The New Sudoku Players' Forum

[Jean-Christophe]

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

[Pyrrhon]

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

[Jean-Christophe]

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

[Smythe Dakota]

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

[HATMAN]

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)