LOGIC
PUZZLE: MASTERS OF LOGIC PUZZLES - DOTS
Masters of Logic wanted to find out who was the wisest among them. So they turned to their Grand Master, asking to resolve their dispute.
How did he guess?
Solution:
"Easy," the old sage said. "I will blindfold you and paint
either red, or blue dot on each man's forehead. When I take your blindfolds
off, if you see at least one red dot, raise your hand. The one, who guesses the
color of the dot on his forehead first, wins."
And so it was said, and so it was done. The Grand Master blindfolded the three
contestants and painted red dots on every one. When he took their blindfolds
off, all three men raised their hands as the rules required, and sat in silence
pondering. Finally, one of them said: "I have a red dot on my
forehead."
How did he guess?
Solution:
The wisest one must have thought like this:
I see all hands up and 2 red dots, so I can have either a blue or a red dot. If
I had a blue one, the other 2 guys would see all hands up and one red and one
blue dot. So they would have to think that if the second one of them (the other
with red dot) sees the same blue dot, then he must see a red dot on the first
one with red dot. However, they were both silent (and they are wise), so I have
a red dot on my forehead.
Here is another way to explain it:
All three of us (A, B, and C (me)) see everyone's hand up, which means that everyone
can see at least one red dot on someone's head. If C has a blue dot on his head
then both A and B see three hands up, one red dot (the only way they can raise
their hands), and one blue dot (on C's, my, head). Therefore, A and B would
both think this way: if the other guys' hands are up, and I see one blue dot
and one red dot, then the guy with the red dot must raise his hand because he
sees a red dot somewhere, and that can only mean that he sees it on my head,
which would mean that I have a red dot on my head. But neither A nor B say
anything, which means that they cannot be so sure, as they would be if they saw
a blue dot on my head. If they do not see a blue dot on my head, then they see
a red dot. So I have a red dot on my forehead.
