There is any easy solution: on a 36x36, let the top row be the numbers 1-36, the second row be 2-36,1, the third row be 3-36,1,2, and so on. But that's not the point of the exercise. The point is to find a way to build some intelligence into a program that will randomly generate solutions of any size.
The problem does have more than one solution. Swapping any two rows or columns of one solution will generate another solution. This can be done repeatedly in any number of combinations to generate thousands of solutions. But again that is not the point of the exercise.
davidj
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