The New Sudoku Players' Forum

[SCLT]

Code: Select all

+-------+-------+-------+
| . 2 . | . 3 1 | . 4 . |
| 1 . 4 | 5 . . | 6 . 3 |
| . . . | . . . | . . . |
+-------+-------+-------+
| 2 . 8 | . . 9 | . . 6 |
| . . 9 | . 1 . | 8 . . |
| 7 . . | 8 . . | 9 . 5 |
+-------+-------+-------+
| . . . | . . . | . . . |
| 4 . 7 | . . 2 | 3 . 1 |
| . 3 . | 1 4 . | . 5 . |
+-------+-------+-------+
.2..31.4.1.45..6.3.........2.8..9..6..9.1.8..7..8..9.5.........4.7..23.1.3.14..5.


There is an esoteric one-step solution. Interested to see what you come up with!

[marek stefanik]

Mine is two steps:

Code: Select all

.--------------------.---------------------.--------------------.
|*5689   2      56   |#9–67   3      1     | 57    4     *789   |  89
| 1      789    4    | 5      2789   78    | 6     2789   3     |
| 35689  56789  356  | 24679  26789  4678  | 1257  12789  2789  |
:--------------------+---------------------+--------------------:
| 2      145    8    | 347    57     9     | 147   137    6     |
| 356    456    9    | 23467  1      34567 | 8     237    247   |
| 7      146    136  | 8      26     346   | 9     123    5     |
:--------------------+---------------------+--------------------:
| 5689   15689  1256 | 3679   56789  35678 | 247   26789  24789 |
| 4      5689   7    | 69     5689   2     | 3     689    1     |
|*689    3      26   | 1      4     #8–67  | 27    5     *2789  |  89
'--------------------'---------------------'--------------------'

Because of the gsp, each of 89 can only appear once in r19c19, forcing them to take the fins.

Code: Select all

.--------------------.-----------------.--------------------.
| 568    2      56   | 9     3    1    | 57    4      78    |
| 1     *89     4    | 5     28   7    | 6     2–89   3     |
| 35689  56789  356  | 24    268  46   | 1257  12789  2789  |
:--------------------+-----------------+--------------------:
| 2      145    8    | 347   57   9    | 147   137    6     |
| 356    456    9    | 2347  1    3456 | 8     237    247   |
| 7      146    136  | 8     26   346  | 9     123    5     |
:--------------------+-----------------+--------------------:
| 5689   15689  1256 | 37    579  35   | 247   26789  24789 |
| 4      5–89   7    | 6     59   2    | 3    *89     1     |
| 69     3      26   | 1     4    8    | 27    5      279   |
'--------------------'-----------------'--------------------'

89 pair r2c2, r8c8 (again because of the gsp); stte

Marek

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 5689  2     56    ! 679   3     1     ! 57    4     789   !
   ! 1     789   4     ! 5     2789  78    ! 6     2789  3     !
   ! 35689 56789 356   ! 24679 26789 4678  ! 1257  12789 2789  !
   +-------------------+-------------------+-------------------+
   ! 2     145   8     ! 347   57    9     ! 147   137   6     !
   ! 356   456   9     ! 23467 1     34567 ! 8     237   247   !
   ! 7     146   136   ! 8     26    346   ! 9     123   5     !
   +-------------------+-------------------+-------------------+
   ! 5689  15689 1256  ! 3679  56789 35678 ! 247   26789 24789 !
   ! 4     5689  7     ! 69    5689  2     ! 3     689   1     !
   ! 689   3     26    ! 1     4     678   ! 27    5     2789  !
   +-------------------+-------------------+-------------------+
184 candidates.

There is a regular solution in W8.

If you insist on 1-step:

Code: Select all

FORCING[3]-T&E(W1) applied to trivalue candidates n3r6c6, n4r6c6 and n6r6c6 :
===> 11 values decided in the three cases: n3r4c8 n3r7c4 n6r5c2 n7r5c8 n7r2c6 n2r9c3 n7r9c7 n5r1c7 n6r1c3 n7r3c2 n7r1c9
===> 88 candidates eliminated in the three cases: n5r1c1 n6r1c1 n5r1c3 n6r1c4 n7r1c4 n7r1c7 n8r1c9 n9r1c9 n7r2c2 n7r2c5 n9r2c5 n8r2c6 n7r2c8 n6r3c1 n8r3c1 n9r3c1 n5r3c2 n6r3c2 n8r3c2 n9r3c2 n6r3c3 n7r3c4 n9r3c4 n2r3c5 n7r3c5 n8r3c5 n9r3c5 n7r3c6 n8r3c6 n5r3c7 n7r3c7 n2r3c8 n7r3c8 n8r3c8 n2r3c9 n7r3c9 n3r4c4 n7r4c7 n1r4c8 n7r4c8 n6r5c1 n4r5c2 n5r5c2 n3r5c4 n6r5c4 n7r5c4 n4r5c6 n6r5c6 n7r5c6 n2r5c8 n3r5c8 n7r5c9 n6r6c2 n6r6c3 n3r6c8 n5r7c1 n5r7c2 n6r7c2 n2r7c3 n6r7c3 n6r7c4 n7r7c4 n9r7c4 n5r7c5 n6r7c5 n9r7c5 n3r7c6 n6r7c6 n7r7c6 n8r7c6 n7r7c7 n2r7c8 n7r7c8 n8r7c8 n7r7c9 n8r7c9 n9r7c9 n6r8c2 n9r8c2 n6r8c5 n8r8c5 n9r8c8 n8r9c1 n6r9c3 n7r9c6 n2r9c7 n2r9c9 n7r9c9
stte

[SCLT]

Mine is two steps:

Because of the gsp, each of 89 can only appear once in r19c19, forcing them to take the fins.
...
89 pair r2c2, r8c8 (again because of the gsp); stte

Marek

Nice work! I think, with this idea, you are able to find the one-step solution. You may also consider this puzzle (SER 8.4) which admits the same one-step solution, as a further hint.

Code: Select all

+-------+-------+-------+
| . 2 . | . . 3 | 5 6 . |
| 4 . 6 | 1 5 . | . . 7 |
| . . . | . . . | . . . |
+-------+-------+-------+
| 2 . 8 | . . 9 | . . 6 |
| . . 9 | . 1 . | 8 . . |
| 7 . . | 8 . . | 9 . 5 |
+-------+-------+-------+
| . . . | . . . | . . . |
| 6 . . | . 2 1 | 7 . 3 |
| . 7 2 | 4 . . | . 5 . |
+-------+-------+-------+
.2...356.4.615...7.........2.8..9..6..9.1.8..7..8..9.5.........6...217.3.724...5.


[m_b_metcalf]

FWIW, your first puzzle has a backdoor, 7r1c9.

Further, two clues can be removed from the second puzzle, making it minimal but still symmetric, and creating a pearl:

Code: Select all

.2...356.4.615...7.........2....9..6..9.1.8..7..8....5.........6...217.3.724...5.

Mike

[SCLT]

Further, two clues can be removed from the second puzzle, making it minimal but still symmetric, and creating a pearl:

Code: Select all

.2...356.4.615...7.........2....9..6..9.1.8..7..8....5.........6...217.3.724...5.

Mike

How fascinating that removing those two clues in particular keeps it unique, as taking them out completely cripples the step I built the puzzle around. Such is the nature of building puzzles for which a uniqueness deduction is crucial - the puzzle must become unique "by coincidence" and only then does the intended deduction become valid - the setup itself may in fact not contribute to the uniqueness of the puzzle at all, as here.

[denis_berthier]

FWIW, your first puzzle has a backdoor, 7r1c9.

Unfortunately, backdoors aren't associated to any resolution technique (except of course guessing), AFAIK.
What's useful in pattern-based solutions is anti-backdoors.
If this candidate was bivalue in any of the 4 2D spaces, the candidate associated to it in the bivalue relation would be an anti-backdoor and could be used so, but this is not the case.

Out of curiosity I looked for the anti-backdoors:
8 BRT-ANTI-BACKDOORS FOUND: n5r8c5 n2r6c8 n6r6c5 n5r5c6 n2r5c4 n7r4c5 n5r4c2 n2r2c5
8 W1-ANTI-BACKDOORS FOUND: n5r8c5 n2r6c8 n6r6c5 n5r5c6 n2r5c4 n7r4c5 n5r4c2 n2r2c5

but none of them leads to a 1-step solution with Subsets, whips or oddagons of any length.