A variant of the $100$ prisoners problem.
$100$ prisoners are given each either a white hat or a black hat. They can see each other's hat but not their own and they cannot communicate.
Each prisoner must write(not yell like in the classic one) on a piece of paper his guess for the color of his hat, which can be "black", "white" or "pass" ($3$ options instead of $2$ in the classic one).
If not all prisoners choose "pass" and all those who didn't pass guess correctly, then all prisoners are sent free.
Invent a strategy for the prisoners that will maximize their chance of getting free, assuming the hats are chosen randomly.
My current thoughts: It is possible to find a strategy in which the chances increase with the number of prisoners. For $3$ prisoners a strategy might be to choose "pass" if the colors of the two hats are different, otherwise to choose the opposite of the same color. This gives a $75$% chance of getting free.