A group of people are each given red or green hats. They cannot see the color of their own hat, but can see the color of everyone else's hat. They are told that there are more green hats than red hats. They are also asked to raise their hand if they know the color of their own hat.
Assuming that the hat-wearers are reasonably intelligent, what must be true about the distribution of hats if everyone eventually raises their hand?
Solution
I had thought I had created a well-posed problem, but Paul Ottaway pointed out a flaw:
If the hat-wearers are intelligent enough to be able to determine how long it takes to follow through in a level of reasoning, then the answer is that any distribution of hats will eventually end up with all peoples' hands raised.
If at the outset the difference between the visible green and red hats is 0 or 1 then your own hat must be green. All people with green hats will see the same difference and all raise their hands simultaneously. The people wearing red hats will see a difference of 2 or 3 respectively and therefore cannot immediately deduce their own hat colour. After all people with green hats have raised their hands, however, they can then deduce their own hat must be red.
Following along this line, if after a reasonable amount of time no one raises their hand, we know that no member of the group can see a difference of 0 or 1. Therefore, if there are any members who see a difference of 2 or 3, they must have a green hat. As before, once all the people with green hats raise their hands, the people with red hats can then raise their hands since they were not part of the group that could have deduced their colour hat initially.
This now continues in the same vein. If after two reasonable lengths of time no one has raised a hand, then no one can see a difference of 0,1,2 or 3 hats. So, if there is someone who sees a difference of 4 or 5 hats, they know theirs is green. As usual, the remaining people must all have red hats and raise their hands afterwards.
Given the flaw, I was generous in awarding points for answers close to the above. Jeremy Alfred earned fours points plus the one point bonus for the first "mostly correct" answer. Other four point earners were Sarah Edwards and Jared Latiolais.