The New Sudoku Players' Forum

[angbur]

Hi I'm new to the board and have specifically joined as I'm curious as to other sudoku players' thoughts on a query I have.
I don't seen to be able to post a screen grab of the board, but hopefully it should be easy enough to describe.

I use the Logic Wiz app and this week's Diabolical special puzzle has left me wondering whether the knowledge that a sudoku should have a unique solution can be used as a logical step in the solve?

The board has multiple rule sets, but is primarily a killer sudoku.
In box 3 on the grid (row A columns 7 & 8) there is a 2 cell cage that totals 11. Also in box 3 (row C cols 8&9) there is a 2 cell cage totalling 15. I know the 15 cage is a 6,9 pair which means the 11 cage must either be a 4,7 pair or a 3,8 pair.

Also on the board, in box 9 (row I cols 7&8 - ie the exact same columns as the 11cage in box 3), is another 2 cell cage totalling 11 - this cage is a 4,7 pair (but which cell is 4 and which 7 is yet unknown).

What I am wondering is if it is good logic to say the 11 cage in box 3 must be 3,8 pair? The reasoning being because if it is a 4,7 cage then, because of the cage in box 9, the puzzle would no longer have a unique solution - ie the 4 and 7 in each cage could be switched round without affecting anything else on the board other than the other 11 cage. NB the other rules on the board don't affect the positions on the two numbers in either of yhe cages.

The TLDR of this question is, is it legitimate to use the knowledge that a sudoku must have a unique solution to help with a solve?

[denis_berthier]

The TLDR of this question is, is it legitimate to use the knowledge that a sudoku must have a unique solution to help with a solve?

Hi angbur
Welcome on this forum.

Using the knowledge that a Sudoku has a unique solution can indeed help solve it. See https://hodoku.sourceforge.net/en/tech_ur.php for a set of specific techniques.
However, your question about legitimacy is different. Making the assumption of uniqueness is a controversial topic. It supposes you fully trust the puzzle creator. In terms of formal complexity of solution, it amounts to using an oracle.
In practice, for human solvable puzzles, it rarely changes significantly the difficulty of the puzzle (see my statistical results here: http://forum.enjoysudoku.com/pattern-based-constraint-satisfaction-2nd-3rd-eds-t32567-11.html and next post).

In rating systems, such as SER, uniqueness rules may create a real mess.

[eleven]

The question is about a sudoku variant.

Generally common uniqueness techniques like unique rectangles cannot be used in variants because of the additional constraints, which would not allow a second solution of the same puzzle, when the digits in one solution are exchanged (thats how unique rectangles are proven to be impossible in unique classical sudokus: if in the solution you have only 2 digits in a rectangle inside 2 boxes, and none of the cells was a given, you could switch the digits to get a second solution).

I cannot say something about the concrete example above without seeing the puzzle and the rules, but i guess, that you must not apply it.

[m_b_metcalf]

The TLDR of this question is, is it legitimate to use the knowledge that a sudoku must have a unique solution to help with a solve?

However, your question about legitimacy is different. Making the assumption of uniqueness is a controversial topic. It supposes you fully trust the puzzle creator. In terms of formal complexity of solution, it amounts to using an oracle.

Also, legitimacy implies an ultimate arbiter. Thre is no High Court of Sudoku, so it's everyone's own choice.

Regards,

Mike

P.S. Backdoor solutions, for example, require uniquness