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'm confused about your problem. It states "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" So although you may not have known from the first sentence what weeks meant, it is clarified later.

Further, you found one example where there is a succession of 20 games. The goal of the problem is to prove there *always* exists that succession.

Posted by Gamer on 2008-10-02 01:35:08