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?

Lets identify the logicians as 1, 2, 3, 4 and 5

1, Lets consider that the colors are R, B, B, G and G respectively.
    The 1st person would have told that his disc is Red seeing to       the others.

2, Lets consider that the colors are R, R, B, G and G respectively
    The 2nd person sees one R, one B and two G
    he knows that if the disc in his head is B then 1st person would have told his disc color.(by point 1)
    As the first person did not tell he knows that his disc color is not B. so he immediately says R

3, Lets consider that the colors are R, R, R, B and B respectively
    The third person sees two R and two B.
    he knows that if the color of the disc in his head is G then second person would have told his disc color. (by point 2)
    As the second person did not tell he knows that his disc color is not G. so he immediately says R

4, Lets consider the colors are R, R, R, B and G respectively
    The third person sees two R, one B and one G.
    he knows that if the color of the disc in his head is B or G then second person would have told his disc color. (by point 2)
    As the second person did not tell he knows that his disc color is not B or G. so he immediately says R 

5, Lets consider the colors are R, R, R, R and B respectively
    The fourth person sees three R and one B
    he knows that if the color of the disc in his head is B then the third person would have told his disc color. (by point 3)
    he knows that if the color of the disc in his head is G then the third person would have told his disc color. (by point 4)
    as the third person did not tell he knows that his disc color is not B or G. so he immediately says R

Now the disc colors are R, R, R, R and R respectively

   The fifth person sees four R
   he knows that if the color of the disc in his head is B or G then the fourth person would have told his disc color as R. (by point 5)
   as the fourth person did not tell he knows that his disc color is not B or G. so he immediately says R.