[數學問題]一四位數按順序排列相減必得出一固定數
由 原來如此 於 星期二 三月 27, 2007 12:36 pm
#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# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#例:7942 1100 5453#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#9742-2479 1100-0011 5543-3455#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#7632-2367 9810-0189 8820-0288#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#6552-2556 9621-1269 8532-2358=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#9963-3699 8532-2358=6174 7641-1467=6174#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#6642-2466 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# #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# #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#