denis_berthier wrote: .... Actually, my numbering is different because I take the 1-cut cell inside the smaller surface:

r2c2, r2c6, r3c7, r7c3, r6c2, r7c7

The 2 you don't count are the small 2x2 squares inside the bigger ones. But I agree they are not useful.

I don't see how you could call, for example, r7c7 a 1-cut in any helpful way. You could just as easily call r7c8 a 1-cut.

In fact, if you interchange the 17 and 14 sums above r7c7 and r7c8, you have an entirely equivalent puzzle.

Cutting r7c7 out of the puzzle would, indeed, divide the remaining puzzle topologically, or graph-theory-wise, into two separate pieces of paper. But these two pieces are not separate kakuro-wise! r7c6 and r7c8 remain connected when r7c7 is removed, just as r7c6 and r7c7 remain connected when r7c8 is removed, because they're in the same sum!

The graph-theory notion of 1-cut is, quite simply, irrelevant in kakuro. I really think you need to use my "singularities" instead -- but you can still call them 1-cuts, if you prefer.

Bill Smythe