As a way to spark some curiosity and generate some pondering before the holiday break, students in grades 7 and 8 were introduced to a non-traditional geometry called taxicab geometry. In this geometry, the distances between points are measured at right angles, rather than in a straight line, as if travelled by a taxi driving on streets between square city blocks.
In the illustration below, the green line is the straight line distance from traditional geometry, but the colored lines each represent shortest paths when staying to the streets. How many shortest paths are there?
