If There's a Loser, Everyone Else is Popular
In a class of
kids, any set of
kids contains at least one pair of friends. It turns out that in any possible arrangement, the most popular kid will have at least
friends. Find
.
Details and Assumptions
- Friendship is a mutual relation.
- The most popular kid is the kid with the most friends.
- If two people tie for most number of friends, then randomly select one of them to be the most popular.
- This problem is not original.
The answer is 1007.
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1 solution
The answer is 1 0 0 7 . Suppose the most popular kid has only 1 0 0 6 friends (or less). Then everyone but the most popular kid and his friends must be friends, so these people each have 1 0 0 7 friends, contradiction.