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Derive an mathematical equation for a beehive puzzle

In Fig.1 a beehive is enclosed in a bee cage. The bees can fly with a speed C. Each bee is flying non-stop from the hive to the wall of the cage and then back. Each time one returns to the hive, it is counted as one hit. There are hundreds and hundreds of bees in the cage and they fly out from the beehive in all directions. In situation 1 the bee cage is at rest and the hits per second is Xo...

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This solution is comprised of a detailed explanation to derive an mathematical equation for a beehive puzzle.