Some of you may have seen this puzzle presented in various forms - I saw it recently on James Randi’s website. Below is the puzzle as he presented it, followed by my answer (which I SWEAR has to be right!). Randi told me I was wrong - I am hoping the Teeming Millions will either back up my answer, or help me to see the light. Either way, at least I’ll be able to sleep nights. Here goes…
{Curly, Larry, and Moe, having nothing much better to do one evening, agree to play a strange game. There are two red and three white caps in a drawer. They turn out the lights, each reaches into the drawer in the dark, removes one cap, and places it on his head. Then the drawer is closed, the lights are switched on, and the players sit down, each to try to guess which color of cap he himself is wearing. Fifteen minutes goes by.
Perhaps unlike others with the same names we might know about, these three chaps are pretty smart. Each knows that there might be ways, by observing, listening, and reasoning, of knowing what color of cap he’s wearing.
Curly is the first to speak. “This is a stupid game! Whose idea was this, anyway? And whose caps are these? I don’t know what color I’m wearing, and I don’t care! I want a cold beer!” And he calls the delicatessen downstairs to order a cold six-pack. Moe smiles, but stays silent.
Larry is next to break the silence. “I don’t know what color I’m wearing, either! I agree this is a dumb game! I might have a green cap, but I’d never know it! Let’s order in some pizza and play poker!” Moe smiles even more broadly. Then he speaks up.
“Well, I’m wearing a white cap! I’m absolutely certain, and I knew it before the beer was on its way! So pass me over a cold brew! And I’ll buy the pizza!”
And he’s right. He is wearing a white cap. He didn’t cheat. He figured it out.
Assume that all three guys are astute and clever, and that they speak the truth. Two questions: How did Moe know? And what was the distribution of caps?"}
Here was my answer, which I STILL think is right:
[They were ALL wearing white hats. Moe figured this out based on what he saw AND his friends’ behavior, but we can determine it without even knowing what he saw:
There’s no way the distribution was two red & one white, because if any one of them had seen two red hats on the others, he would have known immediately (they are all clever) that he himself must have a white hat on; yet no one spoke up right away - so 2R/1W is out.
Similarly, 1R/2W is eliminated - if anyone saw 1R/1W on his companions, he would realize that he was wearing white when the one he saw in white didn’t stand up to announce wearing white (which someone who had seen 2R would have done quickly).
So NO ONE was wearing a red hat, which is the only way three clever men would stay silent for so long.
They all saw two white hats on the others, but only Moe had the patience to wait for the others’ reaction to base his answer on.]
Randi e-mailed me back to tell me: “Nope. Try R-W-W. Would that work?” I replied that it WOULDN’T work, for reasons outlined above - if there was a red hat on anyone, they would have solved it rather quickly. He then told me that neither R-W-W nor W-W-W were correct! All that leaves is R-R-W (unless order matters, but we never established a M-L-C order to begin with!), which should have been solved instantaneously, not after 15 minutes!!! (Remember, he specifically said they were “truthful”, so if they knew an answer and sat on it, they violated that premise.)
He won’t post his answer until next Monday, 10/1 - I can’t wait until then! HHEEELLLLPP!!!