Cross Sums

[A19327]

This is one of the most difficult Cross Sums and would appreciate any help on this.

 

[fresh_42]

What kind of help do you expect?

This is from a mathematical point of view a huge linear equation system $\mathbf{A\cdot x=b}$ with a sparse matrix $\mathbf{A}$ with $0,1$ as matrix entries that has to be inverted. IIRC there are specific algorithms that deal with such problems.

The intention of such puzzles is to find a solution by trial and error. This can hardly be done on the internet. I would start with the lowest numbers $5,6,7$ and $8$ but already these result in a variety of possibilities. Better use a pencil.

 

[blamocur]

These puzzles are called Kakuro. You can play it online. One way to play them is to pencil in all possible digits, then eliminate "wrong" ones according to the rules.