More hat-wearing problems
Apr. 17th, 2015 11:33 am![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackA friend on facebook linked to a variant of the 100 hats puzzle I talked about at: http://cartesiandaemon.livejournal.com/232415.html?nc=21
Suppose there are 100 scientists (or logicians, or philosophers...) and 101 hats. As in the other puzzle, the scientists are told the rules, allowed to confer, and then not allowed to speak. They're lined up all facing the same way, so the one at the back can see everyone else's hats, and the one at the front can see no-one's hats. And no-one can see their own hat.
The hats are numbered "1" to "101". The hats are placed randomly on the heads of the scientists, with one unknown hat left over. In any order the scientists can guess what hat they're wearing. But can't guess a number that was previously guessed.
What's the maximum number of scientists you can get to guess right?
If you have that, can you do it if there are 102 hats and two are left over? I genuinely don't know the answer to that one.
Hints in the comments.
Suppose there are 100 scientists (or logicians, or philosophers...) and 101 hats. As in the other puzzle, the scientists are told the rules, allowed to confer, and then not allowed to speak. They're lined up all facing the same way, so the one at the back can see everyone else's hats, and the one at the front can see no-one's hats. And no-one can see their own hat.
The hats are numbered "1" to "101". The hats are placed randomly on the heads of the scientists, with one unknown hat left over. In any order the scientists can guess what hat they're wearing. But can't guess a number that was previously guessed.
What's the maximum number of scientists you can get to guess right?
If you have that, can you do it if there are 102 hats and two are left over? I genuinely don't know the answer to that one.
Hints in the comments.
no subject
Date: 2015-04-17 06:10 pm (UTC)