Sunday, July 10, 2016
An infinite hat problem and later a point
Problem: There are an infinite number of people. They are labelled 1,2,3,... (I am not a number, I am a free man!) There is the Master who I call The Master. The Master will, at the same time, put a hat on each persons head. Some of the hats are RED, some are BLUE. (Clarification added later- everyone can see all the peoples hat colors except their own.)
The people will then all, at the same time, yell out a hat color. (Clarification added later- NO other form of communicationis allowed.)
If only a finite number of them get their own hat color wrong they win (not sure what they win, but they win!)
If an infinite number of them get their own had color wrong, then they lose.
They can discuss strategy ahead of time; however, The Master overhears all conversation.
Assume that the people and The Master are experts at this game.
Who would you bet to win? How much and at what odds?
I'll post the answer, a meta question about it, and another math question, on Thursday.
Feel free to post your answer as comments. If you do then please also comment on if you've seen the problem before since I'm curious (1) how well known the problem is, and (2) how hard it is to solve if you haven't seen it.
If you want to try to solve it yourself, don't look at the comments in case the right solution is there.