=80，715806/2394=299，715860/3492=205
715968/2034=352，716240/8953=80，716320/8954=80

Answer 2

12345678÷9=1371742
3456792÷18=192044

Answer 3

98765432÷1=整数

9875436÷12=整数

Answer 4

用12456789这八个数无论怎么组合，最后只要除以3都得整数；用13456789者九个数无论怎么组合，只要是双数，最后除以2都得整数；