Hugh was trying to see if he could tile a 2" x 2" board with L-shaped tiles (i.e. a 2 X 2 tile with a missing 1 x 1 square) such that there is exactly a single 1 x 1 square missing from any chosen square. A successful tiling for n = 2 and specifically the top-right square chosen is shown as an example: (But to verify that it is always possible to tile for any chosen square to be missing would require 16 examples.) Prove by Mathematical Induction that Hugh will always be able to perform this tiling on a 2" x 2" board for any chosen 1 × 1 square missing.

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