A famous nursery happiness states, "As i was going come St.Ives, ns 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 numerous were going come St. Ives?" Upon gift presented with this conundrum, most readers start furiously including and multiplying numbers in order to calculate the full quantity of objects mentioned. However, the trouble is a cheat question. Since the man and his wives, sacks, etc. To be met by the narrator top top the method to St.Ives, they to be in fact leaving--not going to--St.Ives. The number going come St.Ives is because of this "at least one" (the narrator), however might be much more since the problem doesn"t cite if the narrator is alone.

You are watching: On my way to st ives riddle

Should a diligent reader nonetheless wish to calculate the sum complete

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


*

(1)

with

*
and also
*
. Therefore,


*

(2)

Computing the sum explicitly (but grouping cleverly),

*
*
*

(3)
*
*
*

(4)
*
*
*

(5)
*
*
*

(6)
(7)
(8)

A comparable question was provided as trouble 79 of the Rhind papyrus, date from 1650 BC. This problem involves 7 houses, each v 7 cats, each v 7 mice, each through 7 spelt, each through 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 with 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 also Interesting Numbers. Middlesex, England: Penguin Books, p.71, 1986.


Referenced ~ above gimpppa.org|Alpha: St. Ives Problem
CITE THIS AS:

Weisstein, Eric W. "St. Ives Problem."From gimpppa.org--A gimpppa.org net Resource. Https://gimpppa.org/StIvesProblem.html


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