Tavel

This isn't a joke or anything, I'm seriously asking for your input. I'm actually getting pretty angry about this riddle because I'm seeing all wrong answers wherever I look.

A friend at work brought this in from his "logic" class (which always made me laugh). He asked me to figure it out, and I did, and he said "no you're wrong." And I said "how so?" and he couldn't prove me wrong...but wouldn't concede that I was right!

Basically, the riddle is here. http://mgonline.com/hats.html

There are 3 hats of color A, and 2 hats of color B (call them white and red respectively). Three people are wearing the hats (with the remaining two hidden). The people are then asked to discern the color of their hat by looking at the others'. They can only say "I know" or "I don't know"...not what colors they see.

The first two go and can't tell, but then the third person says his hat color without even looking...how could he know?

Here's a hint: the only way they could know the color of their hat is by observing two red hats. Then they know they're wearing a white hat because there are only 2 red hats.



Here's my answer:

I think he knew because he's wrong. He can't know.

The system is static, so you don't need to evaluate it in "order of observation." You only need to look at a few possible states (positions for the hats) to draw a conclusion.

Condition 1: they're all wearing white hats.
1. Person one looks and doesn't see 2 red hats - no conclusion.
2. Person two looks and doesn't see 2 red hats - no conclusion.
3. Person three is wearing a WHITE hat.

Condition 2: #1 and #2 have white, #3 has red.
1. Person one looks and doesn't see 2 red hats - no conclusion.
2. Person two looks and doesn't see 2 red hats - no conclusion.
3. Person three is wearing a RED hat.

This proves two states with contradictory conclusions. Therefore it's impossible to know which hat #3 is wearing!

Tavel

oh goodness, in my frustration I think i may have proven myself wrong!

Condition 2 is false because the second person would know he has a white hat on. He'd see #3 has a red hat, and that #1 didn't see two red hats...so that means he's wearing a white hat. It doesn't matter what #1 is wearing...

And since #2 could NOT tell, they all had to be wearing white. I guess order of observation DOES matter, gah!

x leper x

Lucy

The warden's proposal:

"If you can tell me for sure what color hat you have on, you can go free and never return to my jail again."

The warden's question:
"can you tell me for sure what color is your hat?"

The correct answer is "Yes, I can tell what color my hat is."

The warden never asks "Is your hat black or white?."

Tavel

That's the "riddle" answer, but there is a real answer too. I hate riddles because the answers sound like they come from smart-alec teenagers.

"what color is your hat"
"Red or blue, haha LOLOLZ ROFLCOPTER!!!11!"


I'm pretty sure the answer is white...as i reasoned above. I was wrong the first time...but i get bonus points for figuring out the right answer.

MizRamzi

bringlem

This is actually a straightforward chain of deductive logic. (I just used it in my logic class this week.) To make it easier to explain, let's name the three students Al, Bert, and Clara.

Suppose Al is the first student whose blindfold is removed. The one and only way he could know his hat color for sure is if both Bert and Clara are wearing RED (because there are only two red hats available). But Al does NOT know his hat color for sure. So Bert and Clara have learned an important piece of information: that they are not BOTH wearing red hats. In other words, if Clara is wearing RED, Bert has to be wearing WHITE; or if Bert is wearing red, Clara has to be wearing white. (Because, again, if they both had on red, that would be the end of the red hats, and Al would have certainty.)

This is where it gets a little tricky. Bert's blindfold is removed. Now, if he had looked at Clara and seen a RED hat, he would know instantly that his hat has to be white. But he DOESN'T know his hat color.

So, Clara--being a good deductive logician--can instantly conclude that her hat is NOT red . . . and the only other choice is that her hat is WHITE.

(Note: It is not essential to the puzzle that Clara know or be able to state the colors of the other people's hats. They could, in fact, ALL be wearing white . . . But all she is asked to conclude is her own hat color, which she has successfully deduced.)

iloveengl

SO, I was going to tell you that your initial answer was incorrect, but it looks like you figured that out already, which only leaves me to mention that, like you, I kinda hate riddles, but for whatever reason I'm always quick to solve them. I just innately hate them; it's an awkward relationship. I'm glad you figured it out. Have you told your friend yet?

I just quoted this because it exactly sums up why I hate riddles. Thank you for articulating that so well!

Gouramiguy17

Have you considered maybe they are color blind? Other than that I am clue less

MizRamzi

I used to win at cards with my lil sis all the time...only cause I could see her cards reflected in her eyes......I know what color I'm wearing. Hehehe