There are 3 smart old ladies standing in a desert such a way that each lady can see the other two. Each of the 3 ladies has paint on her face. Seeing this, all three ladies begin laughing. After a while, the smartest of them realizes something, and stops laughing. Why? And more importantly, HOW did she realize it?

No, there are no mirrors, they can’t feel the paint on their own face, they don’t speak to each other, there is nothing in the desert, etc. There is nothing physical about this puzzle, it is just logical.

From the perspective of each of the old ladies, both of the other two ladies’ faces are painted. So it would seem that it would be impossible to determine if one’s own face is painted, because even though they are both laughing, they can see each other, and it seems they would laugh whether or not one of them had a clean face.

The clue is found by stepping through possibilities. If two of the three ladies have paint on their face, then one of the two would realize that her face is painted, because she can see that one of the others’ face is painted (who is laughing) and one whose face is not painted (also laughing). She determines that the one whose face is painted could only be laughing if her own face is painted, and thus stops laughing.

Since this does not occur, the smartest old lady determines that her own face is indeed painted.