What hat am I wearing?

Logic Level 3

Assume that A, B, C and D are four scientists standing in a room such that: - They are standing in a single line - A is isolated from the rest of the group by a wall - B,C and D are standing one behind the other (B being the first, D the last) - Everybody is looking towards the wall. Each scientist is wearing either a black or a white hat (there are two white hats and two black hats in total). Each scientist, if not obstructed, can only see the color of the hat the other scientists in front of him are wearing. Who will be able to say the color of the hat he is wearing?

Hints: - The room has no forniture - No scientist cheats, they only use logic - Scientists CANNOT communicate with each other - A scientist will speak as soon as he knows the answer - Consider all possible scenarios

D C B A Nobody will talk C and D A or D B or C

P0156 M by p0156 M , 19, USA

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1 solution

Marta Reece
Feb 14, 2018

If D can see two white hats, he knows that he has a black hat. If he can see two black ones, he has a white one. So in those to cases, D will speak up.

If D does not speak up, C knows that D can see one black hat and one white one. So if C can see a black one, he knows he has white and vice versa.

So C and D are possible speakers, and there is always a speaker.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

In that case, the option should be: C and (B OR D)

D does not always speak up. And if D doesn't speak, C will know his color, and B will know his from the fact that C speaks and D doesn't.

Afkar Aulia - 3 years, 3 months ago

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The problem should have some way of doing rounds. In first round D either speaks up or not. In second round, if D didn't speak up, C speaks up or not. After that the game is over. So the fact that B knows his hat from C's response is irrelevant.

Marta Reece - 3 years, 3 months ago

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If we assume that after someone speaks up, the game is over; then the answer should be "C or D", not "C and D". The only person who will certainly speak up (if the game is not over after D speaks up) is C alone.

Afkar Aulia - 3 years, 3 months ago

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