问一道离散数学题Assume that a chocolate bar consists of n squares arranged in a rect-angular pattern.The bar,a smaller rectangular piece of the bar,canbe broken along a vertical or a horizontal line separating the squares.Assuming that only one piece can be broken at a time,determine howmany breaks you must successively make to break the bar into n sep-arate pieces.Use strong induction to prove your answer.
问题描述：
问一道离散数学题
Assume that a chocolate bar consists of n squares arranged in a rect-
angular pattern.The bar,a smaller rectangular piece of the bar,can
be broken along a vertical or a horizontal line separating the squares.
Assuming that only one piece can be broken at a time,determine how
many breaks you must successively make to break the bar into n sep-
arate pieces.Use strong induction to prove your answer.
答
翻译：
把一块巧克力看成是由 n 块正方形组成的矩形,而其中更小块的矩形又可以或横或竖地被掰开成几块正方形.假设一次只能掰下一块,那么你要得到 n 块需要掰多少次?用数学归纳法证明你的答案.
先假设n=1,则需要掰 0次；
n=2,需要掰 1次
n=3,需要掰 2次
n=4,需要掰 3次
n=5,需要掰 4次
...
那么得出 n块需要掰 n-1次
然后再证明 n+1块 需要掰 n次就可以了