PC Plod, Plod, Plod

  The Problem:  

A policeman has to patrol a certain number of streets, arranged in a   4 by 4 block.  

He tends to walk from one corner of this block (A) to the opposite corner (B), but tries to take a different route each time. In this way, he hopes to deter would-be criminals and also gives himself something intellectual to do, to pass the oh-so-long night hours…

He does like to take an ‘efficient’ route, as short as possible, but still finds he has lots of choice…

How many such routes are there from A to B ?

What would be the answer if the block measured 10 by 10 ?

How long might it take him to try all these routes ?

 

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Last modified: June 18, 2007