Oo, I stumbled on this: https://buttondown.email/hillelwayne/archive/how-to-memorize-a-larger-multiplication-table/ -- I think (with a little thought) that might be the killer insight into memorising times tables.
I think these two grids are all you need to memorise. Suppose you're multiplying by \(10a+b\), [^0]. Rotate the grid so that \( b\) is in the top left. If \( b \lt 5\), write down the \(a\) times table in front, but bump it up by one every time you cross a vertical line. If \(b\gt5\), write down the \(a+1\) times table, but drop it by one each time you cross a vertical line.
[^0] Sigh, because mathematicians: \(a\) and \(b\) integers, \(0\le a\lt10\) and \(1\le b\le 9\), \(b\ne 5\). Honestly.
[Correction in first para: *7 in the top left.]
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