As I Was Going to St Ives
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"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 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?
There are a number of places called St Ives in England and elsewhere.
Solution
The answer to the riddle is usually said to be one: the person reciting the rhyme was going to St Ives, and everyone else was going the opposite way. Depending on how the question is interpreted, the answer could also be zero: the person travelling to St Ives is not any of "kits, cats, sacks, wives".
Going away from St Ives were: one (1) man, seven (7) wives, seven times seven (49) sacks, seven times seven times seven (343) cats, and seven times seven times seven times seven (2,401) kits, making a total of 8 humans, 49 sacks, and a slightly implausible 2,744 felines; a grand total of 2,800 kits, cats, sacks, and wives (or 2,801 if you include the man).
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 [1] (http://pup.princeton.edu/books/maor/sidebar_a.pdf):
| 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).