I would create a data-structure consisting of
- a partly filled square
- the list of numbers you need to place
Then you could use a recursive algorithm like the following:
- select an element from the number-list (*)
- select an empty position
- place the element at the position
- check, if the square is still consistent (all completely filled lines sum up to 175)
- if yes, repeat the step with the new square and the reduced number-list
- if no, restore the previous state (of number-list and square) and try with the next number and/or position
If the number-list is empty in step 1, you have found a solution.
Once you have your basic algorithm, you can optimize. E.g. your selection-algorithms and your consistency-checks.
That's when the real fun starts :-) (because you can add "intelligence" instead of pure "brute-force")
Hope this helps! Rata
(*) a basic selection-algorithm could be going from first to last.
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