Magic Window

step 1

All 3x3 magic square are (rotation and or reflection) symmetrical to the configuration in the picture.

Therefore,

• r5c5 must be 5

• 2468 must be in the corners

• 1379 must be on the edges

step 2

By putting 5 in the center, we can get some easy digits.

step 3

Let's check row 2. Where can 3 and 7 go?

• The gray cells in row 2 sum to 15, because they are part of the magic square.

• Red cells (r2c1, r2c9) must sum to 6

  • 45 - 15 (gray cells) - 10 - 14 = 6

• Therefore, 3 and 7 can only go to r2c{3,4,5}.

• Therefore, 3 and 7 must be in the 10 cage.

step 4

We can put more digits into the grid. And some cells are very restricted.

step 5

Let's come back to row 2 again.

Now 2 must go to box 3 (r2c{8,9}).

And we can eliminate more digits from r2c1 and r2c9.

step 6

This might be the most difficult step.

• The highlighted cells (r1c8, r2c1, r2c8, r2c9) are entangled.

• The highlighted 14 cell (r1c8, r2c1) must be different.

• If r1c8 is 1, there's no place to put 1 in box 1.

• So r1c8 must be 4.

step 7

Placing 4 in r1c8 should unwind all cells in r{2,5,8}, c{2,5,8}.

And now it's just a regular nonconsecutive Sudoku.

solution