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蜗牛爬 10 英尺杆

A snail is climbing up

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

一只蜗牛爬一根 10 英尺高的杆。它每天向上爬 3 英尺；每晚睡觉时会下滑 1 英尺。它什么时候到达杆顶？

英文原题

A snail is climbing up a 10- foot pole. It climbs up by three feet every day. Each night it sleeps. While sleeping, it slides down by one foot. When does it reach the top of the pole?

解析

除最后一天外，每过一昼夜净上升 2 英尺。

按“每天结束后（未下滑前）的高度”计算：

  • 第 1 天结束到 3 英尺，夜里滑到 2；
  • 第 2 天结束到 5，夜里滑到 4；
  • 第 3 天结束到 7，夜里滑到 6；
  • 第 4 天结束到 9，夜里滑到 8；
  • 第 5 天白天再爬 3 英尺到 11 英尺，在白天就已经到达（超过）10 英尺。

所以它在第 5\boxed{5} 天到达杆顶。

英文解析

Except for the last day, the height increases by a net 2 feet per day.

Calculating based on the height at the end of each day (before the nightly drop):

  • At the end of Day 1, the height reaches 3 feet, then drops to 2 feet at night;
  • At the end of Day 2, the height reaches 5 feet, then drops to 4 feet at night;
  • At the end of Day 3, the height reaches 7 feet, then drops to 6 feet at night;
  • At the end of Day 4, the height reaches 9 feet, then drops to 8 feet at night;
  • On Day 5, the height climbs another 3 feet during the day to reach 11 feet, arriving at (and exceeding) the 10-foot mark during the day.

Therefore, it reaches the top of the pole on Day 5\boxed{5}.