...In His Counting House...

Some of you may be wondering how I've been spending my time recently, especially all of those extra hours freed up by not writing blog posts. There are several answers to this question, and today I'm going to talk about the first one.

I've been counting money.

Now, I don't indulge in lotteries or other games of chance, and I haven't got any rich relatives, so I've not suddenly become a millionaire. Sadly the money isn't mine, or anyone else's.

Instead, I've discovered the book "Amusements in Mathematics" by Henry Dudeny, which has been lovingly digitised by the Project Gutenberg.

This book is a classic of recreational mathematics. It was published in 1917, and consists of hundreds of puzzles. These are arranged into sections, and the first one concerns money.

Here is an example of the sort of puzzle that we're talking about:

A man left instructions to his executors to distribute once a year exactly fifty-five shillings among the poor of his parish; but they were only to continue the gift so long as they could make it in different ways, always giving eighteenpence each to a number of women and half a crown each to men. During how many years could the charity be administered? Of course, by "different ways" is meant a different number of men and women every time.

As I said, the book was published in 1917, and Britain's monetary system was non-decimal. A pound was divided into 20 shillings, each of which was further divided into 12 pence. Each penny was worth four farthings. A guinea was worth 21s (£1.05 in today's money). You won't be surprised to learn that lawyers charged their victims in guineas rather than pounds.

As in present day America, they had names for many of their coins, which were presumably designed to confuse foreigners. Coins like tanners, bobs, florins and half-crowns. Interestingly, despite the fact that the whole system was abolished in 1971 in favour of decimalisation, the old shillings and florins were still in circulation until the 1990s, when they made some of our coins smaller. Presumably to save money. And I don't remember seeing any, but according to WIki, the sixpence coin (confusingly worth 2.5 pence) was legal tender until 1980.

Although the system sounds confusing, the British managed to use it for about 1000 years, and like imperial measures, it was more human than decimal. They probably had very little inflation, which would have helped.

Armed with a list of coins and their values, I've been working my way through the puzzles. They're not particularly enlightening, but they are fun. Many of them can be solved analytically (i.e. you just write out the equations and solve), but he has all sorts of traps for the unwary. For example, the fact that you only need 47 cuts to divide a 48-yard length of cloth into individual yards.

Although I begin with a pen and paper, and fill sheet after sheet with calculations, it's also really useful to have the computer around when you end up with multiple possible solutions to check.

Anyway, I've almost run out of money to count. The next set of puzzles is entitled "Age and Kinship". Hopefully they won't all be the kind where Aunt Agatha is twice Harry's age, and 2/17 of Uncle Cuthbert when you reverse the digits. Or whatever. If they are, I might get bored and have to start writing more posts....