Sudoku was quite the craze for awhile. It thrived on simplicity; use the numbers 1-9 once apiece in each row, column and box. Despite being a number puzzle, it had very little to do with mathematics. You could have just as easily replaced the numbers 1-9 with A-I and it would have been essentially the same thing.
I would guess that most are less familiar with Kakuro though (also known as “Cross Sums.”) Kakuro is essentially a number crossword: much like regular crosswords, multiple words/solutions might fit in one spot, but the entire puzzle grid has to be taken into account. The intersection of two solutions have to match up. Kakuro is much like that, but involves the addition of numbers instead of words. Its a fair bit more difficult than Sudoku in my opinion not just because of the light math, but for the same reason crosswords are difficult.
Both of these kind of puzzles influenced my development of NumCode. In NumCode, Kakuro-style crosswords are used but on a much smaller scale:
This crossword follows the basic rules of Kakuro. The vertical column marked with a 5 requires two numbers that add up to 5, while the horizontal row marked with a 6 requires three numbers that add up to 6. With only one square being shared by the two solutions, this isn’t too difficult to work out:
This solution fulfills the addition requirements. But in NumCode, this would not be a valid solution. Not only does NumCode use the basic structure of Kakuro puzzles, but the number limitations of Sudoku. This solution is not valid because it uses 3 twice in the same puzzle.
The importance in the solution lies partially in the shared square. The only number that adds up to 5 with 2 is 3, and vice versa. This means we can’t switch the places of the 3 and 2 in the horizontal row, since the 2 would then be used twice. This means the only logical solution is to stick the 1 in the shared location:
This works, because “1 + 4 = 5” and 4 is available to use.
This simple logic is what drives the basics of NumCode. Most of us can add up to 5 and 6, but the “Sudoku” rule adds a little wrinkle that makes it more interesting. This is the foundation of NumCode’s puzzle logic and lays the groundwork for more creative and challenging puzzles to follow.
Thanks for reading, and stay tuned for more looks into NumCode.