Some public libraries use a barcode on the date slips in their books which is easily cracked by anyone with a knowledge of binary arithmetic, but those with which we are now so familiar on purchased goods are much more of a puzzle, as there appears to be little correlation between the printed digits and the bars by which they are represented – a little trial will reveal that it is certainly not one-one!

Even with a large number of examples to experiment with, I very much doubt if anyone not in the secret would succeed in solving the problem, which it is the object of this article to elucidate.