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Problem of the Day #429: Beehive Management January 3, 2013

Posted by Saketh in : potd , trackback

A local beehive has recently been facing some congestion issues. The hive is made up of $10$ different chambers, and every pair of chambers is connected by a direct tunnel that admits traffic in both directions. Sometimes, this can lead to messy head-on collisions that can really slow down travel around the hive.

In an effort to make travel more efficient, the queen has announced that all tunnels will be made one-way. If the direction of travel for each tunnel is chosen independently and at random, what is the probability that the bees can still get from any chamber to any other chamber?

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