IBM Ponder This #201 · January 2015

Kakuro is a numeric crossword puzzle, in which each square occurs in exactly two definitions: vertical and horizontal. Each definition is on the sum of at least two squares and each "word" is a set of different non-zero digits.

It is easy to see that we can omit any single definition without losing any information, but omitting two definitions may enlarge the set of possible solutions.

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This month's challenge is to design a small Kakuro puzzle which is uniquely solvable, but for which removing any two definitions introduces at least one more solution.

For example, a 2*3 matrix where the sums of the two rows are 7 and 9 and the sums of the three columns are 3, 6, and 7 is not uniquely solvable. Please provide the solution as lines of sum and a list of cell coordinates.

The example above in this format would look like

7 A1 A2 A3
9 B1 B2 B3
3 A1 B1
6 A2 B2
7 A3 B3

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Update (01/03): Bonus '*' for a non rectangular Kakuro.
The missing definitions should still be legal (all different 1-9 digits).

Solution

Best opened after a real attempt

To be added.