## Name for this technique

Everything about Sudoku that doesn't fit in one of the other sections

### Name for this technique

I wonder if the following situation has a name. It's come up for me a few times and relies on the fact that a unique solution should exist for each puzzle.
There were 4 cells at the corners of a rectangle and 3 had the same pair of possible numbers. The 4th cell had the same pair and one other number. I figured the other number had to be the answer to the 4th cell because otherwise there would be the same pair in the four cells and this would lead to 2 equally valid solutions.
Thanks for the input.
pochert

Posts: 2
Joined: 06 January 2006

### Re: Name for this technique

How about uniqueness ?
Red Ed

Posts: 633
Joined: 06 June 2005

This must surely be the single most often independently discovered tactic in the history of sudoku? Nevertheless, well done for finding it, but unlucky that you got to the game rather late.
PaulIQ164

Posts: 533
Joined: 16 July 2005

Is that a chain?
Pi

Posts: 389
Joined: 27 May 2005

### uniqueness

Thanks Red Ed for the input. Paul, I wasn't trying to claim credit for an original idea, it was just a question. If a post of mine seems to trivial or stupid to you please feel free to ignore it and don't
pochert

Posts: 2
Joined: 06 January 2006

Sorry, I wasn't trying to be hostile. Just pointing out that, for whatever reason, this tactic seems to get discovered a lot more than many others.
PaulIQ164

Posts: 533
Joined: 16 July 2005

I am just guessing numbers here

If the candidates were
Code: Select all
`|25------25||------------||256-----25|`

why wouldn't

Code: Select all
`|2------5||---------||5-----2|`

be valid?[/code]
Pi

Posts: 389
Joined: 27 May 2005

Because the 2 and 5 could be interchanged in the solution grid to give another solution. Then the puzzle would have 2 solutions. You could have
2..5
....
5..2

or

5..2
....
2..5
(everything else the same).

We call a set of cells like this an "unavoidable" set, because the set of clues must contain one of these cells, it cannot be avoided.
Moschopulus

Posts: 256
Joined: 16 July 2005

so i asume that actually there wouldn't be any solutions if you didn't use the six
Pi

Posts: 389
Joined: 27 May 2005

Well, it depends. That's why this technique is a tiny bit controversial. If the puzzle is well-formed, and only has one unique solution, then the tactic can help you find it, by exploiting that knowledge. But if it was a bad puzzle to begin with, that had more than one solution, then this technique could get you in trouble.

What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions. But this is a tangent, really. The technique is fine for proper sudoku puzzles.

PS: We've been hacked! How lovely!
PaulIQ164

Posts: 533
Joined: 16 July 2005

PaulIQ164 wrote:What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions. But this is a tangent, really. The technique is fine for proper sudoku puzzles.

I think, that if you for a particular cell place a number that does not appear in that cell in any of the solution grids, you will end up in a contradiction sooner or later. (Example cases are easy to construct). But for proper sudokus the technique works fine.
Ocean

Posts: 442
Joined: 29 August 2005

PaulIQ164 wrote:What I'm not sure about, is whether you can get a 2-solutioned puzzle, use this technique (incorrectly, since it's the 'uniqueness' technique, and you don't have a unique solution to exploit) and end up in a position where you have no solutions.

Here is an example of this.

Consider this grid:
Code: Select all
`5 6 2 3 8 9 4 7 18 4 9 7 1 6 2 5 31 3 7 4 2 5 8 9 63 5 8 1 9 4 6 2 79 7 4 2 6 3 1 8 52 1 6 8 5 7 3 4 96 9 1 5 4 2 7 3 87 2 5 6 3 8 9 1 44 8 3 9 7 1 5 6 2`

Remove the digits in all the cells with 8 and 9, and one further cell (r1c1). Now consider what is left as a puzzle:
Code: Select all
`. 6 2 3 . . 4 7 1. 4 . 7 1 6 2 5 31 3 7 4 2 5 . . 63 5 . 1 . 4 6 2 7. 7 4 2 6 3 1 . 52 1 6 . 5 7 3 4 .6 . 1 5 4 2 7 3 .7 2 5 6 3 . . 1 44 . 3 . 7 1 5 6 2`

If you use the uniqueness rule, then you argue that 5 cannot go in r1c1, because if it did the puzzle has two solutions. But 5 cannot go in any other cell, because you either get two 5s in a row or a column. So the uniqueness rule implies no solution. Not using the uniqueness rule there are two solutions.

Edit: The puzzle was wrong when I first posted it, it got mangled somehow. It's now corrected, sorry.
Last edited by Moschopulus on Mon Jan 09, 2006 11:03 am, edited 1 time in total.
Moschopulus

Posts: 256
Joined: 16 July 2005

Previous post corrected.
Moschopulus

Posts: 256
Joined: 16 July 2005

I think what people fail to mention is that this technique not merely is restricted to "proper/valid" puzzles, it is restricted to "normal/ordinary" i.e. boring sudoku puzzles. Consider all the other variant forms: killer, diagonal (sudoku X), samurai, overlapping, etc. Almost all other normal sudoku techniques are appliable to these variants, but not this. I've seen numerous users complaint to djape on his X puzzles being with multiple solutions, failing to notice the "X" property. Okay, that's irrelevant... So I guess it's a "pure sudoku" technique...
udosuk

Posts: 2698
Joined: 17 July 2005

Yes, good example there, just what I was wondering.

In fact you can use uniqueness on Killer puzzles, as long as the four numbers being used are restricted to 2 cages (there may be more restrictions I can't fathom out in my head). Also in Samurai and X puzzles under similar limitations. But it's certainly true that it doesn't apply straigt away to variants like other rules do, because, I suppose, the extra restrictions that variants add mean that the underlying 'pure' sudoku involved could have more that one solution (eg, the individual puzzles in a Samurai will have multiple solutions, of which the extra restriction of fitting with the overlapping puzzles will restrics the solver to one).
PaulIQ164

Posts: 533
Joined: 16 July 2005

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