Death to

Miscellaneous and Personal Stuff I Must Share
1

  1. No reputable or successful monarch would choose an advisor based on his ability to discern hat colors among 3 hats.

  2. The thought of George Bush, Ralph Nader, and Al Gore wearing hats and struggling to discern the color of these hats in order to win a debate has whimisical merit. Since this format has not been mentioned as a real possibility for the debates, however, it cannot be used to support the existence of “3 hat” puzzles in general.

  3. I know of no actual friends who have attempted to discern “3 hat” colors either as a form of amusement or as intellectual sparring. Even the extraordinary talents of the Straight Dope Message Board have not offered personal examples of “3 Hat” behavior. Careful study of available Dopefest photography yields no examples of “3 hat” horseplay.

  4. Therefore, because “3 hat” puzzles are inherently annoying, I move they be banned entirely from these boards.

That having been said, here is

A 5 Hat Puzzle:

The king is looking for a new advisor to join his current stable. After a kingdomwide search, you and another candidate are named finalists. Because he scored 1 point ahead of you on the prelims, your opponent gets first dibs at solving the puzzle. If he solves the problem correctly, you will not even get a chance, but should he fail you will receive the same puzzle. If you succeed, then you become the next HIGHLY PAID advisor.

The king is a fair-minded man and cares not who wins. However, word comes secretly to you that the king’s advisors, who design the puzzle, would rather you win. Your opponent does not know this. The king’s advisors are Larry, Moe, and Curly. They are identical triplets.

(Hmm…they must have heard about your three identical triplet sisters, who are very beautiful, and very very friendly.)

The first contest is held in private, and you are delighted to hear your opponent has failed. This is especially shocking as he is, you must grudgingly admit, a mathematical scholar of the highest order.

Now it is your turn to solve the exact same puzzle.

You are led into a room and blindfolded. A hat is placed on your head and the blindfold removed.

The king and his advisors surround you. Advisors #1 and #2 each wear a red hat. Advisor #3’s hat is white. The king (himself in a red hat)speaks:

“We are presenting this puzzle exactly as it was presented to your opponent. He failed. Let’s see how you do.”

“You have on either a red or white hat. However, some of our hats are special. If anyone wearing a special hat tells a lie, than all other special hats save his own will change color, either from white to red or from red to white. Regular hats are not effected by lies.”

“Each of my advisors will make a statement. After this round you will be asked to guess the color of your hat. If you are right, you will be my newest advisor. Now, I don’t know much about puzzles, I leave them to my advisors. But you should know 2 things:”

(pause)

“A. One of my advisors is blind.”

(“Oh great!” you think. You look around at the 2 red and 1 white hatted triplets. You cannot tell who is blind.)

“B. There are at most 2 special hats being worn in this room now.”

After the king’s making of statement B you note advisor #3’s hat turn red!

“Let the contest begin!” says the king. He removes his hat and tosses it into a closet and out of sight.

Advisor number #1 speaks:

“I see a white hat.”

After this statement you notice advisor #3’s hat turn back to white.

–

Advisor # 2 speaks:

“I do not see 2 red hats.”

After this statement you see no hats change color.

–

Advisor # 3 speaks:

“I am blind, so I can’t see anyone’s hat color.”

After this, of course, you see no hats change.

–

Now you must guess the color of your hat. Using your superior mind, and knowing everything you know, you say:

“The color of my hat is…”

Is what?

LONG LIVE 5 HAT PUZZLES!

2

Blue. It’s a trick. :smiley:

Serious SWAG: red

3

This thread was supposed to be titled “Death to 3 Hat Puzzles” but something went wrong. I blame the pro “3 hat” puzzle faction. Damn.

Death to 3 Hat puzzles!!

Long live 5 hat puzzles!!

4
5

My girlfriend also claims the answer is “red”. However, I disagree. I think the mistake everyone is making is in their refusal to acknowledge the words of advisor #3.

Death to 3 hat puzzles!
Long live 5 hat puzzles!

6

But I’m not sure there is an answer to this.

Advisor 1 says “I see a white hat.” At the time he says that, all three advisors are wearing red hats. Since Advisor 3’s hat changes colors, it must mean Ad 1’s statement was a lie. He saw no white hats, which must mean your hat was red.

So, at the time of the statement, you know your hat was red. The question is, is it white now?

Ad 2 is of no value, he doesn’t have a special hat.

Ad 3 really is blind, or else he’d have turned Ad 1’s hat white. So he’s of no help to you either.

End result. If you have a normal hat, it’s red now. If you have a special hat, it’s white. But as far as I can tell, there’s no way to know.

However, I would guess white merely because I believe there’s a better than 50% chance the other guy guessed red.

7

Hmmm…

After the king’s second statement, advisor #3’s hat turns red. Therefore, advisor #3 and the king are both wearing special hats. Also, the king is lying, so there are at least THREE special hats being worn.

Advisor #3’s hat didn’t change color after the king’s first statement, so one of the advisors really is blind.

Advisor #3’s hat turns white after advisor #1 says he sees a white hat. Therefore, advisor #1 is ALSO wearing a special hat (which must have turned white after the king made his second statement, even though we aren’t told it did). Advisor #1 is lying, so either advisors #2, #3, and I are ALL wearing red hats at this point (in which case #2’s hat is normal) OR advisor #1 is blind.

Advisor # 2 says he does not see 2 red hats. We know advisors #1 and #3 are wearing white hats at this point, so #2 must be telling the truth (regardless of whether he’s blind). We have no way to tell whether #2 is wearing a special hat.

Advisor # 3 says he’s blind, and no hats change color, so he must be telling the truth. Therefore #1 is not blind. So I was wearing a red hat when #1 made his FIRST statement. If my hat is a special hat, it turned white after this statement. If it’s a normal hat, it’s just plain red.

At this point, the problem seems unsolvable. But I have the additional information that my very clever rival guessed incorrectly when presented with an identical problem. I also know – thanks to the previous replies to this thread – that most people’s first instinct is to guess red.

“White, your Majesty.”

8

apologies

In the original puzzle it is not clear that special hats turn color whenever lies are told, not just lies by another wearing a special hat. However those wearing special hats and who tell lies will not have their hat turn color. Hope this didn’t cause too much of a problem.

Death to 3 Hat Puzzles
Long live accurate 5 hat puzzles.

9

Makes it sound like they’re only affceted by lies told by SH wearers…

10

OHHHHH!

In that case, advisor #1’s hat isn’t necessarily a special hat, and since we’re never told it changed color, I think we can assume it’s a normal hat. But at least three people are wearing special hats, or the king’s second statement would be true. Therefore, the king, advisor #3, and I are wearing special hats. Therefore, my hat is white.

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After reading this thing about twenty times, I think my hat is white, but it hurts my head to try to explain it.

I think the key is that the special hats have to change color whenever a lie is told, whether or not the lier is wearing a special hat.

If this is not the case, then please forget that I said anything.

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I should have read the other posters replies more closely.
:o