nicow wrote:

...

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.