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Interesting number array feature

Labarbapostiza · 2016-07-04 15:55:08

Looking at an array of numbers on a thing on the internet. I noticed something interesting about how the numbers sum when in a square shaped array. 1 2 3 4 5 6 7 8 9 If notice, both diagonals, 1 5 9, and 3 5 7, sum to 15. Both central horizontal and vertical, 2 5 8, and 4 5 6, also sum to 15. There are other rows that…

04-07-2016 3:55pm

#1

Labarbapostiza

Banned (with Prison Access) Posts: 963 ✭✭✭

Join Date: March 2014

Posts: 930

Looking at an array of numbers on a thing on the internet. I noticed something interesting about how the numbers sum when in a square shaped array.

1 2 3
4 5 6
7 8 9

If notice, both diagonals, 1 5 9, and 3 5 7, sum to 15. Both central horizontal and vertical, 2 5 8, and 4 5 6, also sum to 15. There are other rows that don't sum to 15.

1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

For this arrangement, both diagonals, 1 6 11 16, and 4 7 10 13, sum to 34.

This is obviously some kind of mathematical feature, but what is it? Are there other rules about how the numbers can sum. Does it produce any kind of mathematical constant?

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Comments

#2 09-07-2016 8:57pm

Ficheall

Registered Users, Registered Users 2 Posts: 9,034 ✭✭✭

Join Date: August 2010

Posts: 8825

To get from 1,5,9 to 2,5,8 to 3,5,7 to 4,5,6, you're adding 1 to the first number and taking it away from the third number, so unsurprisingly they add up to the same thing.
Etc.

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