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.