2002 Putnam B4

An integer $n$, unknown to you, has been randomly chosen in the

interval $[1, 2002]$ with uniform probability. Your objective is

to select $n$ in an **odd** number of guesses. After

each incorrect guess, you are informed whether $n$ is higher

or lower, and you **must** guess an integer on your next turn

among the numbers that are still feasibly correct. Show that you

have a strategy so that the chance of winning is greater than $2/3$.

一个你不知道的整数 $n$ 已在

区间 $[1, 2002]$ 具有均匀概率。你的目标是

在 **奇数** 次猜测中选择 $n$。之后

每次错误的猜测，您都会被告知 $n$ 是否更高

或更低，并且你**必须**在下一轮猜出一个整数

在仍然可能正确的数字中。表明你

有一个策略，使获胜的机会大于 $2/3$。