A Practical Guide To Quantitative Finance Interviews 收录了一些量化面试中的经典题目. 本文介绍的是来自第二章的「Counterfeit Coins 1」.

Counterfeit Coins 1 #

Problem #

There are $10$ bags with $100$ identical coins in each bag. In all bags but one, each coin weighs $10$ grams. However, all the coins in the counterfeit bag weigh either $9$ or $11$ grams. Can you find the counterfeit bag in only one weighing, using a digital scale that tells the exact weight?

Solution 1 #

将袋子编号为 $1$ 到 $10$, 从袋子 $i$ 取出 $i$ 枚硬币, 总共取出 $1 + 2 + \ldots + 10 = 55$ 枚硬币, 将这 $55$ 枚硬币放在秤上称量, 称重结果 $550 \pm i$ 告诉我们有问题的袋子编号, 以及问题出在轻还是重.