## Puzzle of the Day : 16

Three wise men decided to find out who was the wisest of them all . So they went to the grandmaster and asked him to devise a constent . The grand master agreed and taking them into a dark room, he said ‘I am going to paint a dot on your forehead. It could be either red or blue. Then the lights in this room will be turned on . When you see at least one red dot you should put up your hand. The one to identify the colour of the dot on his own forehead first will be the winner of the contest. He will be declared the wisest among you.’ He then painted red dots on the foreheads of all three of them , and the lights were turned on. At the moment all three put up their hands . After a little while one of them said that he had a red dot on his forehead. How did he find out ?

He feels pain.

He could have used elimination.

If we name them A,B and C

Case 1: A has red dot, then B and C would have raised hand and he would have known dot is on his head.

Case 2: A has red dot, B has red dot and C doesn’t then all three of them would have raised hand. Then A would have known he has the dot.

As both B and C didn’t answer, he would know neither Case is true and he too has the dot.

He could have used elimination.

If we name them A,B and C

Case 1: A has red dot, then B and C would have raised hand and he would have known dot is on his head.

Case 2: A has red dot, B has red dot and C doesn’t then all three of them would have raised hand. Then A would have known he has the dot.

As no Case is true, he would know he too has the dot.

The wisest man could see 2 red dots. Now, he either has a red dot or a blue dot.

If he had a blue dot, the other two men could have easily guessed the dot on their forehead. (Since they could see one red dot and blue dot in front of them and everyone raised their hand)

Since they didn’t answer, he got to know everyone has a red dot.