## What's the name of this technique?

Advanced methods and approaches for solving Sudoku puzzles

### What's the name of this technique?

Suppose I have an X-sudoku (sudoku with the two long diagonals as extra constraint).
Suppose - say - number 1 can only be placed in either the first or the 7th cell in the long diagonal.

So number 1 goes in eithe (1,1) or (7,7) in the diagonal from left-above to right-under.

Then I know I can exclude 1 from cell (1,7), since this cell shares a group with both (1,1) and (7,7).
For the same reason I can exclude 1 from (7,1).

Code: Select all
`X . .|. . .|0 . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- . . .|. . .|. . . . . .|. . .|. . . . . .|. . .|. . . -----+-----+----- 0 . .|. . .|X . . . . .|. . .|. . . . . .|. . .|. . . `

My question now: is this related to a known solving-technique, which may even occur in plain sudoku?
evert

Posts: 186
Joined: 26 August 2005

evert The technique you describe is often known as 'Pointing Pairs' and is frequently encountered in Jigsaw and other variants as well. The number of attacking candidates can be increased ie Pointing Triples etc.
Glyn

Posts: 357
Joined: 26 April 2007

I found "pointing pairs" in the context of box/line interactions.
But that's not what I mean.

I found a more generic definition for my situation:

Triangle:
Three cells a, b and c form a triangle if
-a and b occur in one house
-b and c occur in one house
-a and c occur in one house
-there is no house containing all three of a, b and c.

If a, b and c form a triangle, and a and b are the only two possibilities for a number x within their common house, then x can be excluded from c.

Triangles do not occur in normal sudoku.
Triangles do occur in Sudoku X, windoku and windoku X and probably many other sudoku variants.

Example in Windoku:

Code: Select all
`. . .|. . .|. . .a x x|b . x|x x .. x c|x . x|x x .-----+-----+-----. x x|x . x|x x .. . .|. . .|. . .. x x|x . x|x x .-----+-----+-----. x x|x . x|x x .. x x|x . x|x x .. . .|. . .|. . .`
evert

Posts: 186
Joined: 26 August 2005

The other more general name for the technique is Common Peer Elimination. The Locked candidates of vanilla sudoku are a restricted case of this, but the terminology of pointing has crossed over to variants.

Here is an example from the explanatory notes for the JSudoku solver, which also gives other useful non-vanilla techniques.

http://jcbonsai.free.fr/sudoku/JSudokuUserGuide/jigsawTechniques.html#pointing_pair
Glyn

Posts: 357
Joined: 26 April 2007

Glyn, thanks!

Here's some windoku X puzzles in which they seem to be usefull:

Code: Select all
`000000000000000000903040000000007050000068000050000093000020000600000000004000000000900400000000800400000005000000060000000070030706200000000030000000000001000000000000040000000900000000000002006000000000100700405000000090000000308000500000070080000075000000000000000000001473000000000000098000000900700000000000000030020000`
evert

Posts: 186
Joined: 26 August 2005

This is an intersection or a 1-fish ....

It would be even more interesting when you go for bigger fish....

tarek

tarek

Posts: 2699
Joined: 05 January 2006

This is the same as locked candidates, where the candidates are locked in the diagonal house, so all other candidates that can see both locked candidates can be deleted. In normal sudoku this occurs with intersections of linear houses and nonets. In jigsaws it extends further to form the basis for the Law Of Leftovers. As others have noted these are related to (the same as) fishing/constraint sets as well.
Myth Jellies

Posts: 593
Joined: 19 September 2005