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'Growing Ls' printed from http://nrich.maths.org/
This is a size 1 L:
Four of them can be used to tile a size 2 L:
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.