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."