Mike Barker wrote:Udosuk, A second UR is not clear to me. There are at least 3 easy one step moves that crack the puzzle. A finned X-wing, an XY-wing, or an empty rectangle. Focus on r3c8.
Mike,
There is no 2nd UR, but Carcul already demonstrated to me his super "uniqueness" trick privately which I can't disclose here without his permission... I'll show your 3 "easy one step moves" below plus another one (a remote pair):
- Code: Select all
*--------------------------------------------------*
| 12 8 12 |*46 7 34 |#56 *356 9 |
| 4 3 6 | 5 1 9 | 78 2 78 |
| 7 9 5 | 2 68 38 | 4 -36 1 |
|----------------+----------------+----------------|
| 235 1 237 | 8 4 6 | 57 9 27 |
| 58 4 9 | 17 2 17 | 3 58 6 |
| 28 6 27 | 3 9 5 | 1 4 278 |
|----------------+----------------+----------------|
| 6 2 8 | 47 3 47 | 9 1 5 |
| 13 5 134 | 9 68 2 | 68 7 34 |
| 9 7 34 |*16 5 18 | 2 *68 34 |
*--------------------------------------------------*
Finned X-wing: either r1c7=6 or r19c48 form an x-wing of 6, so r3c8<>6
- Code: Select all
*--------------------------------------------------*
| 12 8 12 | 46 7 34 | 56 356 9 |
| 4 3 6 | 5 1 9 | 78 2 78 |
| 7 9 5 | 2 68 *38 | 4 *36 1 |
|----------------+----------------+----------------|
| 235 1 237 | 8 4 6 | 57 9 27 |
| 58 4 9 | 17 2 17 | 3 58 6 |
| 28 6 27 | 3 9 5 | 1 4 278 |
|----------------+----------------+----------------|
| 6 2 8 | 47 3 47 | 9 1 5 |
| 13 5 134 | 9 68 2 | 68 7 34 |
| 9 7 34 | 16 5 -18 | 2 *68 34 |
*--------------------------------------------------*
XY-wing: r9c6<>8 (otherwise r3c8 will have no candidate)
- Code: Select all
*--------------------------------------------------*
| 12 8 12 | 46 7 34 | 56 356 9 |
| 4 3 6 | 5 1 9 | 78 2 78 |
| 7 9 5 | 2 @68 38 | 4 -36 1 |
|----------------+----------------+----------------|
| 235 1 237 | 8 4 6 | 57 9 27 |
| 58 4 9 | 17 2 17 | 3 58 6 |
| 28 6 27 | 3 9 5 | 1 4 278 |
|----------------+----------------+----------------|
| 6 2 8 | 47 3 47 |#9 1 #5 |
| 13 5 134 | 9 @68 2 | 68 7 34 |
| 9 7 34 | 16 5 18 |#2 68 #34 |
*--------------------------------------------------*
Empty Rectangle: r79c79 don't have 6 + strong link of 6 in r38c5 => r3c8<>6
- Code: Select all
*--------------------------------------------------*
| 12 8 12 | 46 7 34 | 56 356 9 |
| 4 3 6 | 5 1 9 | 78 2 78 |
| 7 9 5 | 2 *68 38 | 4 -36 1 |
|----------------+----------------+----------------|
| 235 1 237 | 8 4 6 | 57 9 27 |
| 58 4 9 | 17 2 17 | 3 58 6 |
| 28 6 27 | 3 9 5 | 1 4 278 |
|----------------+----------------+----------------|
| 6 2 8 | 47 3 47 | 9 1 5 |
| 13 5 134 | 9 *68 2 |*68 7 34 |
| 9 7 34 | 16 5 18 | 2 *68 34 |
*--------------------------------------------------*
Remote Pair: r3c5={68}=r8c5={68}=r8c7={68}=r9c8 => r3c8<>6,8