Simple but challenging logic puzzle

[ujjagrawal]

While a red mark was placed on the forehead of each of three blindfolded men seated facing each other in a circle, they were told that the the mark might be either red or white. Upon removal of the blindfolds, each was to raise his hand if he saw at least one red mark, and then to take it down if he could logically deduce the color of his own mark. All three hands were quickly raised, but then one of them lowered his hand. How did he know?

[MikeD]

Reasoning of the one who lower his hand (Man A):

If my mark was white, then Man B would reason that since man C raised his hand he must see one red dot, therefore could assume that his (Man B's) dot was red.

But since Man B didn't therefore Man B must see two red dots. So Man A dot must be red.

[bhramarraj]

Let three persons be A, B, and C, who have to raise their hand if the see at least one red spot. Since everybody has a red dot on his forehead, therefore everybody sees two red dots, so raises his hand. All three start thinking "If I had a white dot then the other two would be seeing one red & one white dot, therefore would deduce that they had a red mark on their forehead." But nobody lowered his hand. So all of them could guess that they all were seeing two red dots. One of them, fastest, learned it first and lowered his hand.

[ujjagrawal]

Excellent... interpretation by both of you of the solution... the key to the solution was thinking from perspective of other persons also (why they are not raising hands)... Most people put themselves in the place of the first person, but to solve this one, you must then also put yourself in the place of a second man.

[Half Fast]

Half Fast Well, everyone raised their hand, so everyone sees at least one red dot. I'm guy A, the others are B and C. I think to myself, if I have a white dot, guy B would see a red dot (on C) and a white dot (on A, me), and since guy C raised his hand, B would know his dot is red because mine is white. Same with guy C looking at A (me) and B. If neither one can deduce this readily, I must have a red dot also.