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If anyone can offer and advice for me on where to start or how to solve this program let me know.
Simply play the puzzle: cut little squares of paper, write numbers on them and play the puzzle by hand. Draw a grid, number rows and columns. Pay attention to when a move is legal or not, what happen to numbers when a move is done.
A simple observation of what happen when you play the puzzle is your algorithm.
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I have not tried much with this program as I was stumped on where to exactly begin.
Your programm will roughly look like that: