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        riddles >> medium >> Exact batting average 80%
        
(Message started by: gkwal on May 3rd, 2007, 11:33am)
Title: Exact batting average 80%
Post by gkwal on May 3rd, 2007, 11:33am
At some point during a baseball season, a player has a batting average of less than 80%.  Later during the season, his average exceeds 80%.  Prove that at some point, his batting average was exactly 80%.
Title: Re: Exact batting average 80%
Post by Obob on May 3rd, 2007, 12:10pm
This is the first problem on the 2004 Putnam exam.
Title: Re: Exact batting average 80%
Post by Archae on May 3rd, 2007, 1:46pm
Furthermore, if the same situation exists and the inverse of the batting average (= 100% - [the batting average]) can be represented as a fraction of 1 over another integer, then at some point, the player's average was exactly the given percentage


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