# Compact Magic Squares ## Compactk

For an order n compactk magic square, the sum of each k x k block, (including wrap-around), is equal to k2/n of the magic constant. A square that is compactk is compactjk for j=1,2,3, ... ## Examples

### Order 4

See compact2. ### Order 8

Here are some compact2. The 2x2 block sums are 130, (half the magic constant).      Below are some not compact2 but compact4. 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

Here are some compact3. The 3x3 block sums are 369, (the magic constant).    ### Order 12

Here is a compact2. The 2x2 block sums are 290, (one third the magic constant).  Below are some not compact2 but compact4 and/or compact6. 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

Here are some compact5. The 5x5 block sums are 2825, (5/3 times the magic constant).     