Learning how to make a Renzoku

I took a little break after my last blog post. The last kakuro I did really took it out of me since I did it all in one sitting and it was particularly fiendish. I got some feedback from a friend and they found it one of the more difficult ones. It’s great to be in that position to be able to make something difficult, but the true test of good design is creating an experience that introduces new tools to players throughout the game so that they might apply them. With kakuros I’m starting to get to the stage where I can make difficult ones, but there’s still lots of design to improve on.

In the interim I’ve picked up a new puzzle type to start looking at: Renzoku. They’re very similar to the Futoshiki but I think I prefer this variant as all the clue information is given to the player up front. The rules of Renzoku are as follows:

• Each row and column must contain one instance of the numbers 1-5 (if the grid is smaller or larger this range is altered to match the horizontal and vertical maximums)

• Dots between cells indicates that the numbers in those cells are consecutive

As always the first step is to play as many of these puzzles as possible to get familiar with solving solutions. Because of the consecutive rule, Renzokus have their own logical constraints which players use to solve them. At a certain point however, because of the unique number requirement in rows and columns there is a certain point where sudoku logic can be applied to solve areas. I made 3 renzokus in all. The first two were fine, but I’m quite happy with the third one which is the cover image for this blog post (the answer for which is down below)

So this was the first one I made and straight away my own critiques of this puzzle is that there are way too many dots communicating consecutiveness. The dots act as clues, but too many of them and the solving process is a simple matter of filling in the blanks because there aren’t many logical leaps to make. What I learned from this one is that because all of consecutive information is given, the lack of a dot between cells communicates almost as much as if there was a dot there. So it’s important to use a combination of consecutiveness and those that aren’t consecutive.

So the complexity of a Renzoku isn’t determined by the number of dots in it, but it does give a lot of information in these small 5x5 grids. What I tried with this one was to specifically fill in the numbers of the grid so that there were fewer consecutive relationships. This made for a slightly more difficult puzzle but with the given numbers it still manages to be fairly trivial.

It’s worth pointing out at this time that I’m not trying to make the most difficult puzzles. But in the process of making puzzles more difficult and pushing my design in that direction, I learn more about solving solutions and how to design for them.

So, this all leads to the third renzoku. For this I took the lessons of the second one I made to really focus in on making a lack of relationships between adjacent cells. For this I took a couple of rows and the middle column and tried to make a sequential combination of numbers on each horizontal and vertical with as few consecutive relationships as possible. I only had one in the column which worked out well.

This created a good base to work from in terms of making a more difficult puzzle. From that point, it remained to make sure that in filling out the rest of the grid, that each row and column only had one unique instance of each number. Following that it was a case of filling in whatever dots needed to go in the grid and then determine the starting digits that were revealed.

For determining the starting digits it was important to find things that would chain together both in a satisfying way and that would provide enough information for solving the rest of the puzzle. For the first two puzzles I made I only needed the one digit because there were so many consecutive connections. but for this one I needed 3 to really get the ball rolling.

But it’s fascinating from just that point how much more solving logic I was able to learn from the incredibly constrained position that the puzzle forces you into. For my next post on Renzokus I might try the puzzle I made again then map out that solving logic so I can make more based on progression through a few of them.