Two Lady Bug Path Problems

lady bugs on a sojourn

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:

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1 Response to Two Lady Bug Path Problems

  1. Agni says:

    (1) All the paths have length 14 units (there’s not a single shortcut; the guys still have to take a taxi. The girls were smarter – duh!)

    (2) By writing the number of paths to each corner of a unit on the grid, there were 238 paths at the top East corner.

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