The New Sudoku Players' Forum

[denis_berthier]

This one is for seasoned surfers.

Code: Select all

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

..46....7.7..3..2.1....46....13....8.4..1..3.3....27....98....5.5..9..7.4....59..
SER 9.3


[DEFISE]

Hi Denis,

With basic techniques = (singles + alignments + naked pairs + hidden pairs + naked triplets)
my "Simplest First" program gives W =13 (40 whips[<=13]) and B=12.
In order to decrease the number of whips, my "Few Steps" program gives 9 whips[<=13] (see below)

Hidden Text: Show

whip[12]: r3n7{c4 c5}- r9n7{c5 c3}- r7n7{c1 c6}- c6n3{r7 r8}- c3n3{r8 r3}- r1n3{c2 c7}- r7n3{c7 c2}- c2n1{r7 r9}- r9n8{c2 c8}- r3n8{c8 c2}- r3n2{c2 c4}- r9c4{n2 .} => -7L5C4

whip[13]: b2n2{r1c5 r3c4}- c4n7{r3 r9}- c3n7{r9 r5}- c3n2{r5 r8}- r7n2{c1 c7}- r5c7{n2 n5}- r4c7{n5 n4}- c8n4{r4 r7}-
r7c5{n4 n6}- c5n4{r7 r6}- b5n8{r6c5 r5c6}- c6n6{r5 r4}- c6n7{r4 .} => -2L9C5

whip[10]: c3n7{r5 r9}- r9c5{n7 n6}- b5n6{r4c5 r4c6}- c2n6{r4 r7}- r7c1{n6 n2}- r8c1{n2 n8}- r5n8{c1 c6}- c6n7{r5 r7}-
c6n3{r7 r8}- r8c3{n3 .} => -6L5C3

whip[11]: r5c7{n2 n5}- r4c7{n5 n4}- c8n4{r4 r7}- c5n4{r7 r6}- b5n8{r6c5 r5c6}- r5n6{c6 c1}- r5n9{c1 c4}- r6c4{n9 n5}-
r2c4{n5 n1}- r1c6{n1 n9}- r2c6{n9 .} => -2L5C9
Alignment: 2-C9-B9 => -2L7C7 -2L8C7

whip[13]: r7n7{c5 c1}- b4n7{r4c1 r5c3}- c6n7{r5 r4}- c5n7{r4 r3}- r9c5{n7 n6}- b5n6{r4c5 r5c6}- r5n8{c6 c1}- r5n2{c1 c7}- r5n5{c7 c4}- b5n9{r5c4 r6c4}- r6c2{n9 n6}- r4n6{c1 c8}- r7n6{c8 .} => -7L9C4
Single: 7L3C4
Alignment: 2-C4-B8 => -2L7C5
Alignment: 2-L7-B7 => -2L8C1 -2L8C3 -2L9C2 -2L9C3

whip[8]: r9c4{n2 n1}- c2n1{r9 r7}- r7n2{c2 c1}- b7n7{r7c1 r9c3}- r9c5{n7 n6}- r8c6{n6 n3}- c3n3{r8 r3}- c9n3{r3 .} => -2L9C9
Single: 2L9C4
Single: 2L8C9

whip[12]: r8n4{c7 c4}- r8n1{c4 c6}- c6n3{r8 r7}- c7n3{r7 r1}- r1n1{c7 c8}- r6n1{c8 c9}- b9n1{r9c9 r7c7}- r7n4{c7 c8}-
r6n4{c8 c5}- b5n8{r6c5 r5c6}- r1c6{n8 n9}- r2c6{n9 .} => -8L8C7
Single: 8L9C8

whip[13]: r8n8{c3 c1}- r8n6{c1 c6}- r9c5{n6 n7}- r9c3{n7 n6}- r9n3{c3 c9}- r3n3{c9 c2}- r1n3{c2 c7}- c7n8{r1 r2}- r2c3{n8 n5}- r6c3{n5 n8}- r3n8{c3 c5}- c5n2{r3 r1}- b2n5{r1c5 .} => -3L8C3
Naked pair: 68-L8C1-L8C3 => -6L8C6
Alignment: 6-L8-B7 => -6L7C1 -6L7C2 -6L9C2 -6L9C3
Alignment: 6-C2-B4 => -6L4C1 -6L5C1 -6L6C3
Naked triplet: 568-L2C3-L6C3-L8C3 => -5L3C3 -8L3C3 -5L5C3 -8L5C3

whip[8]: r5n6{c6 c9}- c8n6{r4 r7}- c6n6{r7 r4}- c6n7{r4 r7}- r7c5{n7 n4}- r6c5{n4 n5}- b2n5{r1c5 r2c4}- c3n5{r2 .} => -8L5C6
Singles, Alignment, Naked pair, singles to the end.

 

Other method :

Puzzle + 9L3C9 => W=5
“Few Steps” gives 13 whips[<=5] to prove that this new puzzle is invalid.
Puzzle + 3L3C9 => W=5
“Few Steps” gives 9 whips[<=5] to find the solution.

[denis_berthier]

SudoRules finds a different path (not surprising), also in W13, with a first elimination in W8:

Hidden Text: Show

***********************************************************************************************
*** SudoRules 20.1.s based on CSP-Rules 2.1.s, config = W+SFin
*** Using CLIPS 6.32-r778
***********************************************************************************************
198 candidates, 1143 csp-links and 1143 links. Density = 5.86%
whip[8]: r3c9{n9 n3} - r1n3{c7 c2} - r9n3{c2 c3} - c3n7{r9 r5} - r5c4{n7 n5} - r2c4{n5 n1} - r1c6{n1 n8} - r2c6{n8 .} ==> r3c4 ≠ 9
whip[12]: r3n7{c4 c5} - r9n7{c5 c3} - r7n7{c1 c6} - c6n3{r7 r8} - c3n3{r8 r3} - c9n3{r3 r9} - r7n3{c7 c2} - c2n1{r7 r9} - r9n8{c2 c8} - r3n8{c8 c2} - r3n2{c2 c4} - r9c4{n2 .} ==> r5c4 ≠ 7
whip[12]: c4n7{r3 r9} - c3n7{r9 r5} - c6n7{r5 r4} - c5n7{r4 r3} - b2n2{r3c5 r1c5} - c5n8{r1 r6} - b4n8{r6c2 r5c1} - r5n5{c1 c7} - r5n2{c7 c9} - r4c7{n2 n4} - c8n4{r4 r7} - c5n4{r7 .} ==> r3c4 ≠ 5
whip[13]: c4n2{r9 r3} - c4n7{r3 r9} - c3n7{r9 r5} - c3n2{r5 r8} - c9n2{r8 r5} - r5c7{n2 n5} - r4c7{n5 n4} - c8n4{r4 r7} - c5n4{r7 r6} - b5n8{r6c5 r5c6} - c6n7{r5 r4} - b5n6{r4c6 r4c5} - r7c5{n6 .} ==> r9c5 ≠ 2
whip[10]: c3n7{r5 r9} - r9c5{n7 n6} - b5n6{r4c5 r4c6} - c2n6{r4 r7} - r7c1{n6 n2} - r8c1{n2 n8} - r8c3{n8 n3} - c6n3{r8 r7} - c6n7{r7 r5} - r5n8{c6 .} ==> r5c3 ≠ 6
t-whip[11]: c9n2{r9 r5} - r5c7{n2 n5} - r4c7{n5 n4} - c8n4{r6 r7} - c5n4{r7 r6} - b5n8{r6c5 r5c6} - r5c3{n8 n7} - b7n7{r9c3 r7c1} - c6n7{r7 r4} - b5n6{r4c6 r4c5} - r7c5{n6 .} ==> r7c7 ≠ 2
whip[5]: b9n2{r8c9 r9c9} - c4n2{r9 r3} - c4n7{r3 r9} - c3n7{r9 r5} - c3n2{r5 .} ==> r8c1 ≠ 2
whip[5]: r7n2{c2 c5} - b2n2{r1c5 r3c4} - c4n7{r3 r9} - c3n7{r9 r5} - c3n2{r5 .} ==> r9c2 ≠ 2
whip[10]: r3c4{n2 n7} - r9c4{n7 n1} - c2n1{r9 r7} - r7n2{c2 c1} - b7n7{r7c1 r9c3} - r9n2{c3 c9} - r9n3{c9 c2} - r1n3{c2 c7} - r7c7{n3 n4} - b8n4{r7c5 .} ==> r8c4 ≠ 2
hidden-pairs-in-a-column: c4{n2 n7}{r3 r9} ==> r9c4 ≠ 1
whip[6]: r2n4{c9 c7} - r7n4{c7 c5} - b8n2{r7c5 r9c4} - c9n2{r9 r5} - r5c7{n2 n5} - r4c7{n5 .} ==> r8c9 ≠ 4
biv-chain-cn[3]: c9n4{r2 r6} - c4n4{r6 r8} - c4n1{r8 r2} ==> r2c9 ≠ 1
whip[6]: b9n8{r9c8 r8c7} - r8n4{c7 c4} - r8n1{c4 c6} - c6n3{r8 r7} - c7n3{r7 r1} - r1n1{c7 .} ==> r9c8 ≠ 1
whip[7]: r9c8{n8 n6} - r9c5{n6 n7} - r9c4{n7 n2} - r9c3{n2 n3} - b7n7{r9c3 r7c1} - r7n2{c1 c2} - c2n1{r7 .} ==> r9c2 ≠ 8
whip[7]: r9n1{c2 c9} - r9n3{c9 c3} - r9n2{c3 c4} - r9n7{c4 c5} - b7n7{r9c3 r7c1} - r7n2{c1 c2} - c2n1{r7 .} ==> r9c2 ≠ 6
whip[6]: r9c2{n1 n3} - r1n3{c2 c7} - b9n3{r7c7 r8c9} - b9n2{r8c9 r8c7} - c7n8{r8 r2} - c7n1{r2 .} ==> r9c9 ≠ 1
hidden-single-in-a-row ==> r9c2 = 1
z-chain[7]: c7n8{r2 r8} - r8n4{c7 c4} - c4n1{r8 r2} - b3n1{r2c7 r1c7} - b3n3{r1c7 r3c9} - r9n3{c9 c3} - r9n8{c3 .} ==> r1c8 ≠ 8
z-chain[7]: c9n4{r2 r6} - r6n1{c9 c8} - r1c8{n1 n5} - r3c8{n5 n8} - r9n8{c8 c3} - r9n3{c3 c9} - r3c9{n3 .} ==> r2c9 ≠ 9
naked-single ==> r2c9 = 4
whip[7]: r6n1{c9 c8} - r7n1{c8 c6} - r8c4{n1 n4} - r6n4{c4 c5} - b5n8{r6c5 r5c6} - r2c6{n8 n9} - r1c6{n9 .} ==> r8c9 ≠ 1
hidden-single-in-a-column ==> r6c9 = 1
whip[7]: r2n6{c3 c1} - r8c1{n6 n8} - c7n8{r8 r1} - c6n8{r1 r5} - r5n6{c6 c9} - c9n9{r5 r3} - b3n3{r3c9 .} ==> r2c3 ≠ 8
whip[7]: r3n9{c9 c2} - r6n9{c2 c4} - c4n4{r6 r8} - c4n1{r8 r2} - r1c6{n1 n8} - b5n8{r5c6 r6c5} - c2n8{r6 .} ==> r1c8 ≠ 9
whip[1]: b3n9{r3c9 .} ==> r3c2 ≠ 9
whip[8]: r9c5{n6 n7} - r9c4{n7 n2} - r7c5{n2 n4} - r7c8{n4 n1} - r7c7{n1 n3} - r9c9{n3 n6} - r5n6{c9 c1} - c2n6{r4 .} ==> r7c6 ≠ 6
whip[6]: c4n1{r2 r8} - b8n4{r8c4 r7c5} - r7c7{n4 n3} - r7c6{n3 n7} - b7n7{r7c1 r9c3} - r9n3{c3 .} ==> r2c7 ≠ 1
whip[1]: r2n1{c6 .} ==> r1c6 ≠ 1
t-whip[4]: c2n8{r3 r6} - r5n8{c3 c6} - r1c6{n8 n9} - b1n9{r1c1 .} ==> r2c1 ≠ 8
t-whip[5]: b5n8{r6c5 r5c6} - r1c6{n8 n9} - r2c6{n9 n1} - b8n1{r7c6 r8c4} - c4n4{r8 .} ==> r6c5 ≠ 4
finned-x-wing-in-columns: n4{c5 c7}{r4 r7} ==> r7c8 ≠ 4
whip[1]: b9n4{r8c7 .} ==> r4c7 ≠ 4
naked-pairs-in-a-block: b6{r4c7 r5c7}{n2 n5} ==> r6c8 ≠ 5, r5c9 ≠ 2, r4c8 ≠ 5
whip[1]: b6n5{r5c7 .} ==> r1c7 ≠ 5, r2c7 ≠ 5
naked-single ==> r2c7 = 8
hidden-single-in-a-column ==> r9c8 = 8
whip[1]: c9n2{r9 .} ==> r8c7 ≠ 2
z-chain[4]: r2n5{c3 c4} - r5c4{n5 n9} - c9n9{r5 r3} - r3c8{n9 .} ==> r3c3 ≠ 5
t-whip[4]: r1c6{n8 n9} - r2n9{c6 c1} - r2n6{c1 c3} - b1n5{r2c3 .} ==> r1c1 ≠ 8
t-whip[4]: b7n7{r7c1 r9c3} - r9n3{c3 c9} - b9n2{r9c9 r8c9} - b9n6{r8c9 .} ==> r7c1 ≠ 6
z-chain[5]: r1c7{n3 n1} - b9n1{r8c7 r7c8} - r7c6{n1 n7} - b7n7{r7c1 r9c3} - r9n3{c3 .} ==> r7c7 ≠ 3
biv-chain[4]: r6n4{c8 c4} - b8n4{r8c4 r7c5} - r7c7{n4 n1} - r7c8{n1 n6} ==> r6c8 ≠ 6
finned-x-wing-in-columns: n6{c8 c2}{r7 r4} ==> r4c1 ≠ 6
t-whip[5]: c2n6{r6 r7} - c8n6{r7 r4} - r5c9{n6 n9} - r5c4{n9 n5} - r6n5{c4 .} ==> r6c3 ≠ 6
whip-rn[5]: r8n2{c9 c3} - r7n2{c1 c5} - r7n6{c5 c2} - r6n6{c2 c5} - r9n6{c5 .} ==> r8c9 ≠ 6
whip[4]: b9n2{r8c9 r9c9} - b9n6{r9c9 r7c8} - r7c2{n6 n3} - r9n3{c3 .} ==> r8c3 ≠ 2
hidden-single-in-a-row ==> r8c9 = 2
z-chain[4]: b9n6{r7c8 r9c9} - r9n3{c9 c3} - r8c3{n3 n8} - r8c1{n8 .} ==> r7c2 ≠ 6
whip[1]: c2n6{r6 .} ==> r5c1 ≠ 6
biv-chain[4]: r6c3{n8 n5} - r2c3{n5 n6} - c1n6{r2 r8} - c1n8{r8 r5} ==> r5c3 ≠ 8, r6c2 ≠ 8
whip[1]: c2n8{r3 .} ==> r3c3 ≠ 8
z-chain[3]: r5n8{c1 c6} - r1c6{n8 n9} - c2n9{r1 .} ==> r5c1 ≠ 9
biv-chain[4]: r6c3{n5 n8} - c1n8{r5 r8} - c1n6{r8 r2} - r2c3{n6 n5} ==> r5c3 ≠ 5
finned-x-wing-in-columns: n5{c3 c4}{r2 r6} ==> r6c5 ≠ 5
t-whip[3]: c3n8{r8 r6} - r6c5{n8 n6} - b8n6{r7c5 .} ==> r8c3 ≠ 6
biv-chain[3]: c1n8{r5 r8} - b7n6{r8c1 r9c3} - b7n7{r9c3 r7c1} ==> r5c1 ≠ 7
finned-x-wing-in-columns: n7{c1 c6}{r7 r4} ==> r4c5 ≠ 7
whip[1]: b5n7{r5c6 .} ==> r7c6 ≠ 7
z-chain[3]: c6n7{r4 r5} - r5n6{c6 c9} - r5n9{c9 .} ==> r4c6 ≠ 9
biv-chain[4]: r3n8{c2 c5} - r6n8{c5 c3} - r8c3{n8 n3} - r3c3{n3 n2} ==> r3c2 ≠ 2
z-chain[4]: c6n7{r5 r4} - c6n6{r4 r8} - r8c1{n6 n8} - r5n8{c1 .} ==> r5c6 ≠ 9
whip[1]: b5n9{r6c4 .} ==> r2c4 ≠ 9
naked-triplets-in-a-block: b5{r4c6 r5c6 r6c5}{n6 n7 n8} ==> r4c5 ≠ 6
biv-chain-cn[4]: c6n9{r2 r1} - c6n8{r1 r5} - c1n8{r5 r8} - c1n6{r8 r2} ==> r2c1 ≠ 9
stte

I can also confirm the puzzle being in B12.

[DEFISE]

SudoRules finds a different path (not surprising), also in W13, with a first elimination in W8:

At the start, my algo preferred the 7r5c4 target to the 9r3c4 because it has a better 2nd criterion (3 instead of 4).
Indeed the smallest entity containing 7r5c4 has 3 candidates while the smallest entity containing 9r3c4 has 4 candidates.
Concerning the first criterion, the most relevant, these two candidates are tied.