# is there any size $N\cdot N$Sudoku Puzzle where the smaller $\sqrt N\cdot\sqrt N$ squares all form magic squares

Any $N\cdot N$ Sudoku Puzzle has $N$ squares size $\sqrt N\cdot\sqrt N$ that each have the numbers $1$ to $N$ in them.Is there a sudoku puzzle of any size that have magic squares for all of these sub-squares? I think it will be inevitable for large enough $N$, since there will be more possible Sudokus.

• Note that $N$ should be even because in odd size magic squares the centre number is forced and would conflict with sudoku rules. – zwim May 28 '17 at 2:32
• @zwim not if we require magicness only for rows and columns. So rhen we can also find a standard 9 by 9 with this ... – Hagen von Eitzen May 28 '17 at 2:45