Designing For Unique Solutions

Today I struggled with a 3x3 grid Kakuro I was working on. After a few failures I decided to switch tracks and work on a more crossword-looking Kakuro. Balancing a 3x3 grid for all of those 3 cell clues was a bit much at this early stage of starting to make Kakuros. So I went for a more interesting looking grid that incorporates 2 and 3 cell clues, and crucially is easier to create.

In the end I think switching to this design really helped to hammer in a couple of design principles when figuring out number puzzles. One of the more important principles is ensuring the puzzle has a unique solution.

In the above puzzle I’ve used the principle of combining low and high number clues to help guide the player at the start. The 3 cell 7 clue is combined with the high number 19 and 20 clues to help start the player off. Where things get interesting in terms of design are the duel 2x2 grids in the corners. So in the 19 and 20 clues the remaining numbers to fill in the cells were 8/9 and 7/9 respectively.

I found that in the clue for the columns in both of this smaller grids I had to be careful with what the number was as it might allow the player to switch the numbers around as they wish: thus the puzzle would not have a unique solution.

I found that on the column clue on the left hand side, using an 8 would preclude using 4s within the cells which helped me with the other clues. By continuing on with Kakuros this week I’ll continue on with the focus on unique solutions. But I’ll try to keep things easy on myself and use a combination of 2 and 3 cell clues.