小明有a頭牛,每頭賣a元,將賺來的錢與小健分,分法是拿10元給小明,再拿10元給小健,如此分法,經過y次,由小明拿到10元後,剩餘的錢不足10元(有剩餘),求剩下多少錢？ 幾天後再公佈.............
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訪客 (未驗證)

2005-06-29 22:00
將所有正整數以十為模分為十類
依據題目...其十位數字應為奇數
又(10n)^2=100n^2
(10n+1)^2=100n^2+20n+1
(10n+2)^2=100n^2+40n+4
(10n+3)^2=100n^2+60n+9
(10n+4)^2=100n^2+80n+16
(10n+5)^2=100n^2+100n+25
(10n+6)^2=100n^2+120n+36
(10n+7)^2=100n^2+140n+49
(10n+8)^2=100n^2+160n+64
(10n+9)^2=100n^2+180n+81
其中僅10n+4&10n+6兩組十位數字為奇數
故剩餘的錢為6圓