Pisces-9.0

Post puzzles for others to solve here.

Pisces-9.0

Postby denis_berthier » Sat Jul 17, 2021 9:28 am

.
After the Pisces 7.2, here is a Pisces 9.0.

There may be different challenges (after the initial Singles and whips[1] have been applied):
A) find the fewest steps before a Single can be applied
B) find the fewest steps to the end

Code: Select all
6.......1
.2.....4.
..7...8..
..41.59..
381697425
..93.26..
..6...7..
.9.....8.
1.......3

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

6.......1.2.....4...7...8....41.59..381697425..93.26....6...7...9.....8.1.......3 # 67360 FNBTYK C29/S4.hv
29 givens, non-minimal, SER = 9.0
denis_berthier
2010 Supporter
 
Posts: 3967
Joined: 19 June 2007
Location: Paris

Re: Pisces-9.0

Postby denis_berthier » Tue Jul 20, 2021 4:54 am

.
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


2) a fewer-steps solution:
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
denis_berthier
2010 Supporter
 
Posts: 3967
Joined: 19 June 2007
Location: Paris

Re: Pisces-9.0

Postby DEFISE » Fri Jul 23, 2021 3:11 pm

denis_berthier wrote:.
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).

Hello Denis,
Yes I’m still here but less often.
Congratulations, the best I got in W8 is 8 steps, with 50 tries.
In detail:

Hidden Text: Show
Singles: 8r4c5, 7r4c9, 2r4c1, 6r4c2, 3r4c8, 4r6c5, 1r6c8, 8r6c9, 1r3c2, 1r8c7, 7r1c8
Bloc/Line: 9r1b2 => -9r2c4 -9r2c6 -9r3c4 -9r3c6
Bloc/Line: 3r3b2 => -3r1c5 -3r1c6 -3r2c5 -3r2c6

whip[7]: b7n3{r7c2 r8c3}- c3n2{r8 r9}- r9c7{n2 n5}- r7c8{n5 n9}- r9c8{n9 n6}- r9c5{n6 n7}- r9c2{n7 .} => -4r7c2
whip[8]: r2n7{c4 c5}- r2n1{c5 c6}- r2n6{c6 c9}- r2n9{c9 c1}- c1n8{r2 r7}- b8n8{r7c4 r9c6}- r9n9{c6 c8}- c8n6{r9 .} => -7r9c4
whip[7]: c1n9{r3 r2}- r2c9{n9 n6}- r3c8{n6 n9}- r3c9{n9 n2}- r8c9{n2 n4}- r8c1{n4 n7}- r6c1{n7 .} => -5r3c1
whip[7]: r2n7{c4 c5}- r2n1{c5 c6}- r2n6{c6 c9}- r2n9{c9 c1}- r3c1{n9 n4}- c2n4{r1 r9}- r9n7{c2 .} => -7r8c4
Single: 7r2c4
whip[8]: c9n9{r2 r7}- c9n4{r7 r8}- c9n2{r8 r3}- c7n2{r1 r9}- c3n2{r9 r8}- r8c4{n2 n5}
- r3c4{n5 n4}- r3c1{n4 .} => -9r3c8
Bloc/Line: 9c8b9 => -9r7c9
whip[7]: r1c5{n5 n2}- b3n2{r1c7 r3c9}- r7n2{c9 c4}- r8c4{n2 n4}- r9n4{c4 c2}- b1n4{r1c2 r3c1}- r3n9{c1 .} => -5r3c4
whip[7]: c9n6{r2 r8}- c9n4{r8 r7}- c9n2{r7 r3}- r3c4{n2 n4}- r3c6{n4 n3}- r8c6{n3 n4}- c1n4{r8 .}
=> -6r3c8
Singles: 5r3c8, 3r2c7, 2r1c7, 5r1c5, 9r7c8, 5r9c7, 6r9c8
whip[4]: r9c5{n7 n2}- c3n2{r9 r8}- r8n3{c3 c6}- r8n6{c6 .} => -7r8c5
STTE 
DEFISE
 
Posts: 270
Joined: 16 April 2020
Location: France


Return to Puzzles