A well-known nursery rhyme states, "As ns was going to St.Ives, i met a man with seven wives. Every wife had seven sacks, every sack had actually seven cats, every cat had actually seven kitts. Kitts, cats, sacks, wives, how plenty of were going to St. Ives?" Upon being presented with this conundrum, most readers begin furiously adding and multiplying numbers in bespeak to calculate the total quantity of objects mentioned. However, the trouble is a trick question. Because the man and his wives, sacks, etc. To be met through the narrator ~ above the means to St.Ives, they were in reality leaving--not walk to--St.Ives. The number going come St.Ives is as such "at the very least one" (the narrator), however might be much more since the problem doesn"t mention if the narrator is alone.

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Should a diligent reader nevertheless wish to calculation the sum complete

the kitts, cats, sacks, wives, add to the man himself, the prize is easily given by the geometric series

(1)

with

and
. Therefore,

(2)

Computing the sum explicitly (but group cleverly),

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

A comparable question was offered as difficulty 79 of the Rhind papyrus, date from 1650 BC. This problem involves 7 houses, each v 7 cats, each v 7 mice, each with 7 spelt, each with 7 hekat. The total variety of items is then

(9)

(Wells 1986, p.71). In turn, the difficulty of the Rhind papyrus is repeated inFibonacci"s Liber Abaci (1202, 1228).

REFERENCES:

Eisele, C. "The Liber Abaci through the eye of Charles S.Peirce."Scripta Math. 17, 236-259, 1951.

Gillings, R.J. Mathematicsin the moment 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.

Referenced on civicpride-kusatsu.net|Alpha: St. Ives Problem
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Weisstein, Eric W. "St. Ives Problem."From civicpride-kusatsu.net--A civicpride-kusatsu.net net Resource. Https://civicpride-kusatsu.net/StIvesProblem.html

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