Q : Three very intelligent women (rare case :P) are sitting across a circular table. A fourth person notifies them that he will blind fold them and put either blue or red mark mark on their forehead. Then he will open their eyes. If any woman sees a red mark on the forehead of any of the women, she should raise her hand. And as soon as, one can logically deduce the mark of her forehead, she should then lower her hand, if she raised it earlier.
The fourth person then proceeds and mark all their foreheads with red mark and then open their eyes. All three raised her hand initially, after some moment, the most intelligent of the lot lower her hand.
What and how did she conclude about the mark color of her forehead?
A : Possible cases : (2 R, 1 W) and 3 R as all three initially raised their hand which caused the confusion and the corresponding delay in lowering the hands.
For (2R, 1W) case, one of the women with red mark would have thought, that since third lady has white mark, the only reason the other lady raised her hand is that she had red mark on her forehead. Hence would have lowered her hand almost instantaneously.
The most intelligent woman after analyzing all the cases, must have thought that the only reason for none of the women being able to deduce the color of her forehead instantaneously is due to the 3 R case.