Multiplication chart, 1 to 12

What this table holds

Twelve rows, twelve columns, and 144 products in the cells between them. The smallest is 1, where the first row meets the first column; the largest is 144, in the far corner. Counting the header strip across the top and the header strip down the side, the press sets 168 numerals on the sheet, at fifteen point, inside 28 ruled lines. It fits on one sheet of A4, and it is the standard size of the thing: when a times table chart is asked for without a range, this is the chart meant.

Among those 144 products there are 59 distinct answers. That is not a rounding of the count, and it is not a shorter list of the important ones. It is how many different numbers actually appear in the grid, and the reason is worth a section of its own below.

Taking it

Take the sheet as a PDF, a PNG or an SVG. Before you do, you can change the range it runs to, the paper it is set for, whether it stands upright or lies landscape, and whether the cells arrive printed or empty for you to write in. Change any of those and the table is recomputed and redrawn here, in the browser, before it is handed over.

144 cells, 59 answers

The grid is symmetrical about its diagonal. Seven times eight and eight times seven are the same product, so 56 is printed twice, once on each side of the fold. So is every other product that does not sit on the diagonal itself. The twelve squares that do sit on it, 1 and 4 and 9 and so on up to 144, are printed once, because each of them is a number multiplied by itself and there is no second cell for it to occupy.

The arithmetic of that is plain enough on the sheet. Fold the paper along the corner-to-corner line and the two halves agree, cell for cell, all the way down. What comes out of it is the figure above: 144 cells hold only 59 distinct answers, fewer than half as many different numbers as there are places to print one. A handful of them appear more often than twice, wherever a number can be factored more than one way, which is why the count falls as far as it does rather than stopping near half.

It is the plainest and most useful thing the object has to say about itself. Half the sheet is the other half printed backwards.