One is bald

Probability Level 3

In the town of Naogaon , the following facts are true:

  • No two inhabitants have exactly the same number of hairs.
  • No inhabitant has exactly 518 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 Naogaon ?

0 519 518 517

Farhabi Mojib by Farhabi Mojib , 23, Bangladesh

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1 solution

Nicole Tay
Aug 7, 2016

Note the case where one inhabitant is bald.

For number of hairs: 0, 1, 2, 3, ... 517 --> Total of 518 inhabitants

If there exists a person with 519 hairs, there would be 519 inhabitants (->|<-)

Hence there are only 518 inhabitants.

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