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Might Merely Meet (Posted on 2005-06-07) Difficulty: 2 of 5
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?

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (5 votes)

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re: is the boy smart? (and the girl too...) | Comment 11 of 12 |
(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

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