Can You Design a Kakuro Puzzle?

Are you a fan of problem-solving? Do you enjoy challenging your brain with logic games and brain-teasers? If so, we invite you to solve this month’s “Ponder This” challenge by designing a small Kakuro puzzle.

Example of an easy Kakuro puzzle
Example of an easy Kakuro puzzle

Ponder This Challenge:

Kakuro (Japanese: カックロ) 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.


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


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


IBM Research will post the names of those who submit a correct, original solution to their website. If you don’t want your name posted then please include such a statement in your submission!  Please send your submission to the webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

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