Low Leading High
This morning I thought I’d try something a little different. I haven’t made too many Kakuro’s before so I’m still figuring them out. But what’s interesting about them is the designer must get stuck straight in to how you leave breadcrumbs for the player.
First though, what is a Kakuro? It’s a Japanese number puzzle which feels a little similar to Killer Sudoku but it’s in crossword format! Numbered clues are given at the top of a column and on the left of rows. The numbers in the cells of these rows and columns must add up to the clue. But there must be no repeating number within a singular row or column.
What the player ends up doing is figuring out the possible permutations for each clue across the number of given cells. For instance, a clue of 7 across 3 cells is unique as the only possible numbers that add up to this without repeating are 4, 2 and 1. Whereas the clue 15 across 2 cells has two permutations: 9 and 6, 8 and 7. So there’s some interesting cross referencing going on from the player and this leads to some core design responsibilities from the designer.
It’s easy for a designer to put some clues in that have several permutations and ask the player to brute force their way through it. But I think a good puzzle as with any good level should leave enough breadcrumbs to catch a player’s interest throughout. To do this in Kakuros (with such a small puzzle) we mix high clues with low clues.
Low clues like 4 across two cells have only one permutation (3, 1). Similarly with high clues like 16 across 2 cells (9, 7). Using these clues in the above puzzle can help players unfamiliar with the format get started. I didn’t start with these clues, however. I started off trying to make it slightly more difficult. It leads to a puzzle with no unique solution and each clue having several permutations.
Each of the two cell clues have several possible answers and none of them really lead to concrete answers for the 3 cell clues because of that. The numbers of the 15 and 5 clues can also be switched around making this a puzzle with two unique solutions.
From this failed puzzle I altered the clue totals to lead the player through the puzzle a bit more. I think it’s made the puzzle super easy on reflection because the player can instantly place numbers on both the 4 and 16 clues. It’s a lesson to take forward into the next Kakuro though.
It’s an interesting balance comparison with Labyrinth puzzles. They’re of course two completely different types of puzzle (one is spatial, the other mathematical/logic based). But with Labyrinths it almost feels like you’re trying to hoodwink the player into getting lost in them (although there’s a bit of an historical precedent set there) whereas with Kakuros you want the player to get through it.
