There's this problem that my professor showed me that I thought was interesting.

The problem is as follows: If you have a 2^n by 2^n checkerboard and remove one square from it, will you be able to fill it with L-shaped trominos?

The answer to this is yes, the method of which I thought was interesting.

Example

In this example, X is the removed square and the numbers represent the shape of the L-shaped trominos. In every possible permutation of checkerboards, there should be a solution to fill up every square with trominos.

Does anyone know if this kind of problem is named in a field of math? I'd love to learn more about these.

I'm also going to attempt to program this, anyone have any ideas that could help?

CodePudding user response：

There's a broad family of problems called tiling problems that ask when, whether, and how to tile different shapes using a fixed collection of figures.

There are other questions about figure subdivisions, where the question is when, whether, or how to subdivide some larger figure apart into smaller figures of various shapes.