The Prisoners with Hats Riddle

Difficulty	Categories	Source	I know the solution
🌶️🌶️🌶️ Spicy	logic	Old family riddle	Yes

An evil logicion has imprisoned 100 helpless civilians, including you. One day, he gathers everyone up and announces the following:

Tomorrow I will place a hat on each of your heads. Each hat has a 50% chance of being black and a 50% chance of being white. You will not be able to see the color of your own hat, and once the hats are placed on your heads, you will not be able to communicate with each other whatsoever.

After receiving your hats, you will have a chance to view the hats of your fellow prisoners. Again, you will not be able to react in any way that relays any information whatsoever to your fellow prisoners. If you try anything funny, everyone’s executed!

After seeing each others’ hats, you will be pulled aside one at a time to my office (in an order of my choosing), where you will each need to guess the color of your own hat. If a single prisoner guesses wrong, all 100 will be executed. You cannot hear the guesses of the other prisoners, and no one will be executed until the end.

Be assured that your hat color will be determined independently from the hat colors of the other prisoners - they could all be white, or all black, or anything in-between, and each hat has a 50% chance of being either black or white.

With that said, you all have until tomorrow to openly discuss your strategy. Be warned, you cannot guarantee your safety, but I suspect you can do better than random guessing.

…What strategy will maximize your groups chance of survival?

Daniel’s Notes

This is one of the ones I spent a year on, back in the day, though nothing about the answer suggests that it must take such a long time to solve.

A harder variant involves 101 colors of hats.

Good luck!