The New Sudoku Players' Forum

by **yzfwsf** » Fri Sep 24, 2021 3:53 am

Code: Select all: *-----------* |..2|.8.|..6| |...|4..|.2.| |...|..2|3..| |---+---+---| |82.|57.|1..| |...|..8|..2| |6.1|..3|.5.| |---+---+---| |.5.|8..|..7| |..9|..1|...| |3..|7.5|...| *-----------* ..2.8...6...4...2......23..82.57.1.......8..26.1..3.5..5.8....7..9..1...3..7.5...

skfr:8.5

Website · by **denis_berthier** » Sat Sep 25, 2021 7:20 am

.
SER = 8.5, but on the hard side of the 8.5s.

Code: Select all: Resolution state after Singles (and whips[1]): +----------------------+----------------------+----------------------+ ! 14579 13479 2 ! 139 8 79 ! 4579 1479 6 ! ! 1579 136789 35678 ! 4 13569 679 ! 5789 2 1589 ! ! 14579 146789 45678 ! 169 1569 2 ! 3 14789 14589 ! +----------------------+----------------------+----------------------+ ! 8 2 34 ! 5 7 469 ! 1 3469 349 ! ! 4579 3479 3457 ! 169 1469 8 ! 4679 34679 2 ! ! 6 479 1 ! 29 249 3 ! 4789 5 489 ! +----------------------+----------------------+----------------------+ ! 124 5 46 ! 8 23469 469 ! 2469 13469 7 ! ! 247 4678 9 ! 236 2346 1 ! 24568 3468 3458 ! ! 3 1468 468 ! 7 2469 5 ! 24689 14689 1489 ! +----------------------+----------------------+----------------------+ 216 candidates

Having 216 candidates at this point is kind of a record for a 8.5. Was it your purpose to have so many candidates at the start?

I publish the full SudoRules simplest-first resolution path, because:
- the associated rating (W6) is a reference for the length of chains used in any fewer steps solution;
- it seems to be close to a record also in the small number of Singles (21) after the last non-W1 pattern (but this may depend on the resolution path);
- it also seems to be close to a record for the number of non-W1 steps (50).

Hidden Text: Show

Now a lazy few (4) steps solution:

Hidden Text: Show

François, I think this is a good example for your fewer-steps algorithm. Mine is too slow for making enough tries.

by **DEFISE** » Sat Sep 25, 2021 10:36 am

Hi Denis,
I did not find anything of interest in W10 nor in gW10:
It’s slow (more than 60s per try).
With 5 tries I obtained at least 13 steps !

Here is a 3 steps solution with T&E:

Elimination of 1r7c8 by T&E(singles)
Singles: 1r7c1, 2r8c1, 7r8c2, 7r6c7, 8r6c9, 2r6c4
Block/line: 8r8b9 => -8r9c7 -8r9c8
Elimination of 9r4c6 by T&E(singles)
Block/line: 9r4b6 => -9r5c7 -9r5c8
Elimination of 9r4c9 by T&E(singles)
=> solution in W1

N.B : there are solutions with only two T&E(S2).

Website · by **denis_berthier** » Sat Sep 25, 2021 11:27 am

.
I've started to run 1 try. What I get in W8 is quite noteworthy:

Hidden Text: Show

17 steps with a large number of candidates that could be eliminated each time, but all with the same score 1. This implies an astronomical number of possible paths. I may have been very unlucky in the random choices made at each step, but I think there's something more than bad luck.

by **DEFISE** » Sat Sep 25, 2021 4:28 pm

denis_berthier wrote:.
... I may have been very unlucky in the random choices made at each step, but I think there's something more than bad luck.

I think you used as rules only Singles and whip [<= 8]
(since whip [1] = Block/Line and you consider subsets as steps)
With this rules I did 20 tries without using my criterion 2 (like you) and 20 tries using my criterion 2.
Reminder:
criterion 2 is the number of candidates of the smallest CSP variable containing a candidate.
I use this criterion to decide between candidates who all have a score equal to 1.
Here are the results :

1) Number of steps required to obtain a target with a score > 1
a) without criterion 2
14, 16, 13, 15, 16, 22, 9, 12, 10, 12, 11, 13, 12, 12, 9, 21, 11, 20, 14, 14
=> average = 13,8
With 18 you could say you were unlucky.
b) with criterion 2
15, 9, 6, 11, 10, 9, 13, 12, 11, 7, 8, 10, 14, 8, 9, 14, 12, 12, 13, 11
=> average = 10,7

2) Total number of steps
a) without criterion 2
42, 36, 26, 26, 27, 41, 32, 36, 26, 27, 25, 26, 33, 27, 21, 38, 25, 32, 27, 29
=> average = 30,1
b) with criterion 2
28, 22, 23, 26, 28, 24, 25, 22, 22, 21, 26, 23, 29, 17, 23, 27, 26, 28, 22, 23
=> average = 24,3

Conclusion: it seems that criterion 2 is interesting for this puzzle, which does not mean that it is for others, of course.

by **DEFISE** » Sat Sep 25, 2021 4:52 pm

But the most striking fact is that the total number of steps is considerably reduced, if we take as rules
(whips [<= 8] + Singles + subsets) and then consider whips and subsets as step.

Website · by **denis_berthier** » Sat Sep 25, 2021 6:33 pm

The results about criterion 2 are interesting. It'd be worth to test more puzzles.

DEFISE wrote:I think you used as rules only Singles and whip [<= 8]

No, I used Subsets + whips[≤8]. But there are very few Subsets in this puzzle.

DEFISE wrote:But the most striking fact is that the total number of steps is considerably reduced, if we take as rules
(whips [<= 8] + Singles + subsets) and then consider whips and subsets as step.

I don't understand what you mean.

by **DEFISE** » Sun Sep 26, 2021 8:04 am

denis_berthier wrote:No, I used Subsets + whips[≤8]. But there are very few Subsets in this puzzle.

I meant that to calculate a whip's target score you only use singles and whips [1].
But as I did the same thing with my algo, this caused the complete inhibition of the subsets, which is not very realistic I admit.

denis_berthier wrote:I don't understand what you mean.

Sorry, I meant the most striking fact is that the total number of steps is not considerably reduced, if I add the subsets.
Indeed, by executing after each whip (singles + whips [1] + subsets) and with the 2 criteria,
I got with 20 tries:
Average of total number of steps (whips + subsets) => 24,1
Average of number of steps required to obtain a candidate with a score > 1 => 10,1
N.B : There is only one subset per resolution but still eliminates a lot of candidates.

Website · by **denis_berthier** » Sun Sep 26, 2021 8:11 am

DEFISE wrote: I meant the most striking fact is that the total number of steps is not considerably reduced, if I add the subsets.

I see. I'm not very surprised, because this puzzle has very few Subsets.

by **totuan** » Mon Sep 27, 2021 3:27 pm

Just for reference - My very long path for this one, I try to avoid on using more complex diagram. Hope, there is not many typos

Hidden Text: Show

Thanks for the puzzle!
totuan

by **DEFISE** » Tue Sep 28, 2021 6:56 pm

Hi Denis,
it’s much better starting as totuan:

1) whip[4]: r7n1{c1 c8}- r1n1{c8 c4}- c4n3{r1 r8}- r7n3{c5 .} => -1r2c1 -1r3c1
2) whip[5]: r7n3{c8 c5}- b8n9{r7c5 r9c5}- r9n2{c5 c7}- r7n2{c7 c1}- r7n1{c1 .} => -9r7c8
3) whip[3]: r7c3{n6 n4}- c6n4{r7 r4}- r4n6{c6 .} => -6r7c8

From there, 15 executions of my solver “Few Steps” in W8 gave 7 times 10 steps and 8 times 11 steps (with criterion 2 activated).
Here is an example of a 10 steps path:

4) whip[6]: r4c3{n4 n3}- c9n3{r4 r8}- r7c8{n3 n1}- c1n1{r7 r1}- r1n5{c1 c7}- c9n5{r2 .} => -4r7c3
Single: 6r7c3
5) whip[7]: r9c3{n8 n4}- r4c3{n4 n3}- c9n3{r4 r8}- r8n5{c9 c7}- r1n5{c7 c1}- c1n1{r1 r7} - r9c2{n1 .} => -8r8c2
Block/Line: 8r8b9 => -8r9c7 -8r9c8 -8r9c9
6) whip[7]: c2n6{r2 r3}- c2n8{r3 r9}- r9c3{n8 n4}- r4c3{n4 n3}- r2n3{c3 c5}- r7n3{c5 c8}- b6n3{r4c8 .} => -1r2c2
7) whip[7]: c2n6{r3 r2}- c2n8{r2 r9}- r9c3{n8 n4}- r4c3{n4 n3}- r2n3{c3 c5}- r7n3{c5 c8}- b6n3{r4c8 .} => -1r3c2
Block/Line: 1b1r1 => -1r1c4 -1r1c8
8) whip[4]: r1n3{c4 c2}- r1n1{c2 c1}- r7n1{c1 c8}- r7n3{c8 .} => -3r2c5
Single: 3r1c4
9) whip[8]: r7n1{c8 c1}- c1n2{r7 r8}- r8c4{n2 n6}- r3c4{n6 n9}- r1c6{n9 n7}- c8n7{r1 r5}- b4n7{r5c1 r6c2}- r8n7{c2 .} => -1r3c8
Block/Line: 1c8b9 => -1r9c9
10) whip[7]: r8n5{c9 c7}- r1n5{c7 c1}- c1n1{r1 r7}- r7c8{n1 n4}- r9c9{n4 n9}- r4c9{n9 n4}- c6n4{r4 .} => -3r8c9
Singles: 3r4c9, 4r4c3, 8r9c3, 4r7c6
Block/Line: 9b8c5 => -9r2c5 -9r3c5 -9r5c5 -9r6c5
Hidden pairs: 68c2r23 => -3r2c2 -7r2c2 -9r2c2 -4r3c2 -7r3c2 -9r3c2
Singles: 3r2c3, 3r5c2
11) whip[8]: c4n2{r6 r8}- c1n2{r8 r7}- r7n1{c1 c8}- c8n3{r7 r8}- c8n8{r8 r3}- r3c2{n8 n6}- c4n6{r3 r5}- r4c6{n6 .} => -9r6c4
Singles: 2r6c4, 4r6c5, 6r8c4
12) whip[8]: r7n9{c5 c7}- r9c9{n9 n4}- r9c2{n4 n1}- r9c8{n1 n6}- b6n6{r4c8 r5c7}- c7n4{r5 r1}- r1n5{c7 c1}- r1n1{c1 .} => -3r7c5
Singles: 3r7c8, 1r7c1, 4r9c2, 7r8c2, 9r6c2, 1r1c2, 8r6c9, 7r6c7, 2r8c1, 3r8c5, 9r9c9, 2r7c7, 9r7c5, 2r9c5, 6r9c7, 1r9c8
13) whip[4]: r2c2{n6 n8}- b3n8{r2c7 r3c8}- c8n7{r3 r1}- c6n7{r1 .} => -6r2c6
STTE

This makes a total of 13 steps (14 if you want to count the hidden pairs).
N.B: the results are almost identical with 15 tests done by disabling criterion 2.

Website · by **denis_berthier** » Wed Sep 29, 2021 6:09 am

Hi François,

That's finally a good cut in the number of steps

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