# Compact Magic Squares

## Compact_{k}

For an order n compact_{k} magic square, the sum of each k x k block, (including wrap-around), is equal to k^{2}/n of the
magic constant. A square that is compact_{k} is compact_{jk} for
j=1,2,3, ...

## Examples

### Order 4

See compact_{2}.

### Order 8

.txt

Here are some compact_{2}. The 2x2 block sums are 130, (half the magic constant).

Below are some not compact_{2} but compact_{4}.
The 4x4 block sums are 520, (twice the magic constant).

Of the 64 compact blocks, here are the first and last starting in the top row and the first and last starting in the bottom row:

### Order 9

.txt

Here are some compact_{3}. The 3x3 block sums are 369, (the magic constant).

### Order 12

.txt

Here is a compact_{2}. The 2x2 block sums are 290, (one third the magic constant).

Below are some not compact_{2} but compact_{4} and/or compact_{6}.
The 4x4 block sums are 1160, (4/3 times the magic constant);
the 6x6 block sums are 2610, (3 times the magic constant).

### Order 15

.txt

Here are some compact_{5}. The 5x5 block sums are 2825, (5/3 times the magic constant).