Learning and naming new techniques

From my last blog post I endeavoured to keep copying the larger crossword like structures from other apps so I can focus on just the clues and the variety of ways they can be built in. From that as well I’ve been doing more Kakuros in my spare time and learning new solving logic. The combination of these things has led to what I think is a fairly interesting Kakuro above (even just from an analytical standpoint).

There were two things I identified straight away with this structure: two horizontal 6 cell clues and two vertical 7 cell clues that intersect in a square pattern. This makes for a really interesting interrelated puzzle and something that is quite difficult to design for. The first decision then was to make life a little simpler for myself and make them all minimum and maximum clues up to the threshold of the cell count. What I mean by this is that in one of the 7 cell lines using a 28 clue to indicate that the numbers all have to be between 1 and 7 inclusive (no 8s or 9s). For the other 7 cell clue I used a maximum threshold (42 across the numbers 3-9). This allows the rows and columns that intersect with these lines a certain amount of constraint in what they can possibly be.

Beyond this square clue structure, ordinarily it would be a case of picking an area to start with and beginning to layer clues. However, I also wanted to work on some of the solving logic that I’d begun to discover.

Okay, so for my own purposes I’m calling this particular technique a detached cross section. The end product is finding out the order of the 4 clue. But to do that we must understand a chain of events. The maximum digit in a 7 cell 28 clue is 7 so that disambiguates the 16 clue at the bottom, placing a 9 in the lower part of the 10 clue and a 1 in the upper part. It is this 1 that makes the detached cross section. The 4 and 10 clues don’t intersect directly, but by the constraints of the 4 clue and the 1 placed on the row which sees that clue we can ascertain the order of the 3 and 1 which belongs to it.

Learning this type of solving solution doesn’t take a long time of playing Kakuros but it does take a practiced eye at scanning the grid. So I really wanted to utilise this in a couple of different specific ways.

Following on from that I wanted to differentiate this one as long min/maxing. As previously mentioned the 28 is constrained across its 7 cells by the lowest value digits possible from 1-7. The 16 forces out the maximum digit on that range: 7. And the 15 clue, by way of its intersections, forces out the 6. This trickling down of the maximum digits on the 28 clue allowed me to focus on the lower numbers for the rest of the column.

I sat down and didn’t move for 2 and a half hours until I had made all of the clues for this Kakuro. There was a section in the bottom right part of the grid that took a lot of concentration and time however, but I think the result is pretty special in terms of how it constrains higher number clues all for the purpose of forcing a 1 somewhere else in the grid.

So I didn’t want the rest of the puzzle to be just simple intersectional clues, I really wanted to continue experimenting with that detached cross section method. So I concentrated on providing a chain of clues for the 24. I wanted to reveal one of the digits from it. To do that I needed to work the 4, 16 and 10 close by to constrain it. What this led to was trying to get the player to need to force a 1 on the purple square shown above. This maybe took me a good hour of trial and error with different combinations of clues. I initially had really low numbers meaning the 1 could travel anywhere so I had to change a few clues on that bottom right part of the grid.

It took a long time but I’m really pleased with what I was able to come up with because I feel like it’s quite an elegant constraint that cascades a lot of the puzzle.

Because I made this puzzle in about two and a half hours without taking a break and really pushing myself, I was pretty exhausted by the time I cracked that last detached cross section. So the rest of the puzzle (read: the entire top left) just became a series of cascading clues because I couldn’t muster the energy to push forward and create something as interesting for the player on that side.

Ideally I would have worked on something that combines clues across the square intersection of 6 and 7 cell clues but there will be time for that kind of complexity the more I grow as a designer and familiarise myself with loads of different formats. But the more I carry on with this blog series and dipping into more formats I can feel that design instinct latch on quicker and quicker. I’m intimately familiar now with the process of getting better at something, when starting from a position of no knowledge.