nicow wrote:
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Just a simple puzzle for lovers.
Thanks. Apparently easy but soon you observe more complexity. It's very curious, since initially you ignore the rules and the two pending numbers, so you must
demonstrate that the solution is unique and that those numbers are necessarily 4 and 5, i.e., observing that
the sum of the two pending numbers must be 9 (by using, for instance, the "addition rule" applied to three contiguous lines, and assuming that lines always contain
the same numbers as in a normal Calcudoku, what gives you 21 for that sum).
In these conditions, the "unknown" numbers could not be the pairs [1,8], [2,7] or [3,6] due to duplications in rows 2 and 5 and/or in columns 2 and 5 but, even considering a possible duplication, the analysis shows that [3,6], for instance, would not be possible due to cages "10+" or "11+", and similarly with the other two pairs. Other possibilities for a sum of 9, like [0,9], [-1,10], [-2,11], ... , must be analyzed as impossible; we must also demonstrate that non-integer numbers, i.e., other rational/fractional numbers (as it happens with negative numbers) are impossible.