## Extra Groups Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Extra Groups Sudoku

Here is a Sudoku with Extra groups.
Fill in the grid such that each row, column, nonet and extra group (color) contains each digit from 1 to 9.
Should be hard to solve

Code: Select all
`.9..5.........1..6..5...9...7......3..46.92..2......8...2...7..3..4.........2..9.`

Enjoy
Jean-Christophe

Posts: 149
Joined: 22 January 2006

This sub-variant of extra regions sudoku is usually called disjoint groups sudoku. In this exemple I found a a nice collection of (chicken?) wings (wxyz-wing, vwxyz-wing, xy-wing) and a turbot fish.

The result in tiny text:

491856327
723941856
865372941
579284613
184639275
236517489
942165738
317498562
658723194
Pyrrhon

Posts: 240
Joined: 26 April 2006

Correct.

Here is a walkthrough (without singles)

XG means Extra/Disjoint group. Numbering from 1 (red, upper-left) to 9 (light green, lower right)
7 of R8 locked in XG6 -> not elsewhere in XG6
R8C36 forms a naked Pair on {78} within XG6 -> not elsewhere in R8
5 of C8 locked in XG5 -> not elsewhere in XG5
5 of R8 locked in N9 -> not elsewhere in N9
3 of R1 locked in XG1 -> not elsewhere in XG1
5 of N7 locked in R9 -> not elsewhere in R9
R3, N9 and C9, XG7 forms a Grouped X-Wing on 8 -> not elsewhere in C9, XG7
Grouped Turbot Fish on 1 with 3 links R5C1 == XG4 == R8C7 .. C7 .. R46C7 == N6 == R4C8 -> R4C1 <> 1
Grouped Turbot Fish on 1 with 3 links R5C1 == XG4 == R8C7 .. N9 .. R7C9 == XG3 == R1C39 -> R1C1 <> 1
Grouped Turbot Fish on 4 with 3 links R46C7 == N6 == R4C8 .. XG2 .. R7C28 == R7 == R7C9 -> R9C7 <> 4
Grouped Turbot Fish on 4 with 3 links R4C7 == XG1 == R1C17 .. R1 .. R1C6 == C6 == R46C6 -> R4C5 <> 4
Grouped Turbot Fish on 8 with 3 links R2C7 == R2 == R2C5 .. N2 .. R13C4 == C4 == R7C4 -> R1C7 <> 8
Grouped Turbot Fish on 8 with 3 links R13C4 == C4 == R7C4 .. R7 .. R7C2 == XG2 == R47C5 -> R2C5 <> 8
6 of N8 locked in R7 -> not elsewhere in R7
Turbot Fish on 1 with 3 links R8C8 == R8 == R8C2 .. N7 .. R9C3 == C3 == R1C3 -> R7C9 <> 1
1 of XG3 locked in R1 -> not elsewhere in R1
XY-Wing on 3 with R4C1 (XY), R6C2 (XZ), R1C4 (YZ) -> R3C5, R6C4 <> 3
3 of N2 locked in C4 -> not elsewhere in C4
XYZ-Wing on 8 with R7C2 (XYZ), R7C9 (XZ), R4C5 (YZ) -> R7C5 <> 8
8 of C5 locked in N5 -> not elsewhere in N5
XY-Wing on 8 with R4C6 (XY), R7C9 (XZ), R4C1 (YZ) -> R7C4 <> 8
R13C4 forms a hidden Pair on {38} within C4 -> R13C4 = {38}
R13C4 forms a naked Pair on {38} within N2 -> not elsewhere in C4, N2
XY-Wing on 1 with R4C1 (XY), R7C4 (XZ), R4C5 (YZ) -> R4C7, R6C4, R7C258 <> 1
Jean-Christophe

Posts: 149
Joined: 22 January 2006

It may be worth noting that, in this type of puzzle, the grid is equivalent to the grid formed by interchanging the rows as follows:

r1 --> r1
r2 --> r4
r3 --> r7
r4 --> r2
r5 --> r5
r6 --> r8
r7 --> r3
r8 --> r6
r9 --> r9

-- and the columns ditto.

By placing both versions of the puzzle side by side, and updating the puzzles together (placing a digit in either puzzle whenever you place one in its parallel cell in the other), you can have it both ways. Familiar patterns will be easier to see.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

With Disjoint Groups I have been using a different transformation from Row-Column to Nonet-Spot. In this formulation the Rows take the place of the Nonets and the Columns replace the Spots.

r1c123 -> n1s123
r1c456 -> n2s123
r1c789 -> n3s123
r2c123 -> n1s456
r2c456 -> n2s456
r2c789 -> n2s456
r3c123 -> n1s789
etc.

I have been using this for Killers and KiMos as you get some interesting cage overlaps that are difficult to spot. (see www.diceboard.co.uk)
HATMAN

Posts: 275
Joined: 25 February 2006
Location: Nigeria