# NONODOKU, A new game

Nonodoku is a new variant of Sudoku. In this game, the numbers in each row indicate the relative order of the values in that row, but not their exact positions. For instance, in the second row, if the numbers 3 and 2 appear, it means that 3 will be placed to the left of 2, but their exact positions are not specified. The same logic applies to the columns.

• To paraphrase the great Crocodile Dundee: "That's not a nonodoku... That's a nonodoku!" ;-) Nice idea for a puzzle still!
– Stiv
Commented Aug 13 at 15:19
• sudokupad.app/fjff81p1if Commented Aug 13 at 16:42

Surprisingly tricky puzzle! Here's the solution:

Step-by-step:

1:

To start, in the 4th column there are 3 numbers after the 3, and only 3 cells available, so these must all be placed. In the 8th row, 829 must be in order, and in the first row it must also be 76 in order as 7 cannot be top left.

2:

There is only one place for a 7 in the bottom left box, and looking at the bottom row, the 4 must be in the middle box. As the 2 cannot be in the 7th column, the bottom row must end as 29 to complete the clue. In the middle column, there is only one place for a 6.

3:

The bottom row can be completed normally, and 6 must be below 7 in the final column, leaving one place for a 6 in the bottom left box. In the 7th column, there are only 2 cells left free below the 6 which must be 53. This also solves the 7th row.

4:

The bottom right box is clearly solved, and an 8 can be placed in the middle bottom box. As 7 is above 8 in the 6th column, the bottom middle box can then be solved. Using the same logic with the 3 and 9 in the first column, the entire bottom 3 rows can be filled.

Due to the 6 in the middle box, the 7 and 6 can be placed for the 6th column to complete the clue, and the column can also be completed.

5:

The 1 in the middle row can be placed, leaving a 1 to also be placed in the middle right box, completing the clue for the final column.

In the 3rd row, as 4 must be before 6, the cell after the 6 can only be a 7, letting a final 7 be placed in the 8th column. This 7 means a 3 must be below it, completing the clue. This allows the entire 8th column to be solved.

6:

There's only one place for a 9 in the middle right box, and the middle clue is also solved already. The 5th row clue though means a 4 must be in the final column, solving the box.

Theres only place for a 3 in the 4th row, and as 2 cannot be in the first or second cell of the 2nd row due to the surrounding clues, it must be in the middle column of that row.

7:

The final column can be solved, and there is only one place for a 3 in the first column.

Now despite not much being left, it gets quite tricky here.

After a bit, there is an XY-wing at the top. Consider R3C1. If it is an 8, top left is a 5, R3C4 is a 4, and then the top cell in the middle column is left without any possible numbers. As R3C1 cannot be a 4, it must be a 2.

The 3rd row can then be completed.

8:

Finally, the top left box can be completed, followed by the middle left box, middle box and middle column. It leaves us in this final position:

And as 1 must be above 4 in the 4th column, we can solve and finish the puzzle to give the final solution: