perplexus.info :: Logic : Colored hats

Colored hats (Posted on 2002-05-08)

There were three men in a line (facing forward) so they can only see the man (or men) in front of them. There are also five hats, two black and three white. Each man is wearing one of the hats.

When the man at the back of the line was asked "Do you know your hat color?", he replied "No". When the man that was second in line was then asked "Do you know your hat color?" he replied "No". When the man at the front of the line was asked "Do you know your hat color?" he replied "Of course".

What color of hat was the man at the front of the line wearing?

Submitted by Dan

Rating: 3.1818 (11 votes)

Solution: (Hide)

If the first man saw that the second and third men were wearing black hats, he would be able to know that his is white (since there are only two black hats). The fact that he did not know his hat color means that he either saw one black hat and one white, or two white hats.
The second man realized this. He knew that he and the third man could not both have black hats on. Therefore, if he saw the man in front of him wear a black hat, he would immediately know that his was white. Since he didn't know the color of his hat, he must have seen a white hat on the third man.
The third man, realizing this, deduced that his hat is white.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2023-06-23 08:37:33
comment	salil	2006-02-25 07:06:31
No Subject	logischer Verstand	2004-05-03 17:23:59
Simple & short	Federico Kereki	2003-10-27 12:46:50
re: hats	Federico Kereki	2003-10-27 12:43:54
re: hats	nikki	2003-09-24 17:23:55
Answer.	Gautam Joshi	2002-12-03 00:18:44
Solution	Dan	2002-05-10 05:50:25
My hat color	Tim	2002-05-09 20:02:05
hats	Chris Tyson	2002-05-09 18:40:45
My Answer	Tom	2002-05-09 12:23:39
Colored hats	Rich Cowley	2002-05-09 09:22:48

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