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Answer by paste bee for An infinite hat puzzle variation—if we don't know our...
The prisoners cannot win for $\gamma = \omega^2$ even if there are only 2 colours and they know the entire sequence in advance! Assign colour $0$ to anyone whose position is a limit ordinal, and $1$ to...
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This solution, for an unknown position in an $\omega$-sequence with an arbitrary palette of colors for the hats, is apparently due to F. Galvin, American Mathematical Monthly Problem 5348,...
View ArticleAn infinite hat puzzle variation—if we don't know our place, can we still be...
An evil demon is holding uncountably many set theorists captive. He explains to us how he will presently arrange us into a well ordered sequence, with everyone facing the same direction upward in the...
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