Beach Day by Rodger Bliss
April 2024

3 Hats and Super-Smart Slave

Almost the same scenario as “Which Color Hat“. King wants to find the smartest slave and has black hats and white hats. He tells the slaves he will place a hat on each slaves head in a dark room and when the lights are turned on if they see a white hat to stand up. When one figures out what color hat he has on then go tell the king. There is a super-smart slave who figures out which color hat he has on as well as which colors the other two slaves have on before the light is turned on.

How did he know?

Thank you Jim for your submission!

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4 guesses to 3 Hats and Super-Smart Slave

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  • Luca

    The white hats would be visible in the dark because they would still reflect some light.
    So he knew because he saw the hats getting put on the hats of the other slaves, which because of that have to be white.
    Paying attention to the hat being placed on his head, he sees either nothing and suddenly feels the hat. so it would be black or he sees the hat being placed on his head. So then it would be white.

  • The super-smart captive is familiar with the “Which Color Hat” puzzle and knows that the only way to make that interesting—and a decent a test of intelligence—is to have everyone wear the hat that triggers NO ACTION, which in this case is the black hat. Perhaps he’s even done this before. So, while the lights are still out, he lets out a long, bored sigh like a teenager, and says, “We’re all wearing BLACK hats. Yay. I’m the smartest.”

  • Moshe

    He knew that all 3 were wearing white. Any other combination of colors would l be too easy to deduce and therefore not challenging (like 3 black; or 1 white and 2 black).
    3 B- no hands up- everyone knows theirs is black
    2 B & W- since W doesn’t raise his hand and they do, he knows his is white
    1 B & 2 W- is like the classic 3 hat puzzle. Each white knows right away he’s white, otherwise why is the other white raising their hand?

  • Moshe, I like your solution, and it follows the same logic that Jim used, so you are today’s winner. Here is Jim’s answer:
    The super-smart slave reasons that the test must be fair to all the slaves with no slave having an advantage over the others. And if two slaves have on white hats those two will know immediately what color hat they have on and will have a foot race to tell the king leaving the one with the black hat at a disadvantage. He also reasons that if only one slave has a white hat, the two with black hats would stand up, and they will all figure it out quickly and run a race to the king. But if they all have white hats on, no ordinary slave would figure it out quickly, but the smartest would eventually figure it out since it has taken a lot of time.