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Growing Ls

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

This is a size 1 L:

Four of them can be used to tile a size 2 L:

size 2 triomino tiled

Devise a convincing argument that you will be able to tile a size 4, 8, 16, 32... $2^n$ L using size 1 Ls.

If you liked this question, here is an NRICH task which challenges you to use similar mathematical ideas.