A few facts about the male population of Smallvile:

• No two male residents of Smallville have the same number of hairs on their heads.
• No male resident of Smallvile has exactly 1003 hairs on his head.
• There are more male residents of Smallvile than the number of hairs on the head of any of the residents.

So how many male residents of Smallvile can there be?

By condition 1 and condition 3 the number of male residents, R is one more than the number of hairs on the hairiest man, H, and each man can be given a unique number 0 ≤ h ≤ H which corresponds to the number of hairs on his own head.(One man is completely bald, no hairs, h = 0)

Since the above conditions requires that no number between 0 and H be skipped, then 1003 cannot be ≤ H, so H < 1003, and since R = H + 1, then R ≤ 1003. S ince nothing in the conditions listed prevents R from being 10, 20, 30, or any number (including 1, just the bald guy) we can't give an exact number for R.

Posted by TomM on 2002-09-12 17:03:09