Chestful of gold

A pirate crew finds a box full of gold they are mostly crooks, they honor order of command and democracy. The highest rank pirate is supposed to put forward a proposal how do they split the gold. If (strict) majority approves that, the proposal is executed. If it’s rejected, the proposing pirate is executed and the second to highest rank suggests the split, repeat until they make a deal. Note that a dead pirate cannot own any of the gold (i.e. they prefer being alive to owning coins).

Task: What proposal should the captain present (or any other pirate)?

Deadly hats

A band of prison wardens decide to execute prisoners in very convoluted way. They give out black and white hats to the prisoners each prisoner one, yet unknown number of the types. The prisoners stand in a row so that they can see hats of the prisoners standing in front of them but they don’t know their own hat color. The wardens offer to spare those who would correctly tell the color of their own hat.

Task: What strategy should prisoners adopt to maximize number of survivors?

Cooperating prisoners (say number)

Another prison story. There are $n$ prisoners and each is given a number from $1,…,n$ (not all numbers must be used, they can repeat). None of the prisoners know their own number but they can check number of any their mates. If at least one of the prisoners guess their own number, they are all released.

Task: Design a strategy for prisoners to maximize their chances of being released.

Weighting balls

There are nine balls, a single one of them is slightly heavier than the rest of them. You get balance scales but can only use them twice.

Task: Identify the heavier ball.

Task 2: The ball has different weight (ligther or heavier). Identify it.

Monty Hall problem

Wikipedia

Task: To switch or not to switch?

British impact

All cars in the Great Britain switch lanes and begin riding on the right side of the road (it happens during ride).

Task: How much would Earth rotation change due to this change?

Credit goes to my various friends.