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Assume Smallvile has N male residents. Because of the third condition, the maxumum number of hairs on the head of any of them must be N-1. Also, because of the first condition, each man has a different number of hairs on their head. For this to be true, for any number from 0 to N-1, there has to be a male resident with that many hairs on their head.
If even one number from 0 to N-1 is not represented, there are no longer enough numbers for all the male residents to have a different hair count.
Since we know that the number 1003 in not represented, N cannot be such that N-1 >= 1003. Thus, N <= 1003, and 1003 is the maxumum number of men living in Smallvile. |
