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: 4x4 solution

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.

  • $\begingroup$ Oh how silly of me! thanks! what about 4x4 squares? $\endgroup$ – Rafe Sep 4 '14 at 7:39
  • $\begingroup$ 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. $\endgroup$ – Tim Couwelier Sep 4 '14 at 7:51
  • $\begingroup$ Curiousity got the better of me. I was frankly quite surprised how many manipulations could be done with them this easily. $\endgroup$ – Tim Couwelier Sep 4 '14 at 13:13
  • $\begingroup$ "(even without diagonal sum)" should solve the centered '5' of the 3x3 squares. $\endgroup$ – Alix Eisenhardt Jun 2 '17 at 14:58

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