沙漏煮蛋

Boiling an Egg with Two Hourglasses

专题: Brainteaser / 脑筋急转弯
难度: L2
来源: QuantQuestion

个人笔记

题目详情

你想把鸡蛋煮 15 分钟，但只有两个沙漏：一个 7 分钟，一个 11 分钟。如何最快测量出 15 分钟？

英文原题

Suppose you would like to boil an egg for exactly 15 minutes. But you only have two hourglasses: one for seven minutes and one for eleven minutes. What is the fastest way to measure 15 minutes?

解析

同时把 7 分钟与 11 分钟沙漏都翻转开始计时（记为 $t=0$ ）。

$t=7$ ：7 分钟沙漏漏完，立刻翻转它重新开始。
$t=11$ ：11 分钟沙漏漏完。此时 7 分钟沙漏自 $t=7$ 起已走了 4 分钟，还剩 3 分钟。把 7 分钟沙漏在 $t=11$ 再翻转一次，使其变为剩余 4 分钟。
$t=15$ ：7 分钟沙漏再次漏完，恰好过去 15 分钟。

因此可以最快精确计出 15 分钟。

英文解析

Flip the hourglass for 7 and 11 minutes at the same time to start timing (recorded as $t=0$ ).

- $t=7$ : Flip the hourglass after 7 minutes to start over.
- $t=11$ : 11 minutes of hourglass closure.At this point, the hourglass has been gone for 4 minutes since $t=7$ , and there are 3 minutes left.Flip the 7-minute hourglass again at $t=11$ to make it 4 minutes remaining.
- $t=15$ : The hourglass leaked again in 7 minutes, exactly 15 minutes.

Therefore, it is possible to accurately calculate 15 minutes as quickly as possible.