Oo, I stumbled on this: buttondown.email/hillelwayne/a -- 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.

For example, for the 47 times table, write down the grid with 7 in the top right:

| 7 4 1
| 8 5 2
| 9 6 3

Then prepend the five times table, knocked down by one for each line you've crossed:

$$\begin{pmatrix} 47 & 94 & 141 \\ 188 & 235 & 282 \\ 329 & 376 & 423 \end{pmatrix}$$

Boom!

[Correction in first para: *7 in the top left.]

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