The New Sudoku Players' Forum

[denis_berthier]

Code: Select all

+-------+-------+-------+
! . . . ! . 5 . ! . . . !
! . 5 6 ! 7 . . ! . . 2 !
! 8 . . ! 2 3 . ! . 6 . !
+-------+-------+-------+
! . . . ! . . 7 ! 8 . . !
! . . . ! 3 . . ! . 2 . !
! . . 1 ! . 2 . ! 3 . 7 !
+-------+-------+-------+
! 3 4 . ! 9 . . ! . 1 . !
! . . 2 ! 1 . . ! . 7 . !
! . . . ! 8 . . ! . 9 . !
+-------+-------+-------+

....5.....567....28..23..6......78.....3...2...1.2.3.734.9...1...21...7....8...9. 306431
26 givens, SER = 8.3

[denis_berthier]

.
As there's no reply, here are my solutions.

In general, using rules for uniqueness has no impact on the rating of a puzzle - said otherwise, uniqueness doesn't simplify it and is therefore a uselesss assumption. (For general stats about uniqueness, see here: http://forum.enjoysudoku.com/pattern-based-constraint-satisfaction-2nd-edition-t32567.html#p303970)

However, as for almost any claim in Sudoku, there are exceptional cases.
I've chosen this puzzle as an illustration of the most extreme case where using Uniqueness can drastically change the rating of a puzzle. Here from W10 to U+W4.

Code: Select all

Resolution state after Singles:
   +----------------------+----------------------+----------------------+
   ! 12479  12379  3479   ! 46     5      1469   ! 1479   8      149    !
   ! 149    5      6      ! 7      1489   1489   ! 149    3      2      !
   ! 8      179    479    ! 2      3      149    ! 14579  6      1459   !
   +----------------------+----------------------+----------------------+
   ! 24569  2369   3459   ! 456    1469   7      ! 8      45     14569  !
   ! 45679  6789   45789  ! 3      14689  145689 ! 14569  2      14569  !
   ! 4569   689    1      ! 456    2      45689  ! 3      45     7      !
   +----------------------+----------------------+----------------------+
   ! 3      4      578    ! 9      67     256    ! 256    1      568    !
   ! 569    689    2      ! 1      46     3456   ! 456    7      34568  !
   ! 1567   167    57     ! 8      467    23456  ! 2456   9      3456   !
   +----------------------+----------------------+----------------------+
199 candidates, 1274 csp-links and 1274 links. Density = 6.47%

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 12479 12379 3479  ! 46    5     1469  ! 1479  8     149   !
   ! 149   5     6     ! 7     1489  1489  ! 149   3     2     !
   ! 8     179   479   ! 2     3     149   ! 14579 6     1459  !
   +-------------------+-------------------+-------------------+
   ! 2469  2369  349   ! 456   1469  7     ! 8     45    169   !
   ! 45679 6789  45789 ! 3     14689 14689 ! 169   2     169   !
   ! 469   689   1     ! 456   2     4689  ! 3     45    7     !
   +-------------------+-------------------+-------------------+
   ! 3     4     578   ! 9     67    256   ! 256   1     568   !
   ! 569   689   2     ! 1     46    3456  ! 456   7     34568 !
   ! 1567  167   57    ! 8     467   23456 ! 2456  9     3456  !
   +-------------------+-------------------+-------------------+

Without uniqueness, there a solution in W10, with nothing noticeable: Show

whip[2]: c2n2{r1 r4} - c2n3{r4 .} ==> r1c2 ≠ 1, r1c2 ≠ 7, r1c2 ≠ 9
whip[2]: c2n2{r4 r1} - c2n3{r1 .} ==> r4c2 ≠ 6, r4c2 ≠ 9
whip[3]: r8c5{n6 n4} - r9c5{n4 n7} - r7c5{n7 .} ==> r9c6 ≠ 6
whip[3]: r8c5{n6 n4} - r9c5{n4 n7} - r7c5{n7 .} ==> r8c6 ≠ 6
whip[3]: r8c5{n4 n6} - r9c5{n6 n7} - r7c5{n7 .} ==> r9c6 ≠ 4
whip[3]: r8c5{n4 n6} - r9c5{n6 n7} - r7c5{n7 .} ==> r8c6 ≠ 4
whip[1]: b8n4{r9c5 .} ==> r2c5 ≠ 4, r4c5 ≠ 4, r5c5 ≠ 4
whip[3]: r8c5{n6 n4} - r9c5{n4 n7} - r7c5{n7 .} ==> r7c6 ≠ 6
whip[1]: b8n6{r9c5 .} ==> r4c5 ≠ 6, r5c5 ≠ 6
whip[3]: r8n9{c1 c2} - r6n9{c2 c6} - b2n9{r1c6 .} ==> r2c1 ≠ 9
whip[4]: c9n3{r9 r8} - r8n8{c9 c2} - r8n9{c2 c1} - b7n6{r8c1 .} ==> r9c9 ≠ 6
whip[5]: r7n6{c9 c5} - r7n7{c5 c3} - r9c3{n7 n5} - r9c1{n5 n1} - r9c2{n1 .} ==> r9c7 ≠ 6
whip[8]: c9n3{r9 r8} - r8c6{n3 n5} - c7n5{r8 r3} - r7n5{c7 c3} - r9c3{n5 n7} - r3n7{c3 c2} - c1n7{r1 r5} - r5n5{c1 .} ==> r9c9 ≠ 5
whip[9]: r5n5{c1 c3} - r9c3{n5 n7} - c1n7{r9 r1} - r1n2{c1 c2} - r1n3{c2 c3} - c3n9{r1 r3} - r3c2{n9 n1} - r3c6{n1 n4} - r5n4{c6 .} ==> r5c1 ≠ 9
whip[10]: r8n9{c1 c2} - r8n8{c2 c9} - c9n3{r8 r9} - c6n3{r9 r8} - r8n5{c6 c7} - c9n5{r8 r3} - c9n4{r3 r1} - r1c4{n4 n6} - r4n6{c4 c9} - r7c9{n6 .} ==> r8c1 ≠ 6
whip[9]: r4c5{n1 n9} - r5c5{n9 n8} - r2c5{n8 n1} - r2c1{n1 n4} - r5n4{c1 c3} - r5n5{c3 c1} - r8c1{n5 n9} - r6n9{c1 c2} - r6n8{c2 .} ==> r5c6 ≠ 1
whip[1]: c6n1{r3 .} ==> r2c5 ≠ 1
whip[10]: r8c1{n9 n5} - r9c3{n5 n7} - c1n7{r9 r5} - b1n7{r1c1 r3c2} - r3c3{n7 n4} - r5n4{c3 c6} - r2n4{c6 c7} - r8c7{n4 n6} - r7n6{c7 c5} - r7n7{c5 .} ==> r1c1 ≠ 9
whip[10]: c1n9{r6 r8} - c2n9{r8 r3} - r6n9{c2 c6} - r6n8{c6 c2} - r8n8{c2 c9} - r8n3{c9 c6} - r8n5{c6 c7} - r7c9{n5 n6} - r4c9{n6 n1} - r4c5{n1 .} ==> r4c3 ≠ 9
whip[5]: r1n2{c1 c2} - r4c2{n2 n3} - r4c3{n3 n4} - c4n4{r4 r6} - c8n4{r6 .} ==> r1c1 ≠ 4
whip[6]: r5n5{c1 c3} - r9c3{n5 n7} - c1n7{r9 r1} - r1n2{c1 c2} - r4c2{n2 n3} - r4c3{n3 .} ==> r5c1 ≠ 4
whip[2]: r5n4{c3 c6} - b2n4{r1c6 .} ==> r1c3 ≠ 4
whip[2]: b1n4{r2c1 r3c3} - r5n4{c3 .} ==> r2c6 ≠ 4
whip[5]: r6n8{c6 c2} - r6n9{c2 c1} - r8c1{n9 n5} - r5n5{c1 c3} - r5n4{c3 .} ==> r6c6 ≠ 4
whip[6]: r5n5{c3 c1} - r8c1{n5 n9} - r6c1{n9 n6} - r4c1{n6 n2} - r4c2{n2 n3} - r4c3{n3 .} ==> r5c3 ≠ 4
hidden-single-in-a-row ==> r5c6 = 4
hidden-single-in-a-block ==> r1c4 = 4
hidden-single-in-a-block ==> r1c6 = 6
whip[3]: r3c6{n1 n9} - b1n9{r3c2 r1c3} - r1c9{n9 .} ==> r3c9 ≠ 1
whip[3]: r3c6{n1 n9} - b1n9{r3c2 r1c3} - r1c9{n9 .} ==> r3c7 ≠ 1
whip[3]: r1c9{n9 n1} - c7n1{r2 r5} - c7n9{r5 .} ==> r3c9 ≠ 9
whip[4]: r2n4{c7 c1} - b4n4{r6c1 r4c3} - c3n3{r4 r1} - r1n9{c3 .} ==> r2c7 ≠ 9
whip[1]: r2n9{c6 .} ==> r3c6 ≠ 9
naked-single ==> r3c6 = 1
hidden-single-in-a-column ==> r9c2 = 1
whip[4]: c7n7{r1 r3} - r3c2{n7 n9} - c7n9{r3 r5} - c3n9{r5 .} ==> r1c7 ≠ 1
whip[3]: c7n1{r5 r2} - r1c9{n1 n9} - b6n9{r4c9 .} ==> r5c7 ≠ 6
whip[1]: c7n6{r8 .} ==> r7c9 ≠ 6, r8c9 ≠ 6
whip[4]: c7n2{r9 r7} - r7n6{c7 c5} - r7n7{c5 c3} - r9c3{n7 .} ==> r9c7 ≠ 5
whip[4]: r8n8{c2 c9} - r7c9{n8 n5} - r8c7{n5 n4} - r8c5{n4 .} ==> r8c2 ≠ 6
hidden-single-in-a-block ==> r9c1 = 6
whip[1]: b7n7{r9c3 .} ==> r1c3 ≠ 7, r3c3 ≠ 7, r5c3 ≠ 7
whip[3]: c3n8{r5 r7} - c3n5{r7 r9} - c3n7{r9 .} ==> r5c3 ≠ 9
whip[1]: c3n9{r3 .} ==> r3c2 ≠ 9
stte

Using uniqueness, there's a solution in W4:
UR2 is applied after Singles (even before whips[1]):
number n6 : horizontal unique rectangle type 2 in cells r6c8, r6c4, r4c8 and r4c4 ==> r1c4 ≠ 6

Code: Select all

Resolution state after Singles, UR and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 1279  12379 379   ! 4     5     6     ! 179   8     19    !
   ! 149   5     6     ! 7     189   189   ! 149   3     2     !
   ! 8     179   479   ! 2     3     19    ! 14579 6     1459  !
   +-------------------+-------------------+-------------------+
   ! 2469  2369  349   ! 56    149   7     ! 8     45    169   !
   ! 45679 6789  45789 ! 3     1489  1489  ! 169   2     169   !
   ! 469   689   1     ! 56    2     489   ! 3     45    7     !
   +-------------------+-------------------+-------------------+
   ! 3     4     578   ! 9     67    25    ! 256   1     568   !
   ! 569   689   2     ! 1     46    345   ! 456   7     34568 !
   ! 1567  167   57    ! 8     467   2345  ! 2456  9     3456  !
   +-------------------+-------------------+-------------------+

the rest of the path in W4 has nothing noticeable: Show

whip[2]: c2n2{r1 r4} - c2n3{r4 .} ==> r1c2 ≠ 1, r1c2 ≠ 7, r1c2 ≠ 9
whip[2]: c2n2{r4 r1} - c2n3{r1 .} ==> r4c2 ≠ 6, r4c2 ≠ 9
whip[3]: r8c5{n4 n6} - r9c5{n6 n7} - r7c5{n7 .} ==> r9c6 ≠ 4
whip[3]: r8c5{n4 n6} - r9c5{n6 n7} - r7c5{n7 .} ==> r8c6 ≠ 4
whip[1]: b8n4{r9c5 .} ==> r4c5 ≠ 4, r5c5 ≠ 4
whip[3]: r1c9{n9 n1} - c7n1{r3 r5} - c7n9{r5 .} ==> r3c9 ≠ 9
whip[3]: r1c9{n1 n9} - c7n9{r3 r5} - c7n1{r5 .} ==> r3c9 ≠ 1
whip[3]: r8n9{c1 c2} - r6n9{c2 c6} - b2n9{r2c6 .} ==> r2c1 ≠ 9
whip[3]: r3c6{n1 n9} - r2n9{c6 c7} - r1c9{n9 .} ==> r3c7 ≠ 1
whip[4]: r4n1{c5 c9} - r1c9{n1 n9} - r2c7{n9 n4} - r2c1{n4 .} ==> r2c5 ≠ 1
whip[1]: c5n1{r5 .} ==> r5c6 ≠ 1
whip[4]: c9n3{r9 r8} - r8n8{c9 c2} - r8n9{c2 c1} - b7n6{r8c1 .} ==> r9c9 ≠ 6
whip[4]: c9n3{r8 r9} - c9n4{r9 r3} - c9n5{r3 r7} - c9n8{r7 .} ==> r8c9 ≠ 6
whip[4]: c9n8{r7 r8} - c9n3{r8 r9} - c9n5{r9 r3} - c9n4{r3 .} ==> r7c9 ≠ 6
whip[1]: b9n6{r9c7 .} ==> r5c7 ≠ 6
whip[4]: c7n2{r9 r7} - r7n6{c7 c5} - r7n7{c5 c3} - r9c3{n7 .} ==> r9c7 ≠ 5
whip[4]: r8n8{c2 c9} - r7c9{n8 n5} - r8c7{n5 n4} - r8c5{n4 .} ==> r8c2 ≠ 6
whip[3]: r6n9{c2 c6} - r6n8{c6 c2} - r8c2{n8 .} ==> r5c2 ≠ 9
whip[4]: r8n9{c2 c1} - r6n9{c1 c6} - r6n8{c6 c2} - r8c2{n8 .} ==> r3c2 ≠ 9
whip[4]: r1c9{n9 n1} - r2c7{n1 n4} - r3n4{c9 c3} - b1n9{r3c3 .} ==> r1c7 ≠ 9
whip[4]: r1c9{n1 n9} - r2c7{n9 n4} - r3n4{c9 c3} - b1n9{r3c3 .} ==> r1c7 ≠ 1
naked-single ==> r1c7 = 7
whip[3]: r5n5{c1 c3} - r9c3{n5 n7} - c1n7{r9 .} ==> r5c1 ≠ 9
whip[3]: r5n5{c1 c3} - r9c3{n5 n7} - c1n7{r9 .} ==> r5c1 ≠ 6
whip[3]: r5n5{c1 c3} - r9c3{n5 n7} - c1n7{r9 .} ==> r5c1 ≠ 4
whip[3]: r3c2{n7 n1} - r9n1{c2 c1} - c1n7{r9 .} ==> r5c2 ≠ 7
whip[2]: c2n7{r9 r3} - c2n1{r3 .} ==> r9c2 ≠ 6
whip[1]: c2n6{r6 .} ==> r4c1 ≠ 6, r6c1 ≠ 6
whip[2]: r5n7{c3 c1} - r5n5{c1 .} ==> r5c3 ≠ 9, r5c3 ≠ 4, r5c3 ≠ 8
stte