Ben North's blog

On a ferry journey, Jude wanted a pen and paper game that we didn’t already know how to play, so she invented a variant on naughts and crosses (‘tic-tac-toe’). You play it on this board: You still have to get three of your marks in a row, but there are more ways for this to happen than in normal Os and Xs: Three rings: Three radial lines: Three clockwise spirals: Three anti-clockwise spirals: We wanted to know whether there was a winning strategy, so we drew a whole pile of diagrams to work out how the play would develop: and concluded that the first player always wins. Winning strategy for first player One winning starting move is for X to

A friend kindly gave us some flashing-light stickers for Hallowe’en, and the natural thing to do with them once the festivities were over was to dissect them. So we did this, and found that each contained a square circuit board about 25mm on a side. When you press a little button in the middle, three coloured LEDs — red, green, blue — flash rapidly for about twenty seconds. It looked like they were flashing round in a circle, but too quickly for me to be sure of the sequence. To investigate, I set up the flasher approximately vertically, held in a lump of Blu-tack: Then I turned off the lights, pressed the flasher’s button, and took some pictures with a

Connecting a BBC Master to a modern laptop over a serial link allowed me to extract a friend’s old programs from 5¼″ floppy discs.

A ‘plausibility argument of concept’ for the idea that normal Python code can be compiled into a ‘Lambda function’ and a ‘Step Function’ for use on Amazon Web Services.

The school my three youngest children go to runs after-school activities, and I was part of a group of volunteers who ran an ‘Advanced Scratch‘ course. This was aimed at 10–12-year-olds who had done a reasonable amount of Scratch already, and wanted to explore more. We spent several sessions developing a much-simplified version of the great puzzle game SpaceChem, and then a few standalone projects. It went pretty well, with most of the students getting a lot done. As part of this, I wrote a set of worksheets, which I’ve now tidied up and made available under CC-BY-SA in case they’re of interest to anyone else: Scratch worksheets 2017/18 (Image above contains content copyright The Scratch Team, used under CC-BY-SA-2.0.

Via mathblogging.org, I came across Math=Love’s blog entry describing a piece-fitting puzzle, and thought it would be interesting to solve it exhaustively and answer the question in the blog entry: So far, we have found two different possible solutions. I’m looking forward to collecting data to help determine if there are more! I did this via a Jupyter notebook, and the results are here. I confirmed that the two known solutions are the only ones, up to symmetries.

To be able to watch our pinball machine’s display from anywhere in the house, my son and I put together a system using a logic analyzer and a Raspberry Pi to broadcast it as streaming video.

Following on from the previous MazezaM-related post, Aaron Williams and I swapped a few emails about my family of MazezaM levels whose solution lengths are exponential in their sizes. Aaron put forward a simplified family of such levels, and I have now produced an animated demo: Full write-up and demo on GitHub.

I recently got another long-running collaboration to the point of having something to show — a first-person shooter in the browser. This was an idea which Sally, my youngest, had. She drew a bunch of house fronts, and also some ‘zombies’, and then a map of the world where the action takes place. The result is hosted on GitHub pages: It requires a WebGL-capable browser, and I have not put effort into graceful behaviour if this requirement isn’t met. There are some more details, and also the repo itself, on GitHub, although it’s just a dump of the final state of the work rather than a useful history. It was good to experiment with Blender and BabylonJS in the implementation

As a correction and follow-up to a previous post, I constructed a family of Mazezam levels whose solutions are exponential in the size of the level. Many thanks to Aaron Williams for pointing out my error to me. Full write-up and demo on GitHub.