...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?
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?