Ten Minus One

Nine is an awkward number to count in your head, so nobody does. They build it out of ten instead, because ten is the number our whole way of writing works in.

Here you lay out rows of ten and then take exactly one cell out of every row. Ten rows of ten is a hundred; take one from each row and a hundred becomes ninety. Three rows is thirty; take three and it is twenty-seven. That is all nine times anything ever is — ten times it, with one taken from each row.

Then you press pack, and the cells that are left slide up into fresh rows of ten. Now look at two things at once. The holes you left behind, and the cells sitting in the tray, are the same amount: one for every row you laid. And the ink stops one whole row short of what you laid out, with a short row over. The row count is your tens digit and the short row is your ones digit, which is why the finger trick works at all.

The last round goes past ten rows, which is where the trick people memorise falls over. Eleven rows is a hundred and ten, and taking eleven away takes a whole row AND one more, so the tens digit is not ten — there is no such digit. The taking away carries on working perfectly. It is only the pattern that breaks.