Before they are blindfolded, 3 women are told that each one will have either a red or blue cross painted on her forehead. When the blindfolds are removed, each women is supposed to raise her hand if she sees a red cross and to drop her hand when she figures out her own cross color.

The 3 women are blindfolded and a red cross is painted on all of their foreheads. The blindfolds are removed. After looking at each other, the women raise their hands simultaneously. After a short time, one of the women lowers her hand and says, ''My cross is red.''
How did she reason it out?

One of the women reasons as follows:
The other 2 can't determine their color. This means that I too have a red cross. Call the 3 women A,B and C, and A is the one that lowered her hand. Consider A's initial reaction. She looks at B and C and notices they both have a red cross. Naturally, she raises her hand as she has been instructed to do. Similarly, B and C raise their hands at the sight of two red crosses. So how did A figure it out? A must of had a flash as insight, thinking as follows:

"Let me assume that I have a blue cross on my forehead. If that is so,then one of the other two , say B, would know she doesn't have a blue cross because otherwise C, seeing 2 blue crosses-mine and B's- would not have put up her hand. But this has not happened, so B and C cannot determine their color. This means that I too have a red cross."