123456789
设九位数x,y,z(x>y)均为123456789的某个排列, 且 x/y≈z/10^8.求满足条件的所有x,y,z 这个定义不好:x/y≈z/10^8要不然我们找
$z/{10^8}<=x/y<{z+1}/{10^8}$的x,y,z 原帖由 mathe 于 2009-2-11 08:19 发表 http://bbs.emath.ac.cn/images/common/back.gif
这个定义不好:x/y≈z/10^8
要不然我们找
$z/{10^8}
描述得可能有些问题.我的意思是A/B结果取9位有效数字,正好也是1-9的一个排列 我觉得mathe描述没有问题
只是用$<=$和$<$替换你原来的$~~$
原来的“九位数x,y,z(x>y)均为123456789某个排列”仍然是问题的条件
不知我理解的对不？ 原帖由 kofeffect 于 2009-2-11 14:27 发表 http://bbs.emath.ac.cn/images/common/back.gif
我觉得mathe描述没有问题
只是用$
我的意思是商四舍五入小数点后取8位,所以还是有些出入.
我找到的一些解:
152463798÷123456789＝1.23495678
153942687÷123456789＝1.24693578
154263798÷123456789＝1.24953678
156734298÷123456789＝1.26954783
157246398÷123456789＝1.27369584
157468932÷123456789＝1.27549836
157894632÷123456789＝1.27894653
158974632÷123456789＝1.28769453
159847632÷123456789＝1.29476583
163945287÷123456789＝1.32795684
165784932÷123456789＝1.34285796
165798243÷123456789＝1.34296578
172398465÷123456789＝1.39642758
172546398÷123456789＝1.39762584
179863254÷123456789＝1.45689237
194258376÷123456789＝1.57349286
194875632÷123456789＝1.57849263
195468732÷123456789＝1.58329674
196874532÷123456789＝1.59468372
213897465÷123456789＝1.73256948
214756398÷123456789＝1.73952684
214768953÷123456789＝1.73962854
216893754÷123456789＝1.75683942
217689453÷123456789＝1.76328459
238941576÷123456789＝1.93542678
245389176÷123456789＝1.98765234
264153798÷123456789＝2.13964578
265183497÷123456789＝2.14798635
269831475÷123456789＝2.18563497
289613475÷123456789＝2.34586917
291873564÷123456789＝2.36417589
294715386÷123456789＝2.38719465
296143875÷123456789＝2.39876541
298467153÷123456789＝2.41758396
312946875÷123456789＝2.53486971
317528964÷123456789＝2.57198463
319462875÷123456789＝2.58764931
325418697÷123456789＝2.63589147
325861497÷123456789＝2.63947815
328196475÷123456789＝2.65839147
347592186÷123456789＝2.81549673
357429186÷123456789＝2.89517643
359714286÷123456789＝2.91368574
359861274÷123456789＝2.91487635
364792185÷123456789＝2.95481673
385762941÷123456789＝3.12467985
386129574÷123456789＝3.12764958
391268574÷123456789＝3.16927548
391726485÷123456789＝3.17298456
392158674÷123456789＝3.17648529
394721685÷123456789＝3.19724568
396871452÷123456789＝3.21465879
397245618÷123456789＝3.21768954
421937685÷123456789＝3.41769528
423187596÷123456789＝3.42781956
427315896÷123456789＝3.46125879
429576318÷123456789＝3.47956821
453728196÷123456789＝3.67519842
459817263÷123456789＝3.72451986
461923785÷123456789＝3.74158269
462579318÷123456789＝3.74689251
465298173÷123456789＝3.76891524
468952173÷123456789＝3.79851264
475823196÷123456789＝3.85416792
478631529÷123456789＝3.87691542
491537862÷123456789＝3.98145672
539162784÷123456789＝4.36721859
541379862÷123456789＝4.38517692
542168973÷123456789＝4.39156872
542816973÷123456789＝4.39681752
569481273÷123456789＝4.61279835
576814239÷123456789＝4.67219538
579243861÷123456789＝4.69187532
591648372÷123456789＝4.79235186
592137684÷123456789＝4.79631528
613248795÷123456789＝4.96731528
613782495÷123456789＝4.97163825
613784295÷123456789＝4.97165283
634528917÷123456789＝5.13968427
635418972÷123456789＝5.14689372
637528194÷123456789＝5.16397842
647925138÷123456789＝5.24819367
653849172÷123456789＝5.29617834
654127983÷123456789＝5.29843671
659417238÷123456789＝5.34127968
671258349÷123456789＝5.43719268
671452983÷123456789＝5.43876921
694215783÷123456789＝5.62314789
694715238÷123456789＝5.62719348
694715283÷123456789＝5.62719384
718264593÷123456789＝5.81794326
724658193÷123456789＝5.86973142
725461893÷123456789＝5.87624139
725831649÷123456789＝5.87923641
731658249÷123456789＝5.92643187
732854916÷123456789＝5.93612487
738561249÷123456789＝5.98234617
756481293÷123456789＝6.12749853
756493182÷123456789＝6.12759483
759241638÷123456789＝6.14985732
759843126÷123456789＝6.15472938
781425693÷123456789＝6.32954817
781462359÷123456789＝6.32984517
791834526÷123456789＝6.41385972
814657293÷123456789＝6.59872413
839275614÷123456789＝6.79813254
842369715÷123456789＝6.82319475
853794126÷123456789＝6.91573248
862379514÷123456789＝6.98527413
896134725÷123456789＝7.25869134
896257314÷123456789＝7.25968431
897463125÷123456789＝7.26945138
912574836÷123456789＝7.39185624
917236458÷123456789＝7.42961538
925347681÷123456789＝7.49531628
928561347÷123456789＝7.52134698
936125847÷123456789＝7.58261943
941258736÷123456789＝7.62419583
943186725÷123456789＝7.63981254
971524836÷123456789＝7.86935124
974631258÷123456789＝7.89451326
976834125÷123456789＝7.91235648
976835124÷123456789＝7.91236458
978415236÷123456789＝7.92516348
981647235÷123456789＝7.95134268
981745236÷123456789＝7.95213648
982513746÷123456789＝7.95836142 这个太多了吧
前面9位数为123456789的某个排列的也很多
No.1 157468932 / 123456789 = 1.27549836
No.2 157894632 / 123456789 = 1.27894653
No.3 158974632 / 123456789 = 1.28769453
No.4 159847632 / 123456789 = 1.29476583
No.5 165784932 / 123456789 = 1.34285796
No.6 165798243 / 123456789 = 1.34296578
No.7 179863254 / 123456789 = 1.45689237
No.8 194875632 / 123456789 = 1.57849263
No.9 195468732 / 123456789 = 1.58329674
No.10 196874532 / 123456789 = 1.59468372
No.11 213897465 / 123456789 = 1.73256948
No.12 216893754 / 123456789 = 1.75683942
No.13 238941576 / 123456789 = 1.93542678
No.14 245389176 / 123456789 = 1.98765234
No.15 264153798 / 123456789 = 2.13964578
No.16 267158943 / 123456789 = 2.16398745
No.17 267381954 / 123456789 = 2.16579384
No.18 298467153 / 123456789 = 2.41758396
No.19 298714365 / 123456789 = 2.41958637
No.20 312946875 / 123456789 = 2.53486971
............
估计mathe说的那种会很少 看错了，mathe在2#说的情况就是上面的结果了:) 估算一下,可以知道,结果的数目大概在$(9!)^3/{10^9}~=47784725.8$个,是多了些. 原帖由 mathe 于 2009-2-13 08:34 发表 http://bbs.emath.ac.cn/images/common/back.gif
估算一下,可以知道,结果的数目大概在$(9!)^3/{10^9}~=47784725.8$个,是多了些.
结果的准确数目为:22789411
http://blog.csdn.net/northwolves/archive/2009/02/17/3902646.aspx 是不是就是穷举?这样大家就不会太感兴趣了
而估计数目大概差了一倍是因为对于给定的两个数A,B,A>B,那么只允许使用A/B,而不能使用B/A.
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