Two logicians place cards on their foreheads so that what is written on the card is visible only to the other logician. Consecutive positive integers have been written on the cards. The following conversation ensues:

A: "I don't know my number."

B: "I don't know my number."

A: "I don't know my number."

B: "I don't know my number."

........ n statements of ignorance later..........

A or B: "I know my number."

What is on the card and how does the logician know it?

no clue. This is a really hard one because it is almost impossible to think about. How would telling eachother they didn't know their number effect the out come of who guessed first. Since I assume they know they have to be consecutive numbers, then eventually one might guess, but saying I don't know over and over again doesn't change the fact that it could be one higher or one lower than the card on the other's forehead.

Posted by Jon on 2003-04-11 05:44:44