The New Sudoku Players' Forum

[denis_berthier]

.
The pattern for this puzzle is derived from the radiations2 pattern by replacing each line in a block by the orthogonal line, except in the central block, where the complementary pattern is taken.
This pattern has minimal puzzles but not many.

Code: Select all

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

..9...7...7.891.4.4.......2.9..3..5..4.1.7.2..3..2..1.6.......5.5.246.3...3...4.. #  1308 FNBTWXY C28.M/S8.f
SER = 7.2
non minimal

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 135  16   9    ! 4    56   2    ! 7    8    13   !
   ! 235  7    25   ! 8    9    1    ! 35   4    6    !
   ! 4    168  158  ! 357  567  35   ! 15   9    2    !
   +----------------+----------------+----------------+
   ! 12   9    12   ! 6    3    4    ! 8    5    7    !
   ! 58   4    6    ! 1    58   7    ! 39   2    39   !
   ! 578  3    578  ! 59   2    589  ! 6    1    4    !
   +----------------+----------------+----------------+
   ! 6    18   4    ! 39   18   389  ! 2    7    5    !
   ! 1789 5    178  ! 2    4    6    ! 19   3    189  !
   ! 189  2    3    ! 57   1578 58   ! 4    6    189  !
   +----------------+----------------+----------------+
90 candidates

[RSW]

Two Steps.

Code: Select all

 +----------------+---------------+----------+
 | 135  d16   9   | 4   c56   2   | 7  8 13  |
 | 235   7    25  | 8    9    1   | 35 4 6   |
 | 4     16-8 158 | 357  567  35  | 15 9 2   |
 +----------------+---------------+----------+
 | 12    9    12  | 6    3    4   | 8  5 7   |
 | 58    4    6   | 1   c58   7   | 39 2 39  |
 | 578   3    578 | 59   2    589 | 6  1 4   |
 +----------------+---------------+----------+
 | 6   ae8-1  4   | 39 bc1-8  39  | 2  7 5   |
 | 179-8 5    17-8| 2    4    6   | 19 3 189 |
 | 19-8  2    3   | 57   1578 58  | 4  6 189 |
 +----------------+---------------+----------+


(8)r7c2 = (8)r7c5 - (1=586)r157c5 - (6=1)r1c2 - (1=8)r7c2 Loop => -1r7c2 -8r9c1 -8r8c13 -8r3c2 -8r7c5

Code: Select all

 +-----------+-------------+---------+
 | 35  16 9  | 4   56  2   | 7  8 13 |
 | 235 7 b25 | 8   9   1   |b35 4 6  |
 | 4   16 8  | 357 567 35  | 15 9 2  |
 +-----------+-------------+---------+
 | 12  9 a12 | 6   3   4   | 8  5 7  |
 | 58  4  6  | 1   58  7   |c39 2 39 |
 | 578 3  57 | 59  2   589 | 6  1 4  |
 +-----------+-------------+---------+
 | 6   8  4  | 39  1   39  | 2  7 5  |
 | 179 5  7-1| 2   4   6   |d19 3 8  |
 | 19  2  3  | 57  578 58  | 4  6 19 |
 +-----------+-------------+---------+


(1=2)r4c3 - (2=53)r2c37 - (3=9)r5c7 - (9=1)r8c7 => -1r8c3; stte

[P.O.]

after singles and intersections:
r4n1{c3 c1} - c1n2{r4 r2} - r2n3{c1 c7} - r1c9{n3 n1} - c7n1{r3 r8} => r8c3 <> 1
c5n1{r7 r9} - c5n7{r9 r3} - r3n6{c5 c2} - r1c2{n6 n1} => r7c2 <> 1
ste.

[denis_berthier]

.
The puzzle is in BC4.

The best solution I found has 2 steps in BC4:
biv-chain[4]: r4c3{n1 n2} - r2c3{n2 n5} - b3n5{r2c7 r3c7} - c7n1{r3 r8} ==> r8c3≠1
biv-chain[4]: r7c5{n1 n8} - c2n8{r7 r3} - r3n6{c2 c5} - c5n7{r3 r9} ==> r9c5≠1
stte
Alternatively, the 2nd chain can be:
biv-chain[4]: r5c5{n8 n5} - r1c5{n5 n6} - b1n6{r1c2 r3c2} - c2n8{r3 r7} ==> r7c5≠8

A 1-step solution would require a whip[8], much too complicated for a puzzle in BC4:
whip[8]: r7n8{c6 c2} - r3n8{c2 c3} - r6n8{c3 c1} - r6n7{c1 c3} - r8c3{n7 n1} - c7n1{r8 r3} - c7n5{r3 r2} - c3n5{r2 .} ==> r9c6≠8
stte