Multiple choice general knowledge math & puzzles

The founders of Hairytown decreed years ago that: 1. No two people can have the same number of hairs 2. No one can have 999 hairs. 3. No one can have more than, or the same number of hairs as, the population of the town The town has now reached its maximum population - what is it?

  1. 998

  2. 999

  3. 1000

  4. 1001
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

With population N, each person must have a unique hair count from 0 to N-1 (since no one can have N hairs). This gives exactly N possible values. The hair count 999 is prohibited, but if N=999, the allowed range is 0-998, which gives us exactly 999 unique values and avoids the forbidden 999 count entirely.

AI explanation

This is a pigeonhole-principle puzzle: with population N, hair counts must be N distinct values, all less than N (no one can have >= the population), so the natural pool is 0 through N-1. If N were 1000, the pool 0–999 loses the excluded value 999, leaving only 999 usable values for 1000 people — impossible. At N=999, the pool 0–998 never touches the excluded 999 at all, so exactly 999 distinct values are available for 999 people, which is the maximum that works.

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