The New Sudoku Players' Forum

[evert]

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?

[Glyn]

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.

[evert]

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 .
. . .|. . .|. . .

[Glyn]

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

[evert]

Glyn, thanks!

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

Code: Select all

000000000
000000000
903040000
000007050
000068000
050000093
000020000
600000000
004000000

000900400
000000800
400000005
000000060
000000070
030706200
000000030
000000000
001000000

000000040
000000900
000000000
002006000
000000100
700405000
000090000
000308000
500000070

080000075
000000000
000000000
001473000
000000000
098000000
900700000
000000000
030020000

[tarek]

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

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

tarek

[Myth Jellies]

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.