將原先的牌按次序以4n+1,4n+2,4n+3,4n+4分類(n=0~12) 則其經一次變換後順序調整如下: 4n+1= > n+1,4n+2= > 14+n,4n+3= > 27+n,4n+4 = > 40+n 例如:15(4n+3,n=3),30(4n+2,n=7),21(4n+1,n=5),6(4n+2,n=1),15 當4n+1=n+1,4n+2=14+n,4n+3=27+n,4n+4=40+n時,將所求得的n值代入 我們可以發現,第1,18,35,52牌在每一次變換時都不會更動 其餘的牌經四次變換後會回到原先排序位置 以4n+1而言,其為數列1,5,9,13,17,21,25,29,33,37,41,45,49,經四次變換後分別為 (1,2,3,4,5,6,7,8,9,10,11,12,13),(1,14,27,40,2,15,28,41,3,16,29,42,4), (1,17,33,49,14,30,46,11,27,43,8,24,40),(1,5,9,13,17,21,25,29,33,37,41,45,49)
因此經由四次變換後所有牌會回到原先排序位置
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