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G@ry 寫到:只要不是四位相同就行了...#ed_op#BR#ed_cl##ed_op#BR#ed_cl#三位相同是可以的...#ed_op#BR#ed_cl#e.g. 2221-1222 = 999, 9990-999=9801, 9810-189=9621, 9621-1269=8352, 8532-2358-6174..
#ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#嗯，這個，我們都把得出來的999，直接當3位數字，而不是四位數字0999，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#因為它同樣可以記作00999，000999......無限多個可能，所以不作考慮。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而平常的四位數字如1100-0011，是固有的1100，倒轉，不能自己任意加0上去，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不然可能性將會有無限多個如7421不可記作07421等#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#當然，如果說沒顯示的可以自己加0組成一同樣的四位數，你是對的。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不過我最大的疑問是怎麼會這樣= =...而不是其條件，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#因為他最初提出時是指4個不同數字，後來又說不是4個相同就可以，#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我就跟他說3個相同可能會去到3位數，不應該硬加0上前面當4位..#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#

e.g. 2221-1222 = 999, 9990-999=9801, 9810-189=9621, 9621-1269=8352, 8532-2358-6174..

### [數學問題]一四位數按順序排列相減必得出一固定數

#ed_op#DIV#ed_cl##ed_op#DIV#ed_cl#一個四位數，若按大至小順序排列再減以其按小至大順序排列，得出一數亦按大至小順序排列再減其按小至大順序排列，最後必會得出一四位數6174，何解#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(組成該四位數的四個數不能有三個或四個數相同)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#[即不能出現aaaa，因為相減只會得0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#或aaab因為若a=b+1或a=b-1，相減會得出999]#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#例：7942&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;1100&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 5453#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#9742-2479&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;1100-0011&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5543-3455#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#7632-2367&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 9810-0189&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8820-0288#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#6552-2556&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 9621-1269&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8532-2358=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#9963-3699&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8532-2358=6174&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp; 7641-1467=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#6642-2466&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7641-1467=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#7641-1467=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#7641-1467=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#DIV#ed_cl#之前一個同學問我的一個問題，我一直都想不通。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#當去到五位數時卻不能得出一固定的數了，會不斷在一堆數中徘徊，為甚麼？#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#當所有數不同時，五位數相減，最後得出的數永遠都會徘徊在[61974,82962,75933,63954]此五組數不斷重覆。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而當五位數中有部份相同時，都可能得出不同的某幾組數中徘徊。#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#&nbsp;#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(如四位數一樣，五位數的五個數不能有四個或五個數相同)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(即可能出現aaaaa，因為相減會得0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#或aaaab，因為若a=b+1或a=b-1，相減會得出9999)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#(即n位數中，不能有n個數或n-1個數相同)#ed_op#/DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#/DIV#ed_cl#