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 going to St. Ives?


I have often wondered if this was intended as a mathematical puzzle to keep the kids quiet on long trips as the tried to figure it out or if it is simply a nursery rhyme.

Interestingly enought, the total number of objects including the wives and their cargo is

7 + 47 + 243 + 1701 = 2000

Add me and the man and you get 2002.

I wonder if there is a simple way to solve the problem? I used brute force, calculating out the number and then summing them.

While I can do math, doing the products and sums in my had requires a lot of attention, I need to constantly focus and remind myself of the numbers = so I end up pretty zoned out.

Is there a simple property of 7s that can be exploited? Similar, perhaps to properties of 9s? Can I easily calculate it on my knuckles?

Nine is an intersting number. You can easily discover is a number os divisible by nine by simply summing the digits up until you are left with a single digit. If that digit is 9, then the number is divisible by 9. Example: given 523 we would add the digits together 5 + 2 + 3 = 10 => 1 + 0 = 1. So the number of not divisible by 9. Given the number 282429536481 => 2 + 8 + 2 + 4 + 2 + 9 + 5 + 3 + 6 + 4 + 8 + 1 = 54 => 5 + 4 => 9. So the number is divisible by 9.

The same also works for 3s, simply sum up the digits, if you are left with 3, 6 or 9, then the number is divisible by 3.

Comments

that puzzle looks like an scene of "The Da Vinci Code". For me life is a puzzle, each day is a new piece Sometimes pieces don't fit with others. Sometimes sme pieces are robbed from another puzzle.

Life is a puzzle. I hope I don't lose the game.

Greetings from PerĂº
Richard said…
irredento urbanita: I hope I don't lose either. It is a common human endeavor to try and find singificance and meaning in things that may not have it.

run around paris: You are probably right. As usual, I have chosen the hardest possible path.
Cavalock said…
head hurts....
RennyBA said…
I'm out of suggestions and since my computer can't solve it either, I give up - but thanks for the lecture anyway!
Sorry you fell out of my blogroll after a back up – your in again now!
Have a great week ahead and remember; if you can’t use your head, use the overhead.
Richard said…
cavalock: I think run around paris had the correct answer. The nursery rhyme does not say the man and his wives and their stuff were going to St. Ives.

renyba: thanks for trying. As mentioned above, I think run around paris had the right answer and I simply made the problem more difficult than it was.
zingtrial said…
Hi,Thanks for sharing,liked reading through it,head hurts had to come back,He!He!He!
Wish you well :) .
Hey Guys...It really is one.

"On MY way...blah, blah, blah..."

I heard this when I was little.
tin-tin said…
you really computed for it? wow!!!! and the divisibles by 9 and 3.. you lost me. hehehe. i'm just not really good with math.

but i agree with run around paris.. it's one. you just met the man with 7 wives, etc etc. but are they going to st. ives? no!!! according to my theory, they came from st. ives. hehehe ;p
Richard said…
run around paris: I know, I know. It is obvious now, but I guess I had a tree in my eye ;)

tin-tin: yes, I did compute it - in my head. The whole thing about the 9s and 3s is just a simple way to calculate if something divisible by 9 or 3. Kind of like the rule that says "even numbers are divisible by 2" or "numbers ending with 0 or 5 are divisible by 5".

"You know what is odd to me? Numbers that are not divisible by two." - math joke

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