Comments on: How to Find a Mathematician’s Hat Colour

By: Vlad

Vlad — Tue, 11 Jan 2011 20:15:50 +0000

Well, it’s a year and a half later and I just realised I made a really silly mistake when considering the many-person version.

Don’t worry, the 3-person version stands as it is. But with any higher number of people, they can just agree in advance that all except three will pass, then ignore those extra people, essentially reducing the problem back to the 3-person version.

(Credit goes to John above, who realised this tidbit in September 2009.)

By: Livvloooo

Livvloooo — Thu, 22 Oct 2009 22:05:54 +0000

Nice.

By: Vlad

Vlad — Mon, 14 Sep 2009 20:03:43 +0000

@John:

That’s a pretty cool solution.

But the way the problem is set, they have to answer simultaneously. So no waiting for the one guy to pass

By: John Halvorsen

John Halvorsen — Mon, 14 Sep 2009 13:05:53 +0000

The solution is extremely simple.
No matter how many people are in the room, all but three pass.
Then at least two of them are guaranteed to have the same hat color – one person who sees the same color then passes.
The remaining two people then know they are wearing the same color hat and both say the color of the hat on the other’s head. They win 100% of the time.

By: Vlad

Vlad — Wed, 06 May 2009 17:25:35 +0000

@shadowart:
Yes, that’s allowed.

By: shAdOwArt

shAdOwArt — Wed, 06 May 2009 16:03:44 +0000

Will the players recognize each other while playing the game? This is relevant to whether “player X should look at the color of player Y’s hat, and then guess” strategies are allowed.