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25 匹马找最快 3 匹

Horse Race

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

有 25 匹马，速度各不相同且恒定。跑道一次最多比赛 5 匹。

问：要保证找出最快的 3 匹马，最少需要多少场比赛？

You have 25 horses, each with a unique constant speed. There is a track that can race 5 horses at a time. You want to find the fastest 3 horses. What is the minimum number of races (heats) needed to guarantee finding the top 3?

解析

最少需要 7 场。

思路：

  1. 先把 25 匹分成 5 组各 5 匹，组内各跑 1 场，共 5 场，得到每组内部排序。

  2. 让 5 个组冠军再跑 1 场（第 6 场），确定冠军组及其他组的相对强弱。

  3. 只剩少量仍可能进入前三的候选（来自冠军组前 3、亚军组前 2、季军组前 1），再跑 1 场（第 7 场）即可确定总前三。

Original Explanation

The minimum number of races is 7. Strategy:

  1. Divide into 5 groups of 5. Run 5 races, one per group.
  2. Take each group’s winner and run the 6th race among those 5 winners.
  3. Based on the results, eliminate groups that cannot produce a top 3 contender, and run the 7th race among the plausible candidates only.
  4. The final top 3 in the 7th race are the 3 fastest overall.