# is there any sudoku puzzle combined with magic square?

As everyone know in Sudoku sum of each row and column is 45. so all Sudoku solutions are some kind of magic square. but my question is:

Have anyone seen a Sudoku puzzle combined with the magic square rule for all nine 3x3 squares? (even without diagonal sum)

Is it even possible to have such a puzzle?

edit: The same question about 4x4 squares.

It is not possible, for the simple reason all 3x3 magic squares have the 5 in the center spot of the 3x3 block. Therefor you'll always get 3 rows and columns in the 9x9 that hold 3 5's, rendering the sudoku part impossible.

Reference on the possible 3x3's: Dr Mikes math games for kids

EDIT: to add to the answer, here's a possible solution for 4x4's:

Notice how I start in the upper left, I fill the top row by putting 4x4 blocks of which the rows are permutated. From there downwards, I build new 4x4 blocks by permutation columns in the 4x4 blocks from the top row.

As far as I can see all diagonals within the seperate 4x4's work aswell.

• Oh how silly of me! thanks! what about 4x4 squares? – Rafe Sep 4 '14 at 7:39
• That might be a trickier question, with numbers going from 1 to 16... I think there is limited options on what 4x4's are possible, one would have to check if there's viable permutations/symmetries there to get the 'sudoku part' right. There may actually be options. – Tim Couwelier Sep 4 '14 at 7:51
• Curiousity got the better of me. I was frankly quite surprised how many manipulations could be done with them this easily. – Tim Couwelier Sep 4 '14 at 13:13
• "(even without diagonal sum)" should solve the centered '5' of the 3x3 squares. – Alix Eisenhardt Jun 2 '17 at 14:58