Answer 1) The winning knight suddenly realizes that the king has left three white hats sitting on the table. So he must be wearing red!

Answer 2) So we want to think about what hats the knights are wearing. The one that wins (let’s call him ‘Al’) is wearing red. Then, at least one of the other two must also be wearing red because Al raised his hand to say that he saw a red hat. Let’s call the second knight ‘Bob’ and say that he is the one wearing a red hat. Now the third knight (we’ll call him ‘Chuck’) could be wearing either red or white. Let’s think first about the case where he’s wearing a white hat. If that were true, then both Al and Bob would *immediately* know they had red hats, because the other had to see a red hat somewhere (and Chuck didn’t have one on). But no one stepped forward immediately, did they? No. There was a minute pause. So, we can conclude that all three knights were wearing red hats. Now, how did Al know his was red? Well, Al realized that there had to be at least two red hats for the reason above. And he thought, “well, if mine is white and the other two dudes aren’t completely stupid, either Bob or Chuck will soon step forward to claim the prize,” due to the example above when Chuck’s hat was white. When no one did step forward, Al figured that either both Bob and Chuck were complete morons or that he must have on a red hat. He took the risk that at least one of them would’ve stepped forward quickly if he (Al) had been wearing white, and since neither did, he concluded, correctly, that he must be wearing red too.

Interestingly, the king played a neat little trick with the knights, in that each of them had an equal opportunity to figure out that all three were wearing red hats. And so it really was a ruse to determine the cleverest knight.

Unfortunately, Al turned out to be a bad kisser, and the princess lived unhappily ever after. The moral of the story is to make sure you make your own choices, because if you let someone else do it for you, they may make it based on different values than your own.

You’re right; we never did beat Robot Odyssey. I have memories of getting stuck on this four-room puzzle, where you have to avoid the janitor robots (that send you back to the beginning) AND cooperate with another robot. Was quite tricky.

- Margaret’s Hair