logical deduction - Write digits 1 to 9 in the table, each pointing to next 3x3 grid

Write 1 to 9 digits 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. and 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 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:

1. 8 and 9 are in the same row.


2. 8 and 5 are in a diagonal.


3. 5 and 2 are in the same row.

PS. I don't know whether it was a stupid question or not.

PS. PS. an grammatically edit from would be appreciated!

Answer

It is not possible.

Any solution to this puzzle must also be a solution to the 9x9 Queens puzzle. Luckily, that is a well-known puzzle. It has 352 solutions, but due to symmetry, those 352 solutions can be reduced to 46 solutions. After that, it is just a matter of checking against those 46 solutions.

I found a page showing the solutions at: http://stamm-wilbrandt.de/en/xsl-list/n-queens/n-queens.xsl.xml

I then looked at the first answer in each of the 46 columns.

Items that quickly ruled a solution out:

1. Queen in a corner. Any queen in a corner would mean that the box referred to itself.


2. Queen in the center of a side. Again, that box referred to itself.


3. Queen in center box. Same reason.


4. 2 Queens in same 3x3 box / empty 3x3 box.

This left me with very few actual solutions to check. From that page, #'s 19, 20, 31, 39, 42.

To check, I simply started in box 1 and followed the pattern until I returned to a box that I'd already seen. None of those took all 9 boxes.