This is adapted from a more complicated version submitted by Jared Bronski in “The Riddler”. (Thanks to Matt Mooore who gifted me the book this week).

It is one more of those hats on your head and strategy formulation question.

There are three of you. Randomly a white or black hat is put on your head. Each one of you can see the color of the hat on the other two but not the one that is on your own head.

One by one, you will be asked to guess what color hat you have on your head.

Your options are (*) tell a color – Black or White or say (*) Pass.

At any point, if somebody calls a wrong color – you all lose. But if somebody calls a right color – you all win. And if everybody passes at the end of first round, then you all lose.

What strategy can you formulate beforehand to maximize the chances of winning? And what is that probability?

Read this up in the book “Mathematical Circus”.

You have 2 green balls, 2 yellow balls and 2 red balls. One ball of each color is 11 pounds each. The other ball of each color is 9 pounds each. You have a scale and pan balance. (meaning you can compare the weights of two sides – which is heavier and which is lighter but you never know the exact weight).

What is the least number of weighings required to find out which are the three heavier balls and which are the lighter balls?

Send me personal message with the reasoning.