It seems that there were other stages of my life when I was extremely bored; while doing upkeep on the hard drive of my old computer, I came across this unfinished piece:
On Mathematics
Back in the days when my friends and I were all still wearing short trousers, I was very much into problems that were challenging without requiring deep or involved mathematical manipulation, problems that tested what De Bono called “lateral thinking” (an epithet that Americans later transformed into the egregious phrase “thinking outside the box”). One of these problems, and one which I’m sure many of you have heard already, runs as follows:
As I was going to St. Ives
I met a man with seven wives
Every wife had seven sacks
Every sack had seven cats
Every cat had seven kits
Kits, cats, sacks, wives,
How many were going to St. Ives?
The immediate and obvious response to this problem is to dust off the mental abacus and start multiplying. My guess is that the average person would arrive as far as divining that there are 343 cats before giving up in frustration and turning his attention to the more interesting things in life like clipping his toenails or doing the laundry. The more persistent and mathematically inclined (geometric progression anyone?) would struggle on, find out that there are 2401 kittens, add them all up, and arrive at the grand total of 2800 (carefully excluding the man, since the problem only asks for “kits, cats, sacks and wives).
All well and good, until a flip to the back of the book publishing the problem reveals that the answer is one. Why? Because, they claim, you, the narrator, were the only one headed in the direction of the town of St. Ives. The entourage you encountered on the way there was obviously proceeding away from the town, or else you would not have met them.
Well, there is the minor quibble I brought up above: that since the narrator is presumably not a kit, a cat, a sack or a wife, the answer should be zero. Apart from this, should we be satisfied?
Hardly! The word “met” need not at all imply that the man, his harem and the menagerie of felines was coming from the town of St. Ives. What if the narrator met this huge party at the convergence of two roads, for example? What if the narrator was simply proceeding at a faster pace than the 8 humans and 2744 cats? After all, a quick calculation reveals that each wife was carrying 392 cats; thus even a conservative estimate suggests that they were toting more than 200 kilograms of weight apiece. Their peregrinations, in whichever direction they were going, must have been considerably hampered by this load.
To solve this problem, it seems that we have to dig a little deeper. We could tackle it from the angle of motive. Does it seem more likely that this huge party was traveling towards or away from the town? Perhaps St. Ives was a place in which polygamy was ill tolerated and the man was fleeing its fetters to enjoy a licentious existence with his wives and pets. Perhaps the town was a place that turned stray animals into sausage meat and sold it to their unwitting neighbors, and the man was headed there to make a quick buck. The cats, after all, must have been packed quite tightly into the sacks, hardly the most humane way to treat an animal unless it was already destined for slaughter.
So what was St. Ives known for? I did a little research to see if I could shed a little light on the problem that way. The two largest towns that bear that name are in the Huntingdonshire and Penwith districts in Cambridgeshire and Cornwall respectively. The former is most famous for having a “six-arched bridge (c. 1415), with a chapel over the central pier ”, the latter has “winding streets and colour-washed stone cottages housing fishermen, artists and potters ”. In 1920, a gentleman named Edward Leach gave its name to a style of pottery developed in this Cornwallian town.
Not very helpful. What about the narrator of the problem? Do we have any clue what he was up to? One website claims that he was off to the “famous” St. Ives fairs (the St. Ives here referring to the one in Huntingdonshire). This is pure speculation, of course, and has no bearing whatsoever on the direction of travel of the polyamorous husband. Looking at the rhyme itself, the only fact that we may glean is that the narrator had a burning intellectual curiosity, or the question of the size of the party would not have arisen in the first place.
Let’s take a step backward. Does it help at all if we assume that the narrator of the rhyme was also its real-life writer? No, it does not, for the verse is attributed either to Mother Goose or “Anonymous”. There was an earlier version of the problem written in the Rhind Mathematical Papyrus, but this was credited to someone called Ahmose who lived circa 1800 BC, and I highly doubt that St. Ives and its quaint riverside fetes existed back in those days.
(He got the wrong answer, by the way. He thought that 343 x 7 was 2301.)
Perhaps it is best to discard the problem altogether, arguing that such symmetry of numbers is highly improbable anyway. For instance, the average size of a cat litter is four (excepting the Abysinnian and Siamese breeds which have larger and smaller litter sizes, respectively). To be in possession of 343 cats each with a litter size of exactly seven is quite a mind-numbing coincidence. If we are treating the problem metaphysically, and not as merely an exercise in mathematics, it is surely necessary to consider its ecological validity as well. In other words, if the solution to the problem requires that we consider whether the husband is coming from or going to St. Ives, it is essential for us to also question whether such a situation could ever actually occur.
It goes on in this vein for a while. What a weirdo I am.