I heard a riddle once, which goes like this:
There are N lions and 1 sheep in a field. All the lions really want to eat the sheep, but the problem is that if a lion eats a sheep, it becomes a sheep. A lion would rather stay a lion than be eaten by another lion. (There is no other way for a lion to die than to become a sheep and then be eaten).
I was presented with this solution:
If there were 1 lion and 1 sheep, then the lion would simply eat the sheep.
If there were 2 lions and 1 sheep, then no lion would eat the sheep, because if one of them would, it would surely be eaten by the other lion afterwards.
If there were 3 lions, then one of the lions could safely eat the sheep, because it would turn in to the scenario with 2 lions, where no one can eat.
Continuing this argument, the conclusion is as follows:
If there is an even number of lions, then nothing happens.
If there is an odd number of lions, then any lion could safely eat the sheep.
But to me this seems utterly absurd. I think this is similar to the Unexpected Hanging Paradox (Link: http://en.wikipedia.org/wiki/Unexpected_hanging_paradox). I might have forgotten some assumptions, and those assumptions might actually solve this problem.
Is there a fault in the argument which I haven't discovered? Does anyone have any insights? Is the argument sound?