A new kind of hat puzzle!

A forum for good logic/math puzzles.

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Torn Apart By Dingos
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A new kind of hat puzzle!

Postby Torn Apart By Dingos » Mon Aug 09, 2010 2:07 am UTC

I'm loving the recent surge in puzzle threads here! I'll contribute one of my most recent favorite puzzles. I'm posting it in this forum because I think it requires more than just a trick to solve. During the years I've seen lots of hat puzzles on these forums, but I haven't seen this one. I saw this one on MathOverflow and I'll copy-paste the description from there. I'd love to see different solutions to this one!

"You have a hundred people and each one has a (natural) number between 1 and 100 written on his hat. (Numbers may repeat.) As usual, everybody can see only the numbers on other people's hats. Give these guys a strategy for guessing so that at least one will surely make the right guess. (They do not hear each other guesses.)"

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Re: A new kind of hat puzzle!

Postby aleph_one » Mon Aug 09, 2010 2:58 am UTC

Yay puzzles! This one's a classic, and I heartily recommend it to anyone who hasn't seen it, as it is quite beautiful.

I think this puzzle is the same as the one in this thread, making Torn Apart By Dingos a complete message-board criminal for posting something covered by a thread from 2006. :roll: If finitely many hats is too tame for you, also check out the infinite version.

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Factoids are just Datas that haven't grown up yet
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Re: A new kind of hat puzzle!

Postby jestingrabbit » Mon Aug 09, 2010 4:38 am UTC

Yeah, its been done... sorry :(

But it is definitely my favourite hat problem.
ameretrifle wrote:Magic space feudalism is therefore a viable idea.

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