Lesson 7

There is an error in the proof that is easy to miss: in the inductive step, we get subgrids where a corner cell is removed instead of a central one.

To prove the required statement by induction, let's generalize it as follows: “no matter which cell is removed (from a square of size \(2^{n} \times 2^{n}\)), we can divide it into triminoes.” This statement can be easily proven by induction: we divide the square into four squares and in the three squares where no cell is removed, we cover the corner cells with a trimino; we are left with four squares, each of which has one cell removed.