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The “What Color is My Hat” Brainteaser | No BS Job Search Advice Radio

EP767 A wonderful little problem that will stump quite a few of you.

Summary

I have got a lovely little brainteaser for you. I haven't heard is used on interviews but I think it is a good one and I thought I would share it with you.

A teacher puts on 10 hats of either red or blue on 10 students. Each 1 can see the hats on all other 9 students but not his or her own. The teacher tells them that at least 1 of the hats is blue and they then ask the students to write down the color of the hat that they are wearing if they are sure about it. Or, the student can write down, "Don't know." Everyone reveals their answer at the same time and all the right, "don't know." On the 2nd day, they gather in the teacher puts on the same hats on each student. Each 1 of them has to think about the color of their had again. This time, no one can still figure out the color of their hat. Everyone writes down, "don't know."

This game repeats itself on the 3rd day, 4th day until the 9th day and still no one can figure it out. However, on the 10th day, everyone writes down the correct color of their hat. What happened? What is the color that they wrote down? The assumptions here are that throughout the 10 days, the students do not communicate with one another and they assume that everyone is smart in those that everyone else is smart as well. That's the problem we have to solve.

The correct answer is that they are all wearing blue hats. There is a proof to it. Follow the logic here. Credit for the answer goes to Pratik Pradar.

If there are k number of blue hats and, but all of them can tell at time k that they are wearing blue hats. This can be proved by induction. If there is only one blue hat, it would seem that no one has a blue hat. But there has to be someone with the blue hat so it must be him. He gets it in day one.

If there are 2 blue hats, they will think there is only one blue hat, then the person would've said on the 1st day, so it must be a blue hat. And so on. On the kth day, all K people realize that they have blue hats. Since here K equals 10, there are 10 people with blue hats.

That's her solution. If it leaves you puzzled, that happen sometimes! That's what you call brainteasers, got it?

Jeff Altman, The Big Game Hunter is a coach who worked as a recruiter for what seems like one hundred years. His work involves life coaching, as well as executive job search coaching and business life coaching. He is the host of “Job Search Radio” and “No BS Job Search Advice Radio,” both available through iTunes and Stitcher.

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