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Message: <blockquote data-quote="IceM1" data-source="post: 2388489" data-attributes="member: 822155">...contestants are placed in groups of..? Consider a track meet with k^n contestants. In each round, the remaining contestants are placed in groups of size k. The winner in each group advances to the next round.a) Use this to give another combinatorial proof that k-1 divides k^n-1.b) How many races are run in the entire competition?</blockquote>