The other day, I noticed a bunch of lady bugs walking in the grooves of a tiled floor. I caught the snapshot of them above. For whatever reason, they confined themselves to the grooves between the tiles. They all seemed to be going from the lower right corner (S) to the upper left corner (E), but they were taking different paths to get there.
That got me wondering about two questions.
Question 1: What path minimizes the travel distance from S to E?
Question 2: How many different paths from S to E have the minimal distance?
For a hint to the first question, check out this video: