Logic Question (Diagram Included)?

Question

I'm not sure what the answer is but I need help with it. Let me try and explain it clearly. PLEASE see diagram at http://img507.imageshack.us/img507/3369/capum8.png

1. There are four people. Let's name them, in order, #1 #2 #3 #4.
2. #1 can't see anything because of the wall.
3. #4 can only see #3 and only sees a red hat (see the grey sight)
4. #3 can see the yellow hat.
5. #2 can only see the wall so it's hopeless

The answer is #3 but why?
Somehow, #3 can look at #2 but can someone please explain?

Answer 1

You forgot to state the actual riddle - I know a similar one, but it involves only three men and three hats... still, I'll assume it's similar.

So, let's say the question was: These four people are prisoners; they are told there are two yellow and two red hats; if any of them can say which color hat they are wearing, they all go free, but if they can't, something horrible happens to them. No one can see their own hat.



Look at the diagram again.

#1 can't see anything or be seen by anyone.

# 2 can't see anyone, but can be seen from behind

#3 can see #2, and can see #2 is wearing a yellow hat.

#4 can see BOTH #2 and #3 (they are both in front of him, and the wall is between #1 and #2).


#3 knows that #2 is wearing a yellow hat. He therefore also knows that #4 is looking at at least one yellow hat.

IF #4 was looking at *two* yellow hats, he'd immediately know that his own hat MUST be red (since there are only 2 yellow ones; so if #4 saw that #2 and #3 have those, he'd know he must have red by necessity).

However, #4 doesn't say anything. Therefore, #3 knows that #4 is NOT looking at two hats of the same color. Since he also knows that #2 has a yellow hat, he knows that his own hat must be different.

Therefore, he knows his own hat must be red.

Hope this helps. :)

Answer 2

in future use a matrix to solve this type of puzzle.