As I was going to St Ives
The most common modern version is:
- 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 there going to St. Ives?
The following version is found in a manuscript (Harley MS 7316) dating from approximately 1730:
- As I went to St. Ives
- I met Nine Wives
- And every Wife had nine Sacs,
- And every Sac had nine Cats
- And every Cat had nine Kittens
A version very similar to that accepted today was published in the Weekly Magazine of August 4, 1779:
- As I was going to St Ives,
- Upon the road I met seven wives;
- Every wife had seven sacks,
- Every sack had seven cats,
- Every cat had seven kits:
- Kits, cats, sacks, and wives,
- How many were going to St Ives?
There are a number of places called St Ives in England and elsewhere. It is generally thought that the rhyme refers to St Ives, Cornwall, when it was a busy fishing port and had many cats to stop the rats and mice destroying the fishing gear, although some people argue it was St Ives, Cambridgeshire as this is an ancient market town and therefore an equally plausible destination.
All potential answers to this riddle are based on its ambiguity because the riddle only tells us the group has been "met" on the journey to St. Ives and gives no further information about its intentions, only those of the narrator. In modern usage, 'to meet someone on the road' may include the sense of 'passed' or 'overtook'; while the older usage may have referred exclusively to those going in opposite directions. As such, the 'correct' answer could be stated as "at least one, the narrator plus anyone who happens to be travelling in the same direction as him or her".
If the group that the narrator meets is assumed not to be travelling to St. Ives the answer could be one person going to St. Ives: the narrator. This is the most common assumption, as the purpose of the riddle was most likely to trick the listener into making long winded calculations only to be surprised by the simplicity of the answer. Another possible answer is zero, emphasizing how the riddle only asks "kits, cats, sacks, and wives" and does not ask to include the narrator.
If one disregards these 'trick' answers and assumes the narrator overtook the group as they were also travelling to St. Ives, the most common mathematical answer is 2802: 1 man, 7 wives, 49 sacks, 343 cats, and 2401 kits, plus the narrator (the sum of a geometric series, plus one). If one only considers the "kits, cats, sacks, and wives", then the answer would be 2800.
After the riddle was published in the August 4, 1779 issue of The Weekly Magazine, as described above, a subsequent edition of that journal contained the following solution, submitted by reader "Philo-Rhithmus" of Edinburgh:
- Why the deuce do you give yourselves so much vexation,
- And puzzle your brains with a long calculation
- Of the number of cats, with their kittens and sacks,
- Which went to St Ives, on the old women's backs,
- As you seem to suppose? — Don't you see that the cunning
- Old Querist went only? — The rest were all coming.
- But grant the wives went too, — as sure's they were married,
- Eight only could go, — for the rest were all carried.
Rhind mathematical papyrus
The problem appears to be an illustration of an algorithm for multiplying numbers. The sequence 7, 72, 73, 74, 75 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. The equality of the two geometric sequences can be stated as the equation (20+21+22)(70+71+72+73+74) = 71+72+73+74+75, which relies on the coincidence 20+21+22=7.
Note that the author of the papyrus listed a wrong value for 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 l or 1.1 imp gal or 1.3 US gal).
- I. Opie and P. Opie, The Oxford Dictionary of Nursery Rhymes (Oxford University Press, 1951, 2nd edn., 1997), pp. 376–7.
- "A Simple Question". The Weekly Magazine, or Edinburgh Amusement. Edinburgh: Ruddiman. xlv: 132. 1779-08-04.
- "A Hoax Extraordinary". Chambers' Edinburgh Journal. Edinburgh: Chambers (274): 112. 1837-04-29.
- Hudson, Noel (1989), St Ives, Slepe by the Ouse, St Ives Town Council, p. 131, ISBN 978-0-9515298-0-5
- Flanagan, Bridget (2003), The St Ives Problem, a 4000 Year Old Nursery Rhyme?, ISBN 0-9540824-1-9
- The Highway Code. The Stationery Office. 1931. p. 9.
- Gibson, Bryan (April 18, 2014). The Legend of St Yves. Waterside Press. p. 76.
- Ore, Oystein (1948). Number Theory and Its History. Courier Dover Publications. p. 118.
- Philo-Rhithmus (1779-09-08). "To the Publisher of the Weekly Magazine". The Weekly Magazine, or Edinburgh Amusement. Edinburgh: Ruddiman. xlv: 256.
- Maor, Eli (2002) , "Recreational Mathematics in Ancient Egypt", Trigonometric Delights (PDF), Princeton University Press, pp. 11–14 (in PDF, 1–4), ISBN 978-0-691-09541-7, archived from the original (PDF) on 2005-12-24, retrieved 2009-04-19
- "Transcript EPISODE 17 – RHIND MATHEMATICAL PAPYRUS". A history of the world. BBC. Retrieved 26 February 2012.
- Øystein Ore, "Number Theory and its History", McGraw–Hill Book Co, 1944