For many years now Baron GŁnnstefen 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.)
Denote the Baron's sequence of ducks as d1, d2, d3, d4, d5, d6, d7, d8, and d9.
Eight days is possible.
"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:
Nine days is impossible. The quote from the problem requires d2>d9>d7, but the inequality for eight days has d7>d2.
The answer to the problem is eight days.