Trying to understand a 3x3 grid

I took an hour or so at the weekend to try and get back into Kakuros. I’ve definitely found them the most difficult puzzle to figure out and to be honest I’m still a ways off. The thing that’s eluded me the most is a 3x3 grid. Trying to fix the clues in a way that they cascade into each other has been pretty difficult. And I’ve failed more than a few times. But I drew out a whole page of 3x3 grids determined to give it a go and iterate my way to figuring it out!

I started by using lessons learned from my smaller pieces of kakuro practice in the past: low leading high. I used the 6 clue in the top right to trigger the 3 being set from the 20 clue because it forces that minimum. I used the 8 clue on the bottom left against that other 20 clue. This created an ‘8/9’ corner in the top left which is somewhat disambiguated by the 11 clue. This starts to give enough information where all that’s left is a 2x2 to solve. Unfortunately I messed up the maths and it doesn’t work. A sign of things to come in this attempt!

So what I thought was the problem was the 8 clue in the bottom left which I changed to a 9 because it was only a difference of one digit needed from the 14 clue in the top middle. What this then created was an interchangeable ‘1/2’ corner which doesn’t make a unique solve. What then followed was a couple more instances where I changed clues on the bottom left hand side to accommodate this. All I actually had to change was that 14 clue at the top.

What this created was something that I don’t think is too difficult but neither is it particularly interesting. That is until I looked at the puzzle again and forgot that the 20 clue can have 4 different possibilities and when you raise the clue value of the bottom left from a 6 to an 8 you lose that forcing 3 that’s a factor on the top right.

Interestingly enough, I found out a few days later that the reason I feel like I’ve been failing at this ‘simple’ task of making a 3x3 Kakuro grid is that it’s actually one of the hardest things you could start off with making. I’d played through one Kakuro app on the Switch and some of the puzzles they presented were these square grids that relied a lot on bifurcation that was difficult for a beginner Kakuro solver to understand and keep in their head.

I believe that’s because the puzzles were algorithmically designed so there wasn’t a designer behind the puzzles, scaling the progression and difficulty in an accessible way. Downloading another Kakuro app recently showed me that a lot of actual Kakuro puzzles rely not on these difficult 3x3 or 4x4 bifurcation solves, but on grids which have a variety of cell sizes but invariably have different 2 cell clue starting points.

This is a much better way for me to get started with these types of puzzles so what I’ll do is copy the grid structure of one of the introductory kakuros and make my own clues and answers. It’ll be a long process (and probably an even longer blog) but I think my process will improve because of it.