Write the digits from 1 to 9 in an empty Sudoku table with these rules (similar to 9-Queen problem):
- There are 9 boxes indexed from 1 to 9 in the image below. Each box has a 3x3 grid child.
- Every two digits should NOT be in the same row, column or diagonal.
- Pointing rule: You have to place the next number in an specific box. (e.g. if you start to place 1 in top-left box and middle-center child grid, you have to continue with 2 in middle-center box)
- You are free to begin from any box.
- Close the loop: The last number (9) should point to the box that you have placed the first number (1) in it.
- At the end there will be a Sudoku table with only 9 digits in it each in a separate 3x3 box. (other 72 cells will remain empty)
Write down the 9 digits with the rules, or if there is no such a solution, prove it!
See the following example that have some mistakes:
- 8 and 9 are in the same row.
- 8 and 5 are in a diagonal.
- 5 and 2 are in the same row.