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# As I was going to St Ives

"As I was going to St Ives" is a traditional nursery rhyme which is generally thought to be a riddle. The earliest known published version of it dates to around 1730. although a similar problem appears in the Rhind Mathematical Papyrus (Problem 79), dated to around 1650 BC.

## The poem

The words are, in one version, as follows:

As I was going to St Ives
I met a man with seven wives

And every wife had seven sacks
And every sack had seven cats
And every cat had seven kits

Kits, cats, sacks, wives
How many were going to St Ives?

A second version is:

As I was going to St Ives
I met a man with seven wives

Seven wives with seven sacks
Seven sacks with seven cats
Seven cats with seven kits

Kits, cats, sacks, wives
How many were going to St Ives?

There are a number of places called St Ives in England and elsewhere.

The traditional answer is that only one person is going to St Ives: the narrator.

An alternate answer is zero because the question implies how many kits, cats, sacks, and wives are going to st. ives, and none of those 4 categories are going.

This answer is based on the ambiguous language of the riddle.

The narrator, while heading to St. Ives, may have met the large party who are going away from St Ives; this is the most common assumption. Alternatively, the group encountered is not going anywhere - perhaps they are in their home town. In either assumption, the rhyme only tells us that they are "met" on the journey and gives no further information about the intentions of the group, only that of the narrator.

## Mathematical solution

The mathematical solution to the number of people, sacks, and felines involved, is 2,802, calculated as follows:

• Narrator--one
• Other man--one
• Wives--seven
• Sacks--49 (seven wives times seven sacks/wife)
• Adult cats--343 (49 sacks times seven cats/sack)
• Kittens--2,401 (343 cats times seven kittens/cat)

## Rhind mathematical papyrus

A similar problem is found in the Rhind Mathematical Papyrus (Problem 79), dated to around 1650 BC. The papyrus is translated as follows :
A house inventory:
houses 7
1 2,801 cats 49
2 5,602 mice 343
4 11,204 spelt 2,301 [sic]
hekat 16,807
Total 19,607 Total 19,607

The problem appears to be an illustration of an algorithm for multiplying numbers. The sequence 7, 7 × 7, 7 × 7 × 7, ..., appears in the right-hand column, and the terms 2,801, 2 × 2,801, 4 × 2,801 appear in the left; the sum on the left is 7 × 2,801 = 19,607, the same as the sum of the terms on the right. Note that the author of the papyrus miscalculated the fourth power of 7; it should be 2,401, not 2,301. However, the sum of the powers (19,607) is correct.

The problem has been paraphrased by modern commentators as a story problem involving houses, cats, mice, and grain, although in the Rhind Mathematical Papyrus there is no discussion beyond the bare outline stated above. The hekat was 1/30 of a cubic cubit (approximately 4.8 litre).

## Use in popular culture

The rhyme was used as a riddle by Jeremy Irons' villain character Simon Gruber in the movie Die Hard With A Vengeance. Gruber gives Zeus Carver & John McClane thirty seconds to call him back on the number "555 plus the answer" or a bomb would go off. After several guesses, Carver eventually solves the riddle and they call the number 555-0001 which turns out to be correct.

The rhyme was also the basis of a Sesame Street Muppet skit from the show's first season, in which the boy muppet holding a numeral "7" sings the rhyme as a song to the girl muppet twice (the second time, the girl is busy writing down the calculations) and finally, in keeping true to the spirit of the riddle, reveals the answer as 1 (the traditional answer), because the kits, cats, sacks and wives were going the other way. Then the girl asks how many were going the other way and reveals the mathematical answer from her calculations: 2801. Astonished, the boy responds, "How about that?!"

MAD magazine once used in one of its articles the following parody:

As I was going to St. Ives
I met a man with seven wives
Of course, the seven wives weren't his
But here in France, that's how it is

` 2. Oystein Ore, "Number Theory and its History", McGraw- Hill Book Co, 1944`