Those kind of squares made with numbers are called "Magic Square". Among those squares, the 4x4 kind has many interesting properties, such as:

- Built with 1 to 16 without repeat.
- The sum of numbers in any row is 34, e.g. 1 + 8 + 10 + 15 = 34.
- The sum of numbers in any column is 34, e.g. 1 + 12 + 7 + 14 = 34.
- The sum of numbers in both diagonal is 34, e.g. 1 + 13 + 16 + 4 = 34.
- The sum of numbers in any sub 2x2 squares is 34 (even cross the edge), e.g. 1 + 8 + 12 + 13 = 34, 12 + 7 + 6 + 9 = 34.
- The sum of numbers in 4 corners is 34, e.g. 1 + 15 + 14 + 4 = 34.
- The sum of each corner with their relative 3 numbers is 34, e.g. 1 + 6 + 16 + 11 = 34.
- In every sub 3x3 squares, the sum of diagonal 2 numbers is 17, e.g. 1 + 16 = 17, 13 + 4 = 17.

Wolfram Mathworld said there are 48 squares comply those rules. But you can shuffle the square:

All columns shift left/right make a new square:

All rows shift up/down make a new one, too.

Switch red and green square at the same time make a new one!

Shuffle with those 3 rules would generate all 48 squares mentioned in Wolfram Mathworld`s page. The 4x4 app for iOS is developed based on these concept. It will be my pleasure if you like this "Magic", too.

## 0 comments :

## Post a Comment