Multiple choice general knowledge math & puzzles

In a city called Veldhoven the following facts are true: No two inhabitants have exactly the same number of hairs. No inhabitant has exactly 40360 hairs. There are more inhabitants than there are hairs on the head of any one inhabitant. What is the largest possible number of inhabitants of Veldhoven (knowing that the number of inhabitants is not infinite)?

  1. 0

  2. 40359

  3. 40360

  4. 40361
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C Correct answer
Explanation

Let N be the number of inhabitants. Each has a unique number of hairs. If the max hairs is H, then N > H. If no one has 40360 hairs, and each has a unique count, the counts could be 0, 1, ..., 40359, 40361... To satisfy N > H, the max possible N is 40360 (with hair counts 0 to 40359).

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