I had often thought of making a Sudoku afghan but decided it would be a bit boring.
Then, in the summer of 2015, Alex Bellos and Edmund Harriss produced a geometric
colouring book called Snowflake, Seashell, Star : Colouring Adventures in Numberland.
It included a few designs that we had previously used for afghans but one in particular
caught my eye. It was three superimposed Sudoku solutions.
The page in the book has a blank sheet for colouring in but Alex also showed a coloured
version in his weekly blog in The Guardian. The design has squares inside squares
inside squares. It was coloured in pastel shades and created an illusion of squares
that were not all the same size even where they obviously were. He also said he would
like to see it as a quilt. The challenge was too much to resist though I doubt if
he expected a knitted quilt.
When I looked at the triple solution that Alex and Edmund had used, I realised that
some squares were repeated. All the rows, columns, and blocks of nine squares, followed
Sudoku rules but this still allowed repeats to happen. I decided to make my own version
and spent a very long time doing it. It eventually became clear that I was using
the same logical(?) approach that they must have used except that they had worked
vertically and I had worked horizontally.
I was expecting to see Alex in November so decided to get on with making my afghan
and used his original numbers. I experimented with various squares. My first plan
was to make ‘log cabin’ squares but that involved a lot of picking up stitches and
darning in ends and the squares took a long time to get tidy. I then opted for mitred
squares which were much more satisfying as every square is made with stitches picked
up from previous squares.
It created a completely different effect and threw up some zig-zags of colour that
I had not expected to see. They were there in my computer drawings but did not stand
out in the same way as they did in the real thing.
As things turned out I knew I wouldn’t be seeing Alex but did send him a photo of
the finished afghan.
PSEUDOKU
I was still determined to find my own solution that would give me 81 unique squares. I asked Alex and Edmund if they had tried to do this. They hadn’t but both were sure it should be doable. After all there are 504 different ways to make a square with three colours from a selection of nine.
Steve and I then spent several weeks trying to find a solution. It would have been relatively easy to get a computer to do this but we wanted to puzzle it out ourselves. It was very frustrating as it is one of those things where you think you have just solved it only to find that the last line doesn’t work. Arriving at a solution was a bit of a fluke. One day I decided to abandon all previous attempts and start again from scratch. Within a short space of time I had a solution which seemed to be too good to be true. We checked it numerous times but I still half expect an error to appear.
I wanted this second version to replicate the optical illusion from Alex’s article so decided on crochet squares, Actually, this is not strictly true because my first attempt was with circles surrounded by rings surrounded by squares. It destroyed the illusion so, although all the circles and all the rings were already finished, I abandoned that idea and started again. My plan was to use ‘jewel colours’ throughout. As it turned out the Gold parts are rather bright and the Green and Teal are rather much alike - but all this helps to recreate the illusion.
One pleasing thing about these afghans is that they use exactly the same amount of yarn in each of the nine colours, which obviously has to be the case if you stop to think about it but isn’t immediately obvious.
