A school server was hacked. The headmaster suspects five friends based on the fact that they were really good such knowledge. He calls all of them in his room and the five students give the following statements:
Peter:
1. I did not do it.
2. I have never hacked in my entire life.
3. Christy did it.
Jamie
1. I did not do it.
2. The hack was done from within the network.
3. I do not like Misty.
Casey
1. I did not do it.
2. I have never seen Misty in my life.
3. Christy did it.
Christy
1. I did not do it.
2. Misty did it.
3. Peter was lying when he said I did it.
Misty
1. I did not do it.
2. Jamie did it.
3. Casey and I used to be friends.
Now, you know that out of the three statements, every student has speaker two truths and one lie. Reading all these statements, can you identify who hacked the server?
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Solution
First the logicians will have to take a leap of logic. The master has told them that it wont be impossible for any logician to solve the puzzle. Thus it is assure that any of the color cant exist only once. If it did, the one wearing it will have no clue about that color which would be unfair for him.
Now every logician will look around in the circle and count the number of times they see a particular color. If a color is seen only once, then the logician will know that the color on his band must be of the same color (as per the leap of logic). And then the logician will leave on the first bell.
In the similar fashion, any logician who see any color just once will be able to identify his own color and they will leave when the bell rings or they will be disqualified and asked to leave. Equivalently, any color for which there are two bands, will be eliminated after the first bell has rung. Thus there must be three bands of any remaining color at least.
Assume that a logician don’t see any color once, but sees a color twice. If they were the only bands of this color then the two logicians must have left at the first bell. But they did not. Thus it means that his band color is the same and he will leave on the second bell.