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.)
I've only had a quick look at this, but I've got a strategy where he can say it up to (and including) the 5th.
It goes a bit like this:
1st: Shot 1 duck (30th Jul shot 0, 25th shot 2)
2nd: Shot 1 duck (31st Jul shot 0, 26th shot 2)
3rd: Shot 2 ducks (1st shot 1, 27th shot 3)
4th: Shot 2 ducks (2nd shot 1, 28th shot 3)
5th: Shot 3 ducks (3rd shot 2, 29th shot 4)
On the 6th he cant say it as he can't shoot less than the 0 ducks he shot on the 30th.