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?

"To maximise your probability (as someone suggested in the comments) roll a "d20" - a 20 sided die - and only send the letter if you roll a 20. A probability calculation shows that this yields the best odds, with a surprising 37.7% chance that only one of you will roll a 20 and send a letter. Better odds than predicting post office behaviour, surely!"

Once the die has been rolled, you could then wait a random (long) period of time before sending your letter. If another person thinks the same, it is likely that his/her chosen time will be different and the possibility exists that the letter will be received and the prize distributed before a second person submits a letter. This would increase the odds of receiving a prize.

Posted by S on 2003-10-30 12:17:50