After blindfolding them, Paul picks up the five red discs, sticks one on the forehead of each logician, and hides the other discs elsewhere. After removing the blindfolds, everyone sees the discs (all red) on the others' foreheads but not the one on his own.

After a few minutes, one of the logicians (that reasons a little faster than the others) correctly states the color of his disc. How does he work it out?

Let the logicians be A, B, C, D, and E sitting clockwise in a circle.

1. A sees 4 R discs so he cannot say what color disc he has on his forehead.
2. B reasons,” If A had seen 2 B and 2 G discs he would have answered the question. So one of us (B, C, D, and E) must be having a R disc.” But B sees red discs on C, D and E. So he cannot answer the question.
3. C reasons,” A did not see 2B and 2G, which means one of us (B, C, D, E) must have R. If the last three of us (C, D, E) had only B or G discs, B would have guessed R. But B did not know the answer. So at least one of us (C, D, E) must have R. But I see 2 R’s so I cannot answer.
4. D reasons,” If C had seen only B or G on the last two of us(D, E), he would have said R. But he did not, which means one of us has R. But I see an R, so I cannot answer.
5. E reasons,” D sees an R on my forehead so he cannot answer. I must have R.”