Another riddle for you all

[b0mbrman]

This one's kinda nifty

There are 3 black hats and 2 white hats in a box. Three men (we will call them A, B, & C) each reach into the box and place one of the hats on his own head. They cannot see what color hat they have chosen. The men are situated in a way that A can see the hats on B & C's heads, B can only see the hat on C's head and C cannot see any hats.
When A is asked if he knows the color of the hat he is wearing, he says no.
When B is asked if he knows the color of the hat he is wearing, he says no.
When C is asked if he knows the color of the hat he is wearing, he says yes and he is correct.
What color hat and how can this be?

 

[minendo]

black (that would be my guess)

but i cant think of how to explain it

 

[b0mbrman]

It's not as bad as the riddles here yesterday...the trick with this one is to work backwards

 

[khtm]

ok

- if A says no, that means the EITHER B or C has a black hat (since if they both had white hats, then A would know he has a black hat).

- if B knew that C had a white hat, then he would know that his own hat was black (since he heard A say "no"). But B said "no."

- Therefore, C knows he has a black hat!

or, situation #2:

- If B and C both had black hats, then A would have said "no", since he himself could have had a white hat or a black hat.

- If B saw that C's hat was black, then he would have said "no", too, since he himself could have had a white hat or a black hat.
- If B saw that C's hat was white, then C knows that he, himself must have a black hat, and he would have said "yes" (which didn't happen). The reason B would have said "yes" is dependent on the fact that A already said "no".

- Finally, in this situation, just like the other, C MUST know that he has a black hat, due to the previous statements by A and B

 

[tm37]

<< ok

- if A says no, that means the EITHER B or C has a black hat (since if they both had white hats, then A would know he has a black hat).

- B knows that C has a white hat, then he would know that his own hat was black (since he heard A say "no"). But B said "no."

- Therefore, C knows he has a black hat!

>>



Good show!

 

[b0mbrman]

Well met

 

[Vadatajs]

might I point out that neither black nor white are colors

 

[NetworkDad]

Might i point out - I believe white is the absence of color. I believe black is a color, or combination of.

 

[khtm]

might i also point out that you guys are some nit-picky mofos

 

[b0mbrman]

Might i point out - I believe white is the absence of color. I believe black is a color, or combination of.

You got it backwards. Jeez...some people can't even do anal right

 

[Logix]

Here's another riddle involving those non-colors, black and white:

Imagine that you have three boxes, one containing two black marbles, one containing two white marbles, and the third, one black marble and one white marble. The boxes were labeled for their contents (BB, WW and BW) but someone has switched the labels so that every box is now incorrectly labeled. You are allowed to take one marble at a time out of any box, without looking inside, and by this process of sampling you are to determine the contents of all three boxes. What is the smallest number of drawings needed to do this?

 

[khtm]

the answer, my friend, is one drawing.

*EDIT*
I guess I better explain why...

If EVERY box is incorrectly labelled, then you only need to pick one marble.
You need to pick it from the BW box, though. If you get a black one, then you know that the CORRECT label of that box should be BB, and then the WW box must actually be the BW box (since it cannot be the BB box - that choice is already taken). And the BB box must actually be the WW box.

Done and done

 

[TallBill]

The possible scenarios are

bbb
bwb
wbb
wwb

wbw and bbw- not possible, b would know hes black.. knowing that a knew that he didnt know what he was because b and c were not both white
bww - not possible.. a would know hes not white

so hes black

 

[khtm]

you're late, bob

 

[Logix]

Yes, indeed khtm. Do explain.

 

[khtm]

explained in my original answer

-khtm-

 

[TallBill]

<< you're late, bob >>


well no crap.. but i was busy watching your damn videos and it slowed me down....

*hums "like a virgin"*

 

[Ameesh]

<<

<< ok

- if A says no, that means the EITHER B or C has a black hat (since if they both had white hats, then A would know he has a black hat).

- B knows that C has a white hat, then he would know that his own hat was black (since he heard A say "no"). But B said "no."

- Therefore, C knows he has a black hat!

>>



Good show! >>





how does this work, there are 3 black hats and 2 white. A could have seen both of them wear black hats, B sees C wearing a black hat but he has no idea if he is wearing a white or a black hat.

Then all C knows is that A and B could be both wearing a black hat or A xor B could be wearing white hat.



<< - B knows that C has a white hat, then he would know that his own hat was black (since he heard A say "no"). But B said "no." >>

<--- this isnt quite right, A could have seen two black hats, in that case A would still not know whter he had a black or a white cap on.

 

[khtm]

Ameesh,
I thought of that situation, too, but didn't post it (I figured it was too obvious).

- If B and C both had black hats, then A would have said "no", since he himself could have had a white hat or a black hat.

- If B saw that C's hat was black, then he would have said "no", too, since he himself could have had a white hat or a black hat.
- If B saw that C's hat was white, then C knows that he, himself must have a black hat, and he would have said "yes" (which didn't happen). The reason B would have said "yes" is dependent on the fact that A already said "no".

- Finally, in this situation, just like the other, C MUST know that he has a black hat, due to the previous statements by A and B

Does that make sense?

-khtm-

 

[TallBill]

or.. just READ MINE.. its in plain english!

 

[Warblad13]

<<

<< ok

- if A says no, that means the EITHER B or C has a black hat (since if they both had white hats, then A would know he has a black hat).

- B knows that C has a white hat, then he would know that his own hat was black (since he heard A say "no"). But B said "no."

- Therefore, C knows he has a black hat!

>>



Good show! >>

 

[b0mbrman]

Come on...we already got *my* riddle...now the marble one, I'm a little fuzzy on why it's just one...

Here are the incorrectly-labeled boxes with their unknown true contents below where -XX means "not XX":
BB * BW * WW
-BB -BW -WW

Pick from BW, whatever you pull out is the homogenous content of that box.

Assume it's white:
BB * BW * WW
-BB WW -WW

Now, we know that one of the last two are really BW and BB. Because we know they're *all* mislabeled, the box labeled BB cannot be BB
.·. it's BW

BB * BW * WW
BW WW -WW

And finally, the last one is BB