Expert: Rohit Agarwal - 6/16/2009

Question
A wealthy ginger is searching for a suitor for his daughter, so he collects the three smartest men in town. He sits them in a circle and tells them he is going to put a red mark or a white mark on each of their heads while their eyes are closed. He puts a red mark on all three and tells them to open their eyes. He then asks them if they see a red dot then they should raise their hand. They all raise their respective hands. He then says that if you know the colour dot that is on your forehead, then stand up. After a few minutes one man stands and says the correct colour. How does he know?

Thank you so much whoever answers this.


Answer
There are 4 cases

All White:
Negated as all of them can see atleast one red mark

2 White 1 Red:
Negated as all of them can see two red marks

Now everyone knows that everyone knows that there is atmost 1 white

1 White 2 Red:
If this was true, and assuming that there is atmost 1 white, then the person who can see 1 white will know that the mark on his forehead is red. Since this doesn't happen, this also is negated.

All Red:
The last option