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Baker and cakes

A baker sells on the average 20 cakes in one day. What is the probability that he
sells an even number of cakes on any given day? (We assume ...


Five Pints in Space

Show that of any five points in R3 at least four are contained in a closed half-space with the origin O in its boundary.

Tags: math geometry

Even Clubs

In Eventown, with population n, every club has an even number of members. Strangely, any two clubs have an odd number of members in common. At most how many clubs ...

Tags: puzzle

擂台赛的策略

假设两队人马进行擂台比赛。开始两队各派一人比赛,获胜者留在台上,失败者所在一方再出一人于台上的人比赛,而且失败者以后不能再上台。如此下去,直到一方派不出人比赛时该方失败。

假设每个人的能力用一个正数表示。每场比赛的结果是互相独立的随机事件,能力a的人战胜能力b的人的概率永远是a/(a+b)。

现在一队永远派最强的人上场,这是最佳策略吗?如果你是二队的教练,你会采取什么策略?


Interval Scheduling

You have a resource (e.g. a conference room, a supercomputer) and many people request to use the resource for periods of time. Assume that the resource can be used by ...


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