I just entered the solution and deleted numbers until Simple Sudoku said the puzzle had multiple solutions if I deleted another number.
- Code: Select all
Original Puzzle:
*-----------*
|1..|..6|.89|
|...|.2.|4.6|
|...|.8.|...|
|---+---+---|
|9..|.45|6.8|
|6..|...|...|
|.4.|.7.|..2|
|---+---+---|
|..1|...|...|
|567|...|23.|
|.3.|5.7|...|
*-----------*
After basic logic and coloring:
*--------------------------------------------------------------------*
| 1 2 34 | 47 5 6 | 37 8 9 |
| 378 589 389 | 179 2 139 | 4 157 6 |
| 347 59 6 | 1479 8 1349 | 1357 2 357 |
|----------------------+----------------------+----------------------|
| 9 17 23 | 23 4 5 | 6 17 8 |
| 6 17 258 | 189 139 1289 | 13579 4 357 |
| 38 4 358 | 6 7 189 | 1359 159 2 |
|----------------------+----------------------+----------------------|
| 48 89 1 | 23 36 24 | 5789 5679 57 |
| 5 6 7 | 1489 19 1489 | 2 3 14 |
| 2 3 489 | 5 16 7 | 89 69 14 |
*--------------------------------------------------------------------*
I found the following loop with an almost x wing. For a good explanation check this forum(Almost X-Wing) and this forum(Multiple implication and grouped nodes).
Here are some pictures:
In the picture above:
[r4c3]-3-[r6c1]=3=[Almost X-Wing:r23c16]-3-[r3c79]=3=[r1c7]-3-[r56c7]=3=[r5c9]-3-[r5c5]=3=[r4c4]-3-[r4c3] => [r4c3]<>3
Where the extra -3's around the x-wing are those exclude by the x-wing and its locked candidates.
In the picture above:
[r4c3]-3-[r4c4]=3=[r5c5]-3-[r5c9]=3=[r56c7]-3-[r13c7]=3=[r3c9](-3-[r3c1])-3-[r3c6]=3=[r2c6]-3-[r2c13|(r3c1)]=3=[r1c3]-3-[r4c3] => [r4c3]<>3
Where you really have to follow the chain in a particular direction to see the conclusion easily.