Reducing CPLS


Introduction

I’m trying to show that I can convert any partial latin square problem into an arbitrary variant of a puzzle game in poly-time.

Example

./Welcome to Random Puzzle-Game Creator ./Loading n x n Latin Square  [0][1][0]  [2][0][5]  [4][5][0]  ./Convert into    Maximum Valid Numbers  Maximum n{1....n} amount to satisfy nxn?   ./Rules- Filling Instances n! times to yield unique invalid grid. And find the correct instances.  [3][1][4]  [2][4][5]  [4][5][3]  ./Print only found 1 x 1 Maximum Satisfy  [3][1]  [2][4] 

Therefore Maximum Valid Numbers of an invalid square is NP-complete for n^2 x n^2 size.

Question

I know this should be trivially true, because the algorithm reveals a reduction of CLPS in poly-time to my custom puzzle. So, is my reduction correct?