5 ms·
There's an infuriating variant, which I have as yet been unable to solve: An infinite sequence of people have either blue or brown eyes. They must shout out a
by Smaug123 13y ago
There's an infuriating variant, which I have as yet been unable to solve:
An infinite sequence of people have either blue or brown eyes. They must shout out a guess as to their own colour of eyes, simultaneously. Is there a way for them to do it so that only finitely many of them guess incorrectly?
- pavelrub 13y agoThis is not a variant of the puzzle above. This is a variant of the hat puzzle, and the solution requires some set-theory.
- anonymoushn 13y agoAnd none of them have any knowledge about anything?
- Smaug123 13y agoThey can all see everyone else's eyes. That is, person N can see person M's eyes, for all M,N. [I don't know whether it's possible or not - it feels not, but it has been hinted to me that it is possible.]
- miguelrochefort 13y agoThey could all shout "red". 0 is finite.
- thaumasiotes 13y agoTwo points: - It is very, very, very frequent in mathematics to describe a number as "finite" specifically to indicate that it is nonzero. This is because while zero is boundedly large, it is not boundedly small (it is "infinitesimal"). - The problem statement asks for finitely many to guess incorrectly, not for finitely many to guess correctly.