Consider a square grid in which six north-south streets, separated by gaps of 10 miles each, are elevated above six east-west streets laid out in a similar fashion. Entrance and exit ramps connect the streets at every intersection. Because there are no traffic lights, switching from a north-south street to an east-west street (and vice versa) takes essentially zero time. The grid has very little traffic, but the local police patrol very carefully for speeders.

The speed limits follow an unusual pattern. The limit is 10 miles per hour for the southernmost east-west street, 20 miles per hour for the east-west street immediately to the north, and so on. (Therefore, the limit for the northernmost east-west street is 60 miles per hour.) Similarly, the speed limits for the north-south streets range from 10 miles per hour for the westernmost to 60 miles per hour for the easternmost. Let's label the intersections using their column and row numbers: the southwestern corner of the grid is (1,1), the southeastern corner is (6,1), the northwestern corner is (1,6), and so on. As a warm-up problem, can you determine the fastest legal way to get from (1,1) to (6,3)?

This article was originally published with the title Grid Speed.

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