A boy and a girl agree to meet in the park. Each will show up at a random time between 12:00 and 13:00, and wait for the other person 20 minutes, but not past 13:00.

What is the probability that they will actually meet?

(In reply to is the boy smart? by jduval)

Funny, but If they are BOTH smart, they will show up at exactly same time; 12:30. This is why;

The boy realizes that to maximize my chances of meeting the girl he should show upt between 12:20 and 12:40. This way he will have a 4/6 chance of meeting her, as oposed to a 5/9 chance if he chose a random time between 12:00 and 1:00.

Next, the boy realizes that the girl is also smart and will do the same thing as him; she is going to show up between 12:20 and 12:40. At this point he realizes that  they are going to meet for sure, and that he can minimize his maximun wait time to 10 min by showin up at 12:30.

The girl will be thinking along the same lines, so they will both meet at exactly 12:30.

Which proves that logicians are soul-mates.

Posted by ajosin on 2005-06-08 18:35:57