[QUOTE=fivemack;159395]I remember seeing the odd-magic-square recipe in a children's book long, long ago, and not being able to get it to work.

Well, I am older and more foolish now, and I still can't get it to work: I get

[code]
19 25 1 7 13
24 5 6 12 18
4 10 11 17 23
9 15 16 22 3
14 20 21 2 8
[/code]

which has rows summing to 65, diagonals summing to 65, but columns are wrong[/QUOTE]

When your '5' ran into '1' you need to drop below the '5' NOT below the '1'.

The process for any ODD magic square of any size is simply.
1. Start at top center.
2. Every move is diagonal up-right.
3. If you:
a. Hit a filled square drop below the current number (Your 6 should have been below your 5)
b. Exit at the right (excluding Top-right corner) go to the far left in the next row up (i.e. Your 3 - 4)
c. Exit Top (excluding Top-Right Corner), go to the bottom row, next column over (i.e Your 7-8)
d. Exit Top-Right corner. Drop below as in a. (14 should have been right below 13)

[quote=petrw1;159423]2. Every move is diagonal up-right.[/quote]

Or diagonally up-left - it is symmetrical so doesn't matter.