# JOST A MON

Jun 30, 2008

## Puzzling Math

Here is a puzzle 1.
As I was going to St. Ives,
I met a man with seven wives.
Each wife had seven sacks,
Each sack had seven cats,
Each cat had seven kits.
Kits, cats, sacks, and wives,
How many were going to St. Ives?
I am fairly certain that a close reading of this rhyme will reveal the cunning answer. If not, I fervently hope you are not furiously scribbling away on a piece of paper, multiplying sevens and worrying about carry. Hint: a geometric series. Another hint: you don't really need the previous hint.

Anyway, the point of this post is - you guessed it - the provenance of this rhyme. It's mathematical ancestry is fairly well established. In 1202, Fibonacci (yes, he with the immortal and perennially bonking rabbits) proposed a variant of this problem in his Liber Abaci 2. His intention, we like to think, was to encourage facility in the Hindu-Arabic numerals that he was attempting to introduce into Europe. In all aims, he succeeded a bit too well, as evidenced in this wry excerpt from Foxtrot.

The puzzles predates even Fibonacci, however. The scribe Ahmes in 1650 BC created the wonderful papyrus that goes by the name of its English collector Rhind, in which he showed his ability to multiply numbers in geometric series. Ahmes, too, it appears, was not the original author: he was copying a scroll predating him by about three centuries. There is some evidence that that scroll was copied from another two hundred years older. The puzzle of the powers of seven was the 79th problem in the Rhind papyrus. So there you have it - a mathematical problem four thousand years in the going.

Ahmes wasn't paying attention when he scribed his work. 74 should be 2401, but he wrote 2301. Bad Ahmes.

On the other hand, Ahmes didn't multiply the sevens in long-hand. Instead, he performed a clever trick - repeated doubling 3. And he used a recursion relation for a geometric series. Smart Ahmes.

As an aside: Egyptian hieroglyphics, in general, elide vowels (very like Arabic writing today). The Egyptian for cat is myw, which - with added vowels - reads meey'a uw 4.

References

1. Weisstein, Eric W. "St. Ives Problem." From MathWorld--A Wolfram Web Resource.

2. Fibonacci's Liber Abaci

3. Weisstein, Eric W. and Zobel, Dave. "Russian Multiplication." From MathWorld--A Wolfram Web Resource.

4. Eli Maor, Trigonometric Delights, Princeton University Press, 2002.

Paul said...

I'm terrible at math but it seems as though the speaker in the rhyme is the only one going to St. Ives......

Fëanor said...

Indeed, sir, you are right.

Ludwig said...

You are doubtless aware, that said riddle is a fairly critical plot element in that modern classic, "Die Hard With a Vengeance"?

Jeremy Irons rasps it out as something that the thespians Bruce Willis and Samuel L. Jackson have to decipher, else k-a-b-o-o-m.

Text at IMDB. A performance not to be missed.

Fëanor said...

Ludwig: I did see the film when it came out aeons ago, but had no recollection of the puzzle. Thanks for pointing it out.