Let A B C be three cells such that
- each of A, B and C contains a subset of the candidates {x,y,z}
- each of the cells that contain three candidates lie in the same unit as each of the other cells.
Let D be a fourth cell, such that
- D lies in the same unit as any of the cells that contain x [or y, or z].
- the cell that does NOT contain x [or y, or z] (if any) lies in the same unit as each of the other cells.
Then you can remove x [or y, or z] from the set of candidates for D.
The following four cases are possible.
Notation: A~B means A and B are in the same unit
1/
A=xyz, B=xyz, C=xyz
A~B, A~C, B~C => A,B,C in same unit
x,y,z: D~A, D~B, D~C => A,B,C,D in same unit - standard naked triplet
2/
A=xyz, B=xyz, C=xy
A~B, A~C, B~C => A,B,C in same unit
x,y: D~A, D~B, D~C => A,B,C,D in same unit - standard naked triplet
z: D~A, D~B => if NOT D~C then D,A,B in same box (xyz wing), otherwise standard naked triplet
- Code: Select all
. . . | . . . | * * *
. xy----------------|-xyz-xyz *
. . . | . . . | * * *
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
3/
A=xyz, B=xz, C=yz
A~B, A~C
x: D~A, D~B, C~A, C~B => A,B,C in same unit - if NOT D~C then D,A,B in same box (xyz wing), otherwise standard naked triplet
y: D~A, D~C, B~A, B~C => A,B,C in same unit - if NOT D~B then D,A,C in same box (xyz wing), otherwise standard naked triplet
z: D~A, D~B, D~C => if NOT B~C then D,A,B in same box (xyz wing), otherwise standard naked triplet
- Code: Select all
. . . | . . . | * * *
. xz----------------|-xyz-yz *
. . . | . . . | * * *
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
- Code: Select all
. . . | . . . | . yz .
. . . | . . . | ./ . .
. xz----------------|-xyz * *
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
4/
A=xy, B=xz, C=yz
x: C~A, C~B, D~A, D~B => xy-wing, or standard naked triplet
y: B~A, B~C, D~A, D~C => xy-wing, or standard naked triplet
z: A~B, A~C, D~B, D~C => xy-wing, or standard naked triplet
- Code: Select all
* * * | . . . | . yz .
. . . | . . . | ./ . .
. xz----------------|-xy * *
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
- Code: Select all
. . . | . . . | * * *
. xy----------------|-yz-xz *
. . . | . . . | * * *
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
----------+----------+----------
. . . | . . . | . . .
. . . | . . . | . . .
. . . | . . . | . . .
