# Tetris Cube and n-dimensional Tetris

Recently I attempted to solve the Tetris Cube I found in a box under my bed. Just like normal Tetris but extended to 3D in a 4x4x4 cube. How hard can it be to to fit 12 pieces into this cube? Well by my rough estimates itâ€™d be on the order of trillions of (very) naive brute force attempts to find just one solution. Tetris in 2D is already NP-complete; this is definitely not any easier.

In the spirit of completing the puzzle (and also to prove to my brother), I decided to solve the puzzle with progrmaming. It took a bit of time to realise that the problem reduces to an instance of the set-cover problem. Once it becomes a set-cover problem everything becomes rather trivial and just a matter of coding. To solve the set-cover problem, I converted it to an ILP problem and just solved with a LP package in python.

But what about n-dimensional Tetris? Well the program deals with that as well. Things get a bit hard to conceptualise after 3D but nothing really complicated is going on since pieces. Everything can be generalised to n-dimensionsâ€“it might just take some more thinking.