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There's no no-computers, and it was easy enough to hack my Kyoto CNF generator to produce a SAT instance for the problem: a 9×9 bit array where each row, column and box has two 1s and no two adjacent variables may be both 1. no-computers proof:


This is a difficult puzzle, especially for an interview. It seems that there ought to be a clever solution, rather than a brute-force or trial and error kind of solution. Typically, I would expect something hinted at by @FlorianF where the puzzle is equivalent to something that has an obvious solution. Or that there would be some simple algorithm that yields ...


I'm not really sure I understand the question, especially the meaning of "such that the sums of the prefixes of lengths 1,2,… of the 6 permutations are distinct" - as it is ambiguous as to whether or not 'distinct' carries across all sums of all prefixes of all permutations, or just the sums of the prefixes of each permutation. An additional clue ...



Here is a solution What I have not considered


I think you are Reasoning


Two solutions: And (Verified both with online character counters) Explanation: And through this analysis, I can also be confident there are no other solutions.


The easiest way to count is

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