Just wondering if there is anyone else not quite getting the answer to Mad Hatter puzzler. We were told all the wiseguys raised their hands when the king said: “If you can see a red hat, raise your hand.”

Of course that would be the case if all of them was wearing red hats but suppose if wiseguy #1 was wearing white hat instead. Wiseguy #1 would see #2 and #3 wearing red hats. Wiseguy #2 and #3 would see each other wearing red hats.

Everything follows along until step 3…

The key is that all three were wise enough to know that if anyone sees a red and a white hat, he would immediately know he had a red hat and would quickly stand up. Why? Because there could then be only one white hat. (If there were two white hats, one of them wouldn’t have raised his hand. The fact that all were hesitating meant all had red hats, and #1 was the only one to figure that out. Hope this helps.

Thanks, that helps but the explanation is not as crystal clear still but I get it now. I get that all hands raised means either all red hats or two red and one white hat and can’t mean two or more white hats.

Seeing one red and white hat does indeed imply one is wearing red hat. In my example, wiseguy #2 would see wiseguy #1 with white hat and wiseguy #3 with red hat. Wiseguy #1 could be raising hand due to wiseguy #3 but wiseguy #3 must be raising hand due to wiseguy #2 (self).

Wiseguy #3 is in same/similar situation to wiseguy #2.

Right, why all of them would hesitate can be illustrated through wiseguy #1 because wiseguy #1 sees two hands raised but wiseguy #2 can be raising hand due to wiseguy #3 and wiseguy #3 due to wiseguy #2 and does not provide any additional information.

With all red hats, everyone sees two red hats and would have no idea about themselves…

So thanks for pushing me in the right direction.

This clever puzzle is similar to that Sherlock Holmes story, Silver Blaze I think is the title, where Holmes deduces the solution by focusing not on something unusual that happened, but by something unusual that didn’t happen. i.e. The dog that didn’t bark.

Is nice once I know the answer. I didn’t listen to show the week it (re)aired and ended up reading answer first. As I said, I didn’t understand the answer and ended up spending more time on why answer can’t possibly be right…

he key is that all three were wise enough to know that if anyone sees a red and a white hat, he would immediately know he had a red hat and would quickly stand up. Why? Because there could