What was the test?
Let A, B and C be the names of three logicians and C be the logician who correctly guessed the color of dot on forehead.
Now, this could be the C's logic behind his correct guess -
"If I had blue dot on my forehead then A and B must had raised hands after looking red dots on the foreheads of other. In case, what A (or B) would have thought? His logic would be -
"If C is with the blue dot then B (or A) must have raised hand after noticing
red dot on my forehead, hence I must have red dot."
So A (or B) would have successfully guessed color of dot on own forehead easily.
But neither A or B not responding that means I must have red dot on my forehead!"
The logician who guess it correctly could be either A or B not necessarily be C; here it is assumed C is wisest for the sake of convenience.