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.)

(In reply to Solution by Brian Smith)

Regarding

"I shot more ducks than two days ago" means d8>d6>d4>d2 and d7>d5>d3>d1.
"But fewer than a week ago" forces d1 to d8 to satisfy the following inequality:
d7>d5>d3>d1>d8>d6>d4>d2

But d2 has to be greater than d0 (not mentioned but must be existing) while d7 must be less than d0 (so we can't ignore it on the assumption that he wasn't hunting then). So d6 is the last day it would work.

Posted by Charlie on 2003-11-07 11:23:44