.
I proposed this puzzle because it allows a shortened resolution path with steps not much longer than in the simplest-first solution (i.e.
7 steps in W8 instead of 31 in W7).
This is an application of my implementation of a "fewer steps" technique inspired by François Defise, but with different criteria for choosing each step (not yet pushed to GitHub, still under testing).
- Code: Select all
Resolution state after Singles and whips[1]:
+----------------------+----------------------+----------------------+
! 6 345 358 ! 24589 25 489 ! 235 7 1 !
! 589 2 358 ! 578 1567 168 ! 35 4 69 !
! 459 1 7 ! 245 2356 346 ! 8 569 269 !
+----------------------+----------------------+----------------------+
! 2 6 4 ! 1 8 5 ! 9 3 7 !
! 3 8 1 ! 6 9 7 ! 4 2 5 !
! 57 57 9 ! 3 4 2 ! 6 1 8 !
+----------------------+----------------------+----------------------+
! 458 345 6 ! 24589 1235 13489 ! 7 59 249 !
! 457 9 235 ! 2457 23567 346 ! 1 8 246 !
! 1 457 258 ! 245789 2567 4689 ! 25 569 3 !
+----------------------+----------------------+----------------------+
1) The "standard" simplest first solution: Show whip[6]: r9c7{n5 n2} - r9c3{n2 n8} - c1n8{r7 r2} - r2n9{c1 c9} - r7c9{n9 n4} - r7c1{n4 .} ==> r9c2 ≠ 5
t-whip[7]: b7n3{r7c2 r8c3} - c3n2{r8 r9} - r9c7{n2 n5} - c8n5{r9 r3} - c8n6{r3 r9} - r9c5{n6 n7} - r9c2{n7 .} ==> r7c2 ≠ 4
whip[7]: c1n9{r3 r2} - c1n8{r2 r7} - c1n4{r7 r8} - c9n4{r8 r7} - c9n9{r7 r3} - r2c9{n9 n6} - r3c8{n6 .} ==> r3c1 ≠ 5
z-chain[4]: r3n5{c5 c8} - c7n5{r1 r9} - c7n2{r9 r1} - r1c5{n2 .} ==> r2c5 ≠ 5
z-chain[4]: r3n5{c5 c8} - c7n5{r1 r9} - c7n2{r9 r1} - r1c5{n2 .} ==> r2c4 ≠ 5
z-chain[4]: r3n5{c5 c8} - r2c7{n5 n3} - r1c7{n3 n2} - r1c5{n2 .} ==> r1c4 ≠ 5
t-whip[4]: r1c5{n2 n5} - r3n5{c5 c8} - r2c7{n5 n3} - r1c7{n3 .} ==> r1c4 ≠ 2
t-whip[4]: r7c8{n9 n5} - r9c7{n5 n2} - r1n2{c7 c5} - r7n2{c5 .} ==> r7c4 ≠ 9
t-whip[7]: c5n7{r9 r2} - r2n1{c5 c6} - r2n6{c6 c9} - r2n9{c9 c1} - r3c1{n9 n4} - b7n4{r7c1 r9c2} - r9n7{c2 .} ==> r8c4 ≠ 7
whip[5]: r9c7{n5 n2} - r1n2{c7 c5} - r7n2{c5 c4} - r8c4{n2 n4} - r3c4{n4 .} ==> r9c4 ≠ 5
whip[5]: r7c2{n5 n3} - r8c3{n3 n2} - r8c4{n2 n4} - r9n4{c4 c2} - b7n7{r9c2 .} ==> r8c1 ≠ 5
naked-pairs-in-a-block: b7{r8c1 r9c2}{n4 n7} ==> r7c1 ≠ 4
z-chain[3]: r8n5{c5 c3} - c3n2{r8 r9} - r9c7{n2 .} ==> r9c5 ≠ 5
z-chain[4]: r8n5{c5 c3} - c3n2{r8 r9} - c7n2{r9 r1} - r1c5{n2 .} ==> r7c5 ≠ 5
whip[5]: r7n2{c5 c9} - c9n4{r7 r8} - c1n4{r8 r3} - r3c4{n4 n5} - r8c4{n5 .} ==> r9c4 ≠ 2
whip[6]: r1n9{c4 c6} - b8n9{r9c6 r9c4} - c4n7{r9 r2} - c4n8{r2 r7} - b2n8{r1c4 r2c6} - c1n8{r2 .} ==> r1c4 ≠ 4
finned-x-wing-in-columns: n4{c1 c4}{r3 r8} ==> r8c6 ≠ 4
finned-x-wing-in-rows: n4{r1 r9}{c2 c6} ==> r7c6 ≠ 4
z-chain[4]: r8c6{n3 n6} - r3c6{n6 n4} - b1n4{r3c1 r1c2} - c2n3{r1 .} ==> r7c6 ≠ 3
z-chain[5]: r7n4{c9 c4} - r7n2{c4 c5} - r1n2{c5 c7} - r3c9{n2 n6} - r2c9{n6 .} ==> r7c9 ≠ 9
whip[1]: b9n9{r9c8 .} ==> r3c8 ≠ 9
biv-chain[4]: r1c5{n5 n2} - b3n2{r1c7 r3c9} - r3n9{c9 c1} - b1n4{r3c1 r1c2} ==> r1c2 ≠ 5
biv-chain[4]: r8n7{c5 c1} - c2n7{r9 r6} - c2n5{r6 r7} - r7n3{c2 c5} ==> r8c5 ≠ 3
biv-chain[4]: c5n3{r3 r7} - r8c6{n3 n6} - b9n6{r8c9 r9c8} - r3c8{n6 n5} ==> r3c5 ≠ 5
whip[4]: c5n3{r3 r7} - r8c6{n3 n6} - b2n6{r2c6 r2c5} - c5n1{r2 .} ==> r3c5 ≠ 2
hidden-pairs-in-a-block: b2{n2 n5}{r1c5 r3c4} ==> r3c4 ≠ 4
whip[1]: c4n4{r9 .} ==> r9c6 ≠ 4
finned-x-wing-in-rows: n2{r3 r7}{c9 c4} ==> r8c4 ≠ 2
biv-chain[3]: r1n4{c6 c2} - r9n4{c2 c4} - c4n9{r9 r1} ==> r1c6 ≠ 9
hidden-single-in-a-block ==> r1c4 = 9
finned-x-wing-in-columns: n8{c1 c4}{r2 r7} ==> r7c6 ≠ 8
biv-chain[4]: c2n5{r7 r6} - c2n7{r6 r9} - r9n4{c2 c4} - r8c4{n4 n5} ==> r8c3 ≠ 5, r7c4 ≠ 5
biv-chain[4]: c4n5{r8 r3} - r3n2{c4 c9} - r3n9{c9 c1} - c1n4{r3 r8} ==> r8c4 ≠ 4
singles ==> r8c4 = 5, r3c4 = 2, r1c5 = 5, r1c7 = 2, r9c7 = 5, r2c7 = 3, r7c8 = 9, r7c6 = 1, r9c8 = 6, r3c8 = 5, r2c5 = 1, r2c4 = 7, r9c6 = 9, r2c3 = 5
biv-chain[3]: r7c5{n2 n3} - r8n3{c6 c3} - b7n2{r8c3 r9c3} ==> r9c5 ≠ 2
stte
whip[8]: c3n2{r8 r9} - r9c7{n2 n5} - c8n5{r9 r3} - r3c4{n5 n4} - r1n4{c6 c2} - r9c2{n4 n7} - r9c5{n7 n6} - c8n6{r9 .} ==> r8c4 ≠ 2
whip[7]: r9c7{n5 n2} - r9c3{n2 n8} - c1n8{r7 r2} - r2n9{c1 c9} - r7c9{n9 n4} - r7c1{n4 n5} - b9n5{r7c8 .} ==> r9c5 ≠ 5
whip[8]: r2n1{c5 c6} - r2n6{c6 c9} - c8n6{r3 r9} - r9c5{n6 n2} - r9c7{n2 n5} - r9c3{n5 n8} - c1n8{r7 r2} - r2n9{c1 .} ==> r2c5 ≠ 7
hidden-single-in-a-block ==> r2c4 = 7
whip-rc[8]: r2c9{n9 n6} - r3c9{n6 n2} - r8c9{n2 n4} - r8c4{n4 n5} - r3c4{n5 n4} - r3c1{n4 n5} - r8c1{n5 n7} - r6c1{n7 .} ==> r3c8 ≠ 9
whip[1]: c8n9{r9 .} ==> r7c9 ≠ 9
whip[8]: c9n4{r8 r7} - c1n4{r7 r3} - r3n9{c1 c9} - b3n2{r3c9 r1c7} - r1c5{n2 n5} - r1c2{n5 n3} - r7c2{n3 n5} - r8n5{c1 .} ==> r8c4 ≠ 4
naked-single ==> r8c4 = 5
whip[7]: b9n6{r9c8 r8c9} - c9n4{r8 r7} - c9n2{r7 r3} - r3c4{n2 n4} - r3c6{n4 n3} - r8c6{n3 n4} - c1n4{r8 .} ==> r3c8 ≠ 6
singles ==> r3c8 = 5, r2c7 = 3, r1c7 = 2, r1c5 = 5, r9c7 = 5, r7c8 = 9, r9c8 = 6, r2c3 = 5
whip-rc[5]: r6c1{n5 n7} - r8c1{n7 n4} - r7c2{n4 n3} - r8c3{n3 n2} - r8c9{n2 .} ==> r6c2 ≠ 5
stte
This was obtained after only 5 tries of the fewer-steps algorithm.
Remember that the simplest-first strategy tends to produce a large number of steps, the more so as more types of resolution rules are activated. (These steps are not useless as they may simplify posterior ones.)
This can be considered as an advantage (in addition to the main one of computing the rating) or not, depending on one's goals.
In case one looks for 1-step or 2-step solutions, a systematic review of all the possible paths remains possible (see many of the puzzles in this forum where I have proposed such solutions; see also CSP-Rules user manual (
https://github.com/denis-berthier/CSP-Rules-V2.1 or
https://www.researchgate.net/profile/Denis-Berthier/research)
But in case no such solution exists, a systematic exploration of all the resolution paths is impossible. In this case, the "fewer steps" algorithm chooses each step randomly among the "most promising ones" in all the available ones. I may have been lucky in the present case. Sometimes I need many more tries before finding such a reduction in the number of steps. I also think, sometimes, no much reduction is possible.
François, if you're still here, can you try this puzzle?
See here for a more
detailed explanation of the fewer steps algorithm:
http://forum.enjoysudoku.com/reducing-the-number-of-steps-t39234.html
