TOPICS

St. Ives Problem

A well-known nursery rhyme states, "As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven kitts. Kitts, cats, sacks, wives, how many were going to St. Ives?" Upon being presented with this conundrum, most readers begin furiously adding and multiplying numbers in order to calculate the total quantity of objects mentioned. However, the problem is a trick question. Since the man and his wives, sacks, etc. were met by the narrator on the way to St. Ives, they were in fact leaving--not going to--St. Ives. The number going to St. Ives is therefore "at least one" (the narrator), but might be more since the problem doesn't mention if the narrator is alone.

Should a diligent reader nevertheless wish to calculate the sum total of kitts, cats, sacks, wives, plus the man himself, the answer is easily given by the geometric series

 (1)

with and . Therefore,

 (2)

Computing the sum explicitly (but grouping cleverly),

 (3) (4) (5) (6) (7) (8)

A similar question was given as problem 79 of the Rhind papyrus, dating from 1650 BC. This problem concerns 7 houses, each with 7 cats, each with 7 mice, each with 7 spelt, each with 7 hekat. The total number of items is then

 (9)

(Wells 1986, p. 71). In turn, the problem of the Rhind papyrus is repeated in Fibonacci's Liber Abaci (1202, 1228).

Explore with Wolfram|Alpha

More things to try:

References

Eisele, C. "The Liber Abaci through the eyes of Charles S. Peirce." Scripta Math. 17, 236-259, 1951.Gillings, R. J. Mathematics in the Time of the Pharaohs. Cambridge, MA: MIT Press, 1972.Wells, D. The Penguin Dictionary of Curious and Interesting Numbers. Middlesex, England: Penguin Books, p. 71, 1986.

St. Ives Problem

Cite this as:

Weisstein, Eric W. "St. Ives Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StIvesProblem.html