"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.
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]:
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).
See also
