denis_berthier wrote:But my point is, the whole puzzle cannot be solved using only information from one sector at a time (and with no T&E).

For Sudoku T&E generally means setting a cell to a candidate value and then testing the resulting grid. "Can (R, C) be D?" is the question. Can the puzzle be completed, or is there some contradiction found that enables the candidate's removal from the cell's domain (candidate list). So for me, T&E solving involves some form of DFS, ie "look-ahead".

For Kakuro, however, the same question "Can cell (R, C) be D?" can be asked in two different ways :

- can this puzzle be completed with (R, C) = D? (DFS/look-ahead)

- can this sector be completed with (R, C) = D? (simple arithmetic)

If we have a sector of length 3, with sum = 16, and the current candidates for the 3 cells are {1, 4}, {3, 5, 7}, and {6, 7, 9}, then the question "can the second cell be 7?" has answer "no", because you can't make a sum of 9 out of the first and third cells.

These are single-sector context tests, and don't involve any look-ahead, so for me this particular type of test is not the same as T&E. And the puzzle is solvable using information from one sector at a time.