Adrian needs to practise his times tables. He knows them, mostly, but not fast enough, and sometimes he still gets some of them wrong.

So we do some maths every day around dinnertime. At first we did it orally – I came up with problems one by one and he told me the answer. The talking slowed both of us down, though, so recently we switched to written practice. I fill a sheet of paper with problems and he then does them as fast as he can.

Initially I made up problems more or less randomly but with extra focus on the ones I knew he knew less well. But now he wants to see if he gets faster, so I need to make the exercises more consistent. I make sure to cover the entire table from 2×2 to 9×9 evenly. But I also want each day’s sheet to have a different order so he doesn’t just learn them by heart by order – “18, 24, 25, …”

My algorithm for making up his worksheet has evolved. The first iteration was a simple one. I drew up a 10×10 square on a piece of scrap paper, randomly picked an unused square (such as 4×5) and put a dot in it when I wrote down “4×5” on Adrian’s sheet.

This was time-consuming and fiddly. My second algorithm was to take the previous day’s sheet and shuffle it. Take three problems from the top of the first column, then three from the bottom, then from the top of the second column, etc. I was hoping this would be faster because I can just follow along, but it was easy to lose my place and forget which row I had just copied and where I should continue.

My third algorithm was the opposite of the first one. Instead of filling the sheet top to bottom with exercises in random order, I went through the table top to bottom (2×2, 2×3, …) and wrote each combination in a random place on Adrian’s sheet.

At this point I noticed that I must have made mistakes in my first algorithm. When I was done with a sheet using the third algorithm, I noticed that the finished sheet had fewer problems than the previous sheets. I double-checked, and apparently I had previously inadvertently included some duplicates. To keep the worksheets consistent in length, I now have to repeat my previous mistakes intentionally and add some random duplicates.

This task is of course just crying out for automation. But then the results would need to get from computer to paper somehow and I don’t have access to a printer. Perhaps at some point I’ll get sufficiently fed up to automate it anyway and cycle to the office and print out a few dozen variations.