帕斯卡三角形 Pascal Triangle

in #cn7 years ago (edited)

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最近在cn 板看到一个数学题目, 题目是问说从A 到 B ,在从 B 到 C 只可以向上跟右走的话,一共可以用几个方式。。。

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很自然的,我一看到图就然我想起Pascal Triangle。 这个Pascal Triangle 对我来说有很多用途的。

为什么我对 Pascal Triangle 有种很熟悉的感觉呢?

原因是因为以前很喜欢赌博。 那赌博跟这个有何关系呢?

因为当时总是要算一个东西, 那就是如果我有 p 的胜算, q 的败算, 要在 n 盘里 胜x 盘的 胜算是多少。。。 这个时候总是会用到 binomial distribution

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用久了就会很习惯, 因为 pascal triangle 给的恰恰就是它的coefficient 。。 那个 nCr

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当然这个pascal triangle 还有很多有趣的 pattern

不过先声明,本人不是什么数学家,只是一个有点好赌的数学爱好者。。。

不过看看以下这个泰国餐馆的wifi password, 然后在看看上面那个binomial distribution 的函数。。。

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