You are an inmate at Infinity Prison, where prisoners must work together to solve a challenging riddle every day to ensure their very survival. But today is your lucky break; the warden has decided to throw a pizza party!
The catch: the prisoners only get to eat the pizza if they divide it fairly, one slice per prisoner. If the warden is not satisfied with fairness, they'll all be executed.
The other catch: no one but the warden knows how many prisoners there are; just that it's a very large number.
The warden places a single, giant, circular pizza in a room, otherwise empty except for:
- A pen and sheet of paper.
- A pizza cutter.
- An InfinityTech™ digital protractor (can measure angles of arbitrary precision).
The rules:
- Each prisoner enters the room once, one at a time.
- Each prisoner must make a single, straight cut from the edge of the pizza to the center.
- If anyone interacts with the pizza in any other way, every prisoner will be executed.
Eventually your turn is called, and to your dismay you find an untouched pizza and blank piece of paper; you're the first one in the room. What do you do to absolutely guarantee your survival?
Some assumptions you can make (not really spoilers, just clarifications):
All other prisoners want to survive as well, and know the rules, but you're not sure how smart they are.
Each prisoner can make perfectly straight cuts, and use the protractor to measure any real angle with perfect accuracy.
There's absolutely no way to determine how many prisoners there are; cells are soundproof with no windows and only one prisoner is let out at a time.
"Fairly" is to be judged by the warden; you're not 100% sure how it's judged but you have some guesses. Different solutions are possible given different definitions and that's ok; we're no longer looking for a single "best" solution.
Don't worry about toppings. You'll only be judged on crust volume.
There's no trick or outside-the-box thinking required. Just pure logic. For instance, the answer is nothing like "live in the room and eat the infinitely large pizza until you die of old age".
EDIT: The top answers are already better than the answer I had in mind; in retrospect this is because I didn't add enough constraints, but the solutions people are coming up with are so interesting I think it's best to leave it open-ended.
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