# MASTERS OF LOGIC PUZZLES (HATS)

After losing the “Spot on the Forehead” contest, the two defeated Puzzle Masters complained that the winner had made a slight pause before raising his hand, thus derailing their deductive reasoning train of thought. And so the Grand Master vowed to set up a truly fair test to reveal the best logician amongst them.

He showed the three men 5 hats – two white and three black. Then he turned off the lights in the room and put a hat on each Puzzle Master’s head. After that the old sage hid the remaining two hats, but before he could turn the lights on, one of the Masters, as chance would have it, the winner of the previous contest, announced the color of his hat. And he was right once again.

What color was his hat? What could have been his reasoning?

The important thing in this riddle is that all masters had equal chances to win. If one of them had been given a black hat and the other white hats, the one with black hat would immediately have known his color (unlike the others). So 1 black and 2 white hats is not a fair distribution.

If there had been one white and two black hats distributed, then the two with black hats would have had advantage. They would have been able to see one black and one white hat and supposing they had been given white hat, then the one with black hat must at once react as in the previous situation. However, if he had remained silent, then the guys with black hats would have known that they wear black hats, whereas the one with white hat would have been forced to eternal thinking with no clear answer. So neither this is a fair situation.

That’s why the only way of giving each master an equal chance is to distribute hats of one color – so 3 black hats.

I hope this is clear enough.

### Your Answer

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