You receive a strange letter stating the following:
You are one of 20 logicians worldwide to receive this letter. You don't know each other, but you all think alike. An address is given, and you are told that if a letter is received from one and only one of you, all 20 will equally split a large sum of money. If no letters are received, or more than one, no prize.
What would you to for a chance of winning the prize? What could you do in order to maximise the probability of winning?
(In reply to
probabilistic approach by Cheradenine)
An interesting point here is that no closing date seems to be given. Also, if the recipient receives 1 letter, how long do they wait to see if another turns up before deciding you all have won/lost? If there is really no closing date, we could roll a 100-sided dice on the first of each month and if it comes up '1' we post a letter. The chance of the logicians sending more than 1 letter each month is then quite slim, it doesn't matter if none are sent (as there is no closing date), and will the recipient be willing to wait a full month after receiving 1 letter before deciding if you've won? Perhaps not....
re: probabilistic approach
