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September 18th, 2008, 01:14 PM   #1
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URGENT HELP !

25 wrestlers attend a tournament.

In each 5 wrestlers who are chosen randomly, there is at least one wrestler who played with the other four wrestlers.

How many wrestlers who play with the all wrestlers who attend the tournament can be there? (Minimum!)
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September 18th, 2008, 03:04 PM   #2
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Re: URGENT HELP !

I think the answer is 1.

Pair all the wrestlers up (except #25). Every wrestler plays every other wrestler *except* their partner. Since we select at random 5 wrestlers (an odd number), there must be at least one wrestler without their partner in the 5 - in which case, he will have played everyone else.

Agree?
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