For many years now Baron Günnstefen has gone to a lake every day to hunt ducks. Every day starting on August 1, 2000, he says to his cook: "Today I shot more ducks than two days ago, but fewer than a week ago." For how many days can the baron say this?

(Assume he is never lying.)

My initial instincts say that at most he could say this truthfully for 14 days. On the 14th day, he can not have shot fewer than a week ago, since we know he has been shooting progressively more and more ducks in every two-day period. Day 14 is the first day that we KNOW he has shot more on the seventh weekday than the first.

Posted by John on 2003-11-07 10:38:41