In Normandy, there is monastery of 100 Trappist monks. They are highly logical and can determine the answer to any solvable mathematical problem. The monks also keep strictly to the rule of St Benedict. To discourage vanity, they have no mirrors or any other reflective surfaces. They remain completely silent and all times and indeed do not communicate with each other in any way at all. However, they always take meals together each day at breakfast.

On a routine medical visit, the local doctor informed them one afternoon that at least one of the monks had contracted a rare and fatal disease. All affected monks displayed the characteristic symptom of a red dot on their forehead. He told them that the illness had already passed the contagious stage so that no new monks would be affected. Most bizzarely, the disease works directly on the brain and kills those infected during the night on the day they realise that they are ill.

The Puzzle: Everything is fine until the morning of the 13th day after the announcement, when some of the monks do not turn up for breakfast (for they are dead). How many monks died?

The Puzzle: Assume that the pirates are clever logicians, so that they can analyze this problem completely. Also assume that the pirates have the following priorities (in order): to protect their own lives, to maximize their profits, to kill their fellow pirates. What distribution of the gold sovereigns should Ed propose?

Hints and solutions available here.

Further thoughts: If you manage to solve this problem, think about what would happen if there were 6 pirates. To start with, we need to clarify one of the conditions. Rather than saying that the pirates try ‘to maximize their profits’ (a somewhat vague notion), we’ll insist that each pirate tries to maximize their minimum profit.

For example, Ahab may be faced with two choices. Following the first path, he may win 90 gold coins or 10 gold coins, depending on the choices of the other pirates. However, let’s suppose that following the second path he could win 50 gold coins or 11 gold coins. According to our principle, he’d choose the second path. The reason is that the minimum winnings are 10 coins and 11 coins respectively. So the second path maximizes his minimum profit.

Using this idea, you should be able to solve the 6 pirates problem, then solve the n-pirate problem for arbitrary n. Can you write a computer program that simulates the arbitrary problem?