Brain Teaser 1
Brain Teaser Questions
Question #1:
A father wanted to discover which of his three sons was the
smartest. The problem he gave them was this: He blindfolded each boy
and then painted a white dot or a black dot on each forehead. "The
paint on your forehead," he told them, may be black, or it may be
white. When you remove your blindfold, look at your brothers. If you
see two black dots, you are to laugh. And when you have figured out
which color must be on your own forehead, come and tell me how you
know." He then instructed them to remove their blindfolds and left
the room. There was dead silence; yet after a minute
the youngest ran to his father with the correct answer. How did he
know?

Answer #1:
In order to solve this problem, it would be helpful to assume that these three boys are intelligent and masters of logic. When the blindfolds were removed there was dead silence. No one laughed because no one saw two black dots. Therefore, only two combinations of dots are possible among these three boys: Three white dots or two white dots and one black dot. The youngest son (Steven) must have seen a white dot on both of his brother's foreheads. How Steve knew the color of his dot is based on the responses of his brothers. If Steve had a black dot on his forehead, then his brothers should have figured this out rather quickly, assuming they are quick thinkers! Only one brother could have a black dot and the other two must be white. The fact that his brothers could not figure this out indicates that Steve had a white dot. His brothers simply could not rule out the possibility of a black dot on one of their foreheads.

Question #2:
The two brothers who lost in the above question wanted another chance to redeem themselves. They especially wanted to beat their liberal brother Steven. So their father showed them five hats, two white and three black. Then he said: "I will turn off the lights and put a hat on each of your heads and hide the other hats. When I turn on the lights you will have equal chances to win. Each of you will see the hats of your two brothers, but not your own. The first one saying the color of his hat will win." Then before he could even turn off the light, the bright Steven guessed what the color of his hat will be. What color was it and how did he know?

Answer #2:
The important sentence in Question #2 is that all brothers have an equal chance to win. Remember that there are five hats: Three black and two white. There are four possible combination of the three hats worn by the three brothers: Black + White + White, Black + Black + White, or Black + Black + Black. Three whites is not possible. If one of them had a black hat and the other two had white, the one with black would immediately know that his hat and the two hidden hats were black. So one black and two white hats is not a fair combination. If two boys had black hats and one had a white, then the boys with black hats would have the advantage. They would each see one black and one white hat. If they both had white hats, then the one with a black hat would know immediately that his hat and the two hidden hats were black. It is easier to show the three hat combinations in the following tables. I have assigned the names Tom, Dick and Harry to the three boys in order to keep track of the different combinations.

Combination 1: White + White + White
Combination of three whites is not possible.

Combination 2: Black + White + White
Name

Hat Color

Observed Hat Colors

Tom

Black

White + White

Dick

White

Black + White

Hairy

White

Black + White

Tom sees two whites; therefore his hat and remaining two hidden hats must be black. Dick and Hairy have the disadvantage in this comnination..

Combination 3: Black + Black + White
Name

Hat Color

Observed Hat Colors

Tom

Black

Black + White

Dick

Black

Black + White

Hairy

White

Black + Black

If Tom had a white hat he would not see white. This scenario also applies to Dick. Hairy has the disadvantage in this combination.

Combination 4: Black + Black + Black
Name

Hat Color

Observed Hat Colors

Tom

Black

Black + Black

Dick

Black

Black + Black

Hairy

Black

Black + Black

Tom, Dick and Hairy all have black hats; therfore, they all have an equal chance of guessing their hat color correctly (or incorrectly). In this combination the two hidden hats are white.

