A chessmaster who has 11 weeks to prepare for a tournament decides to play at least one game every day, but in order not to tire himself, he agrees to play not more than twelve games during any one week (consider "week" as periods of 7 consecutive days, starting from the first day of preparation; that is: if the first day is Sunday, each one of the eleven weeks ends on each one of the next eleven Saturdays.)

Prove that there exists a succession of days during which the master will have played exactly twenty games.

I have already composed a reply twice, and posted, but they did not appear.  I will try once more (but without full elaboration).  There seems no ambiguity about "weeks".  The issue is with "a succession of days".  Perhaps pcbouhid meant, that we are to find (i.e. prove by example) a NUMBER of days such that for every subset of consecutive days of that number within the 77 days (11 weeks) exactly 20 games were played.  ??

 

Posted by ed bottemiller on 2008-10-02 11:19:18