Earlier this week, I received an interesting e-mail from Werner Miller, whom I've discussed before on Grey Matters, and whose books push the boundaries of mathematical magic in amazing ways.

The e-mail concerned a new puzzle he's developed that relates to magic squares.

You're given the same set of 4 starting numbers grouped together in similar locations in a 3 by 3, 4 by 4, and 5 by 5 grids. The object is to fill out the grids with other numbers in such a way that the following conditions are satisfied when the grid is completed:

1) Only positive whole numbers are used.

2) No number is duplicated in a single grid (the same number may be used once in each of the 3 grids, however).

3) Each row, each column, and both diagonals of a single grid must total the same sum. All 3 grids in a puzzle, however, are not required to have the same sum (and usually won't). In other words, each grid must be a magic square, but all 3 grids do not have to have the same magic square total.

He sent me several of these puzzles, and I've decided to post 1 each Sunday, with the answers to follow on the following Sunday. For example, here's today's puzzle, the answers to which will appear next Sunday (March 23, 2010).

3 by 3 grid:


4 by 4 grid:


5 by 5 grid:


Can you get the answers to these magic square puzzles? If you can solve it before next Sunday, let me know in the comments! You can either describe your solution there, as best as you can, or link to a graphic of your solution.