Hat Trick (riddle)

[Deku Trii]

The riddle says the men were versed in logic. That's riddle code to tell you that, "they wouldn't think of that," is not something you need to consider in your approach.

If switching hats/finding a way to look at one's own hat were a viable solution, they all would have done it immediately.

[CaptHayfever]

Add one of these clauses:
"They are all very proud men who refuse to back down from a challenge or take shortcuts by their code of honor, & thus will not simply look at their own hats."
or
"Their host will have executed any of the men who removes his own hat to check its color; however, the men did not know that until after they were already locked into playing the game."

Now are you guys happy?
Geez, at least my question was just a matter of misunderstanding the instructions.

And remember, "I'm-a Luigi, number one!"

[chibimod3]

The entire point I'm trying to make is that you can't force a riddle to be what you interpret. Logical men would think of this. The versed in logic part just means they are smart and have wisdom. But since no one is going to tell them they can just switch hats then the wouldn't try to begin with they would try for a complicated one and if that didn't work they would find the easy route.

[Deku Trii]

You know, you're right.

Actually, the simplest solution would be for each of them to slit their wrists and bleed all over their hats. Of course, they'll have to be careful to use enough blood to make the hat red, but not so much that they won't pass out when they attempt to stand up and leave.

[Ace Mercury]

I think the point of the riddle is that information is to be had when you know that other people don't have information. It's a subtle shift from knowing nothing to knowing that no one knows nothing, which then eventually resolves to a definite answer.

To avoid this particular solution to the riddle, of which the riddle is crafted around, is like eating the ingredients of your sandwich alphabetically; you can do it to spite the creator, but it's not doing you any good and people stare at you in the cafeteria.

[chibimod3]

So you're saying that if you don't give the exact answer the person who stated the riddle wants then you're wrong? A riddle is what who hears it makes of it not who states the riddle to the public. The answer makes the people think of their own answers and try to also accept the other answers that people give.

[Ace Mercury]

I'm not saying it's wrong, just like how there's no wrong way to eat a sandwich. I'm saying, okay, that's a somewhat valid answer given the literal interpretation of the riddle, but without that loophole you discovered, how would you answer the riddle?

So, yes, I'm trying to lure you to the answer I want, because it's the interesting answer. The "try to find reflective surfaces" answer was kind of interesting, but it's not really logic related. The "they take off their hats and look at it" answer is not particularly enlightening.

[chibimod3]

But the only problem with DT's I see is that after the 3rd to possibly the 5th hat it stops working due to the fact that there is such a high number logically you wouldn't assume that you are wearing a red hat. After that then it wouldn't come down to those who know the others hats but trying to figure out a way to discern your own hat through a guess and check style of thinking.

After running the problems through your head you eventually would have to come up with the conclusion that every answer you come up with to find your hat's color has a flaw therefore making it impossible to discern with 100% certainty the color of your hat.

[Deku Trii]

It doesn't stop working. The men aren't assuming they are wearing a red hat. The men are deducing they are wearing a red hat.

[Ace Mercury]

The solution is closely related to mathematical induction:
Mathematical induction - Wikipedia, the free encyclopedia

[chibimod3]

Like I said I understand up till around 4th hat but can you give an explanation to the fact that once it gets so high they still can figure it out.

[Deku Trii]

Spoiler Below

One person can figure out he has a red hat if he's alone in wearing red hats. Agreed?

With 2 red hat wearers, each red hat wearer sees 1 man with a red hat. Each man knows that if that one were the only wearer of a red hat, he could have figured out that he had a red hat and left. That means there is another red hat than the one each of them sees, which must be his own.

With 3 red hat wearers, each red hat wearer sees 2 men with red hats. Each man knows (by the logic in the previous paragraph) that if those 2 were the only wearers of red hats, they could have figured out that they had red hats and left. That means there is another red hat than the ones each of them sees, which must be his own.

With 4 red hat wearers, each red hat wearer sees 3 men with red hats. Each man knows (by the logic in the previous paragraph) that if those 3 were the only wearers of red hats, they could have figured out that they had red hats and left. That means there is another red hat than the ones each of them sees, which must be his own.

With 5 red hat wearers, each red hat wearer sees 4 men with red hats. Each man knows (by the logic in the previous paragraph) that if those 4 were the only wearers of red hats, they could have figured out that they had red hats and left. That means there is another red hat than the ones each of them sees, which must be his own.


With 6 red hat wearers, each red hat wearer sees 5 men with red hats. Each man knows (by the logic in the previous paragraph) that if those 5 were the only wearers of red hats, they could have figured out that they had red hats and left. That means there is another red hat than the ones each of them sees, which must be his own.

Do you see how this can be extended to work for any number of hats?

[chibimod3]

Ok I do now I was getting lost around five hats but I just wrote it out on word and a notepad to 15 and it makes a lot more sense now.