Thank you to everyone who commented, emailed, or puzzled along in silence.
If you enjoyed any of my preambles here, I promise you plenty of intrigue over there.
In the first puzzle, the group can guarantee that all but one person survives.
Photo: Maryna Babych (Shutterstock)
The person in the back has no information about their hat color.
The person in the back will count up the number of red hats they see.
Now, how can the next person in line deduce their own hat color?
They see eight hats.
Thats enough information to deduce that their hat must be red to make the total number of reds even.
If they say blue, then everybody else passes and the group wins unless all ten hats are red.
If the person in back passes, then that means they saw some blue hat ahead of them.
Otherwise, they pass.
The first person in this situation guesses blue.
The probability that all 10 hats are red is 1/1,024, so the group wins with probability 1,023/1,024.
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