求教二個數學題

1、Several football teams enter a tournament in which each team plays every other team exactly once. Show that at any moment during the tournament there will be two teams which have played, up to that moment, an identical number of games.

2、 (A) list the partitions of 8 into distinct terms
       (B) list the partitions of 8 into odd terms
       (C) Prove that the number of partitions of a positive integer n into distinct terms is equal to the number of partitions of n into odd terms, using the case n=8 for illustration

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