Paul shows nine colored discs (five
red, two
blue and two
green) to five logicians.
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?
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Submitted by pcbouhid
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Rating: 4.0833 (12 votes)
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Solution:
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(Hide)
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a) Obviously, if anyone were to see 2 blue and 2 green, he would know immediately that he was red.
b) If anyone were to see 2 blue, 1 green and 1 red, he would know that he could not be green, for, if he were, the man with the red disc would see 2 blue and 2 green, and would know that he is red.
Similarly, if anyone were to see 1 blue, 2 green and 1 red.
c) If anyone were to see 1 blue, 1 green and 2 red, he would know that he could not be green, for, if he were, either of the man wearing red, would see 1 blue, 2 green and 1 red, and would reason as (b) above.
d) If anyone were to see 2 blue and 2 red, he would reason that he could not be green, for if he were, someone would see 2 blue, 1 green and 1 red, and would reason as (b) above, too.
e) If anyone were to see 1 blue and 3 red, he would reason that he could not be green, for if he were, someone would see 1 blue, 1 green and 2 red, and would reason as above; similarly, he would know that he could not be blue.
Therefore, if anyone sees someone wearing blue or green, he can deduce his colour.
Therefore, since nobody anounce after a few seconds the colour of his own disc, all of them deduce (what needs some more time) that his disc must be red.
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