Proof a $2^n$ by $2^n$ board can be filled using L shaped trominoes and 1 monomino Suppose we have an $2^n\times 2^n$ board. Prove you can use any rotation of L shaped trominoes and a monomino to fill the board completely.
You can mix different rotations in the same tililng.

Forgive me if what is below is ‘old hat’ or easily found on some other site. I only found this site whilst solving the similar problem: for which $n$ can an $n\times n$ square be covered without overlapping by T shapes each comprising four small squares. The fact that an nxn square can be almost covered by L shapes comprising three small squares leaving any prechosen square free is true for all $n\ge6, 3\nmid n$. A very simple proof can be found in The Mathematical Gazette of November 1999.
Dr. R.B.J.T.Allenby (long retired from Leeds University,)
