Three Hats Puzzler


I still haven’t figured out where the obfuscation is, but I wonder if this is intended to teach kids that there can be more than one answer.


There’s only one CORRECT answer.


It’s actually a simple logic problem…In fact in college for a class on logic…a variation of this is the first thing taught…Most of the students get it in just a few minutes…


Yeah, nevermind. I knew I should have waited until I could read it instead of listen to it. I misheard “the guy with the green hat” as “Mr. Green”.


It’s a microlesson in “cyclic permutations”. Given three things, there are only two ways they can be shuffled so that nothing is in its original position. (Take that fact as the equivalent of “no one is wearing a cap that matches his name”.) One of those two ways is eliminated by having the guy in the green hat respond insultingly to Mr White, strongly suggesting that they’re not the same person. (I’ve been to lunch with people where you can’t actually make that assumption; it’s fun to watch them argue with themselves over dividing up the tab.)


According to the transcript, the guy in the green hat said “Oh you stup’, that doesn’t mean anything, it’s just coincidence. Shut up and eat your doughnut.” I assume that “stup’” is short for “stupid”.


That was the obfuscation. Would people recognize that the guy in the green hat was answering Mr. White or take that as just being some color?


It’s a fun puzzle, but it isn’t rocket science. No “cyclic permutation” theory req’d etc. Just write them down on paper — all the possible ways the hats can be arranged. You’ll quickly see there’s only two ways the hats can be distributed among the three fellows, with nobody wearing his own hat color. The conversation implies Mr White is a different person than the fellow wearing the green hat. This fact eliminates one of the combinations, and the solution is therefore the other one. Most puzzle solvers get mixed up when they read “the man wearing the green hat” means “Mr Green”, which of course it doesn’t.

I’m no expert on these puzzles. But I did get the hat one correct. Finally, I got one! Last week they asked “what is this?”. Some part on a car. I thought the gadget which used to be made of cotton, leather, and steel wool was the muffler!