How to solve an algebra problem from "I Met a Man on the Way to St. Ives"?

Milan

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I was thinking about that old nursery rhyme, "I Met a Man on the Way to St. Ives":
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 kittens
Kittens, cats, sacks, and wives
How many were going to St Ives?

Okay, I KNOW that the answer to the riddle is "1". But I really want to figure out how many "Kittens, cats, sacks, and wives"! How can I get the answer using an algebraic equation? (I thought it may have been a geometric sequence equation, but it just wasn't so.)
 
Hello, Milan!

\(\displaystyle \begin{array}{cccccc} \text{As I was going to St. Ives} \\ \text{I met a man with seven wives} &&& 7& \text{wives} \\ \text{Every wife had seven sacks} & 7\times7 &=& 49 & \text{sacks} \\ \text{Every sack had seven cats} & 49\times 7 &=& 343 & \text{cats} \\ \text{Every cat had seven kittens} & 343 \times 7 &=& 2401 &\text{kittens} \\ \hline \text{Total:} &&& 2800 \end{array}\)


You were right: it IS a geometric series.
It has: first term \(\displaystyle a = 7\), common ratio \(\displaystyle r = 7\), and \(\displaystyle n = 4\) terms.

The sum is: .\(\displaystyle S_n \:=\:a\dfrac{r^n-1}{r-1}\)

Therefore: .\(\displaystyle S \;=\;7\left(\dfrac{7^4-1}{7-1}\right) \;=\;7\left(\dfrac{2400}{6}\right) \;=\;7(400) \;=\;2800\)
 
Actually, that's very old joke. I was going to St. Ives, and I met a number of other people. It is NOT said that any of them were also going to St. Ives. I met them as they were going the other direction. There is only one person going to St. Ives.
 
Actually, that's very old joke. I was going to St. Ives, and I met a number of other people. It is NOT said that any of them were also going to St. Ives. I met them as they were going the other direction. There is only one person going to St. Ives.
The characters of Bruce Willis and Samuel L. Jackson were challenged with this question by a villain in the movie "Die Hard: With a Vengeance."
 
The characters of Bruce Willis and Samuel L. Jackson were challenged with this question by a villain in the movie "Die Hard: With a Vengeance."
So they promptly pulled out their guns and shot him? (The "sword of Damocles" solution!)
 
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