Pick two points at random on a circle and draw the chord connecting them.
Pick two more points and connect them with a second chord.
What is the probability that these chords intersect?
(In reply to difficulty-one
by ed bottemiller)
The original poser of the question initially selects a difficulty level when submitting the puzzle.
It appears as a set of bars to the right of the envelope to the right of the title of the puzzle, when it's presented on the site. You can mouse-over it to see the actual number, or just count the bars.
When the puzzle gets into the visible, votable queue, the Journeymen and Scholars can discuss the difficulty level. Either the original poser or a scholar has the capability of changing the level, but it's generally agreed to need a sort of concensus to change it.
Difficulty 1 is generally agreed to be a puzzle capable of being worked out in one's head. In the present case, there is a strategy for working this out in one's head, without complicated calculus as would be needed by integrating areas over different original placements of the first chord.
In that way, the difficulty rating of 1 in fact acts as a clue that there is an insightful way of solving this puzzle so that it can be worked out in one's head.
Edited on May 11, 2009, 5:23 pm
Edited on May 11, 2009, 5:24 pm
Posted by Charlie
on 2009-05-11 17:20:48