The New Sudoku Players' Forum

by **yzfwsf** » Wed Aug 04, 2021 1:37 am

Code: Select all: ..9.8..5.7..6....9.6...28.42.....7......47.2..5..3.....9.1....2.....41..5......7.

Code: Select all: .----------------------.----------------------.---------------------. | 134 1234 9 | 347 8 13 | 236 5 1367 | | 7 12348 123458 | 6 15 135 | 23 13 9 | | 13 6 135 | 3579 1579 2 | 8 13 4 | :----------------------+----------------------+---------------------: | 2 1348 13468 | 589 1569 15689 | 7 134689 13568 | | 13689 138 1368 | 589 4 7 | 3569 2 13568 | | 14689 5 14678 | 289 3 1689 | 469 14689 168 | :----------------------+----------------------+---------------------: | 3468 9 34678 | 1 567 3568 | 3456 3468 2 | | 368 2378 23678 | 235789 25679 4 | 1 3689 3568 | | 5 12348 123468 | 2389 269 3689 | 3469 7 368 | '----------------------'----------------------'---------------------'

by **pjb** » Wed Aug 04, 2021 4:30 am

3 steps; surely there is something shorter ...

1) BUG-lite (type 1) at r1c16, r2c68, r3c18 => -13 r2c6;
(21 singles)
2) (4)r4c8 = (4)r4c23 - (4)r6c1 = (4)r7c1 - (4)r7c8 => -4 r7c8;
(37 singles/basics)
3) (6)r4c5 = (6)r89c5 - (6)r7c6 = (6)r7c8 => -6 r4c8; stte

Phil

Website · by **denis_berthier** » Thu Aug 05, 2021 4:49 am

.
This is an interesting example of a moderately difficult puzzle (SER = 6.6), where using uniqueness significantly changes the rating: from Z4 without it to finned-x-wings with it.
Moreover, there's no whip 1- or 2- step solution without using uniqueness.

1) Simplest-first solution, in Z4 (only reversible chains used), with no assumption of uniqueness

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 13 2 9 ! 4 8 13 ! 6 5 7 ! ! 7 1348 1348 ! 6 15 135 ! 2 13 9 ! ! 13 6 5 ! 7 9 2 ! 8 13 4 ! +----------------------+----------------------+----------------------+ ! 2 1348 13468 ! 589 156 15689 ! 7 4689 13568 ! ! 13689 138 1368 ! 589 4 7 ! 359 2 13568 ! ! 14689 5 7 ! 2 3 1689 ! 49 4689 168 ! +----------------------+----------------------+----------------------+ ! 3468 9 3468 ! 1 7 568 ! 345 468 2 ! ! 368 7 2368 ! 3589 256 4 ! 1 689 3568 ! ! 5 1348 123468 ! 389 26 689 ! 349 7 368 ! +----------------------+----------------------+----------------------+

Code: Select all: naked-pairs-in-a-column: c1{r1 r3}{n1 n3} ==> r8c1 ≠ 3, r7c1 ≠ 3, r6c1 ≠ 1, r5c1 ≠ 3, r5c1 ≠ 1 whip[1]: c1n1{r3 .} ==> r2c2 ≠ 1, r2c3 ≠ 1 whip[1]: c1n3{r3 .} ==> r2c2 ≠ 3, r2c3 ≠ 3 finned-x-wing-in-rows: n9{r8 r4}{c8 c4} ==> r5c4 ≠ 9 finned-x-wing-in-columns: n4{c1 c8}{r7 r6} ==> r6c7 ≠ 4 singles ==> r6c7 = 9,r8c8 = 9, r5c1 = 9 whip[1]: c7n4{r9 .} ==> r7c8 ≠ 4 z-chain[3]: r5n6{c3 c9} - c8n6{r4 r6} - c1n6{r6 .} ==> r7c3 ≠ 6 z-chain[4]: b5n6{r4c6 r6c6} - r7n6{c6 c1} - c1n4{r7 r6} - c8n4{r6 .} ==> r4c8 ≠ 6 z-chain[4]: c8n6{r7 r6} - r6n4{c8 c1} - r7c1{n4 n8} - r7c8{n8 .} ==> r7c6 ≠ 6 biv-chain[3]: b9n5{r8c9 r7c7} - r7c6{n5 n8} - r7c8{n8 n6} ==> r8c9 ≠ 6 biv-chain[3]: r7c6{n8 n5} - c7n5{r7 r5} - r5c4{n5 n8} ==> r8c4 ≠ 8, r9c4 ≠ 8, r4c6 ≠ 8, r6c6 ≠ 8 biv-chain[3]: r8c4{n3 n5} - r7n5{c6 c7} - r7n3{c7 c3} ==> r8c3 ≠ 3 z-chain[3]: r6n8{c9 c1} - r6n4{c1 c8} - r4c8{n4 .} ==> r4c9 ≠ 8 z-chain[3]: r6n8{c9 c1} - r6n4{c1 c8} - r4c8{n4 .} ==> r5c9 ≠ 8 z-chain[3]: r8n8{c3 c9} - b9n5{r8c9 r7c7} - r7c6{n5 .} ==> r7c1 ≠ 8 biv-chain[3]: r6n4{c8 c1} - r7c1{n4 n6} - c8n6{r7 r6} ==> r6c8 ≠ 8 biv-chain[3]: r6c8{n6 n4} - r4c8{n4 n8} - r6n8{c9 c1} ==> r6c1 ≠ 6 whip[1]: c1n6{r8 .} ==> r8c3 ≠ 6, r9c3 ≠ 6 biv-chain[3]: r6c1{n8 n4} - r6c8{n4 n6} - r5n6{c9 c3} ==> r5c3 ≠ 8 z-chain[3]: r8n8{c3 c9} - b9n5{r8c9 r7c7} - r7n3{c7 .} ==> r7c3 ≠ 8 biv-chain[4]: r7c3{n3 n4} - r7c1{n4 n6} - c8n6{r7 r6} - r5n6{c9 c3} ==> r5c3 ≠ 3 biv-chain[4]: c7n5{r5 r7} - r7c6{n5 n8} - c8n8{r7 r4} - c4n8{r4 r5} ==> r5c4 ≠ 5 naked-single ==> r5c4 = 8 whip[1]: r5n5{c9 .} ==> r4c9 ≠ 5 biv-chain[4]: r5n5{c9 c7} - r7n5{c7 c6} - r7n8{c6 c8} - b9n6{r7c8 r9c9} ==> r5c9 ≠ 6 hidden-single-in-a-row ==> r5c3 = 6 z-chain[4]: r8n8{c3 c9} - c9n5{r8 r5} - r5n1{c9 c2} - r9n1{c2 .} ==> r9c3 ≠ 8 z-chain[4]: c6n9{r9 r4} - c6n6{r4 r6} - c8n6{r6 r7} - r7n8{c8 .} ==> r9c6 ≠ 8 stte

3) Simplest-first solution, requiring only finned x-wings, after the two pjb's Lite Bug eliminations
Notice that SudoRules doesn't have Lite Bugs, but the two eliminations can be simulated by setting:
(bind ?*simulated-eliminations* (create$ 126 326))

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 1 2 9 ! 4 8 3 ! 6 5 7 ! ! 7 48 48 ! 6 1 5 ! 2 3 9 ! ! 3 6 5 ! 7 9 2 ! 8 1 4 ! +-------------------+-------------------+-------------------+ ! 2 1348 1468 ! 589 56 1689 ! 7 4689 13568 ! ! 689 138 168 ! 589 4 7 ! 39 2 13568 ! ! 4689 5 7 ! 2 3 1689 ! 49 4689 168 ! +-------------------+-------------------+-------------------+ ! 468 9 3 ! 1 7 68 ! 5 468 2 ! ! 68 7 268 ! 3589 256 4 ! 1 689 368 ! ! 5 148 12468 ! 389 26 689 ! 349 7 368 ! +-------------------+-------------------+-------------------+

Code: Select all: finned-x-wing-in-rows: n9{r8 r4}{c8 c4} ==> r5c4 ≠ 9 finned-x-wing-in-rows: n4{r7 r4}{c8 c1} ==> r6c1 ≠ 4 singles ==> r7c1 = 4, r9c7 = 4, r6c7 = 9, r5c7 = 3, r4c2 = 3, r4c3 = 4 naked-single ==> r2c3 = 8, r2c2 = 4, r6c8 = 4, r8c8 = 9, r5c1 = 9,r5c9 ≠ 1 finned-x-wing-in-columns: n6{c8 c5}{r4 r7} ==> r7c6 ≠ 6 stte

3) Two-step solution using Forcing[3]-T&E:
Starting from the resolution state after Singles and whips[1]:

Code: Select all: FORCING[3]-T&E(BRT) applied to trivalue candidates n4r4c2, n4r4c3 and n4r6c1 : ===> 3 values decided in the three cases: n9r6c7 n9r8c8 n9r5c1 ===> 16 candidates eliminated in the three cases: n9r4c8 n1r5c1 n3r5c1 n6r5c1 n8r5c1 n9r5c4 n9r5c7 n9r6c1 n9r6c6 n4r6c7 n9r6c8 n4r7c8 n9r8c4 n6r8c8 n8r8c8 n9r9c7 CURRENT RESOLUTION STATE: 13 2 9 4 8 13 6 5 7 7 1348 1348 6 15 135 2 13 9 13 6 5 7 9 2 8 13 4 2 1348 13468 589 156 15689 7 468 13568 9 138 1368 58 4 7 35 2 13568 1468 5 7 2 3 168 9 468 168 3468 9 3468 1 7 568 345 68 2 368 7 2368 358 256 4 1 9 3568 5 1348 123468 389 26 689 34 7 368 FORCING[3]-T&E(BRT) applied to trivalue candidates n5r7c6, n5r8c4 and n5r8c5 : ===> 9 values decided in the three cases: n8r5c4 n2r9c5 n2r8c3 n6r5c3 n1r3c8 n3r2c8 n3r1c6 n1r9c3 n8r2c3 ===> 59 candidates eliminated in the three cases: n3r1c1 n1r1c6 n1r2c2 n3r2c2 n8r2c2 n1r2c3 n3r2c3 n4r2c3 n3r2c6 n1r2c8 n1r3c1 n3r3c8 n1r4c2 n4r4c2 n1r4c3 n3r4c3 n6r4c3 n8r4c3 n8r4c4 n5r4c5 n5r4c6 n6r4c6 n8r4c6 n6r4c9 n8r4c9 n8r5c2 n1r5c3 n3r5c3 n8r5c3 n5r5c4 n3r5c9 n6r5c9 n8r5c9 n6r6c1 n8r6c6 n6r6c8 n3r7c1 n8r7c1 n6r7c3 n8r7c3 n6r7c6 n3r7c7 n3r8c3 n6r8c3 n8r8c3 n8r8c4 n2r8c5 n3r8c9 n6r8c9 n1r9c2 n3r9c2 n2r9c3 n3r9c3 n4r9c3 n6r9c3 n8r9c3 n8r9c4 n6r9c5 n8r9c9 CURRENT RESOLUTION STATE: 1 2 9 4 8 3 6 5 7 7 4 8 6 15 15 2 3 9 3 6 5 7 9 2 8 1 4 2 38 4 59 16 19 7 468 135 9 13 6 8 4 7 35 2 15 148 5 7 2 3 16 9 48 168 46 9 34 1 7 58 45 68 2 368 7 2 35 56 4 1 9 58 5 48 1 39 2 689 34 7 36 stte

FORCING[3]-T&E(BRT) can be re-formulated in terms of conjugated tracks or of kites.

by **DEFISE** » Thu Aug 05, 2021 5:30 pm

Hi Denis,
I don't like to use uniqueness but I like trying to reduce the number of steps:

Hidden Text: Show

Website · by **denis_berthier** » Fri Aug 06, 2021 6:23 am

Hi François

DEFISE wrote:I don't like to use uniqueness but I like trying to reduce the number of steps

So do I, but not at the cost of having much longer chains than in the simplest-first solution.
My Forcing[3]-T&E solution was more of a joke than a serious solution.

DEFISE wrote:whip[2]: c8n4{r4 r7}- c1n4{r7 .} => -4r6c7
Singles: 9r6c7, 9r5c1, 9r8c8
Bloc/line: 4c7b9 => -4r7c8
whip[12]: b9n5{r7c7 r8c9}- b6n5{r4c9 r5c7}- r5c4{n5 n8}- c6n8{r4 r9}- b9n8{r9c9 r7c8}- b9n6{r7c8 r9c9}- r5n6{c9 c3}- r7n6{c3 c1}- c1n4{r7 r6}- r6c8{n4 n6}- c6n6{r6 r4}- c6n9{r4 .}
=> -5r7c6
Singles: 5r7c7, 3r5c7, 4r9c7
Bloc/line: 3r7b7 => -3r8c1 -3r8c3 -3r9c2 -3r9c3
whip[5]: r5c4{n5 n8}- r5c2{n8 n1}- r9c2{n1 n8}- r8n8{c1 c9}- r8n3{c9 .} => -5r8c4

As you know, I count this as 3 steps, because there's no serious reason for not counting some Subsets (indeed, the only reason ever advocated for this is the existence of an antiquated software, "simple sudoku").
In the present case, there's no real 2-step solution with whips[≤15] (a totally absurd length for such an easy puzzle).
I haven't tried my fewer steps implementation on this puzzle. I wonder if I can get 3 or 4 steps with whips[≤5]. But my Mac is running other things; I'll see later.

by **DEFISE** » Fri Aug 06, 2021 8:48 am

denis_berthier wrote:My Forcing[3]-T&E solution was more of a joke than a serious solution.

I understood that well but I wonder why you consider a Forcing [3] as a single step, knowing that it requires 3 T&E.
Indeed, my solution has 3 steps, it was found by my "Few Steps" program with 10 tries.
There is no 2 steps solution with whips or braids if we consider whip [1] as non-step and subsets as steps.

Website · by **denis_berthier** » Fri Aug 06, 2021 12:10 pm

DEFISE wrote:
denis_berthier wrote:My Forcing[3]-T&E solution was more of a joke than a serious solution.

I understood that well but I wonder why you consider a Forcing [3] as a single step, knowing that it requires 3 T&E.

It's just one more example that the notion of a step has no real meaning. Some people consider a kite as 1 step; but a kite does exactly the same thing as FTE. Similarly, conjugated tracks do the same as FTE; why would they be counted as one step?

by **Chrono** » Fri Aug 06, 2021 2:02 pm

BUG{13}: R13C1, R12C6, R23C8 => R2C6=5

Code: Select all: .--------------------.------------------.------------------. | 13 2 9 | 4 8 13 | 6 5 7 | | 7 48 48 | 6 15 135 | 2 13 9 | | 13 6 5 | 7 9 2 | 8 13 4 | :--------------------+------------------+------------------: | 2 1348 13468 | 589 156 15689 | 7 4689 13568 | | 689 138 1368 | 589 4 7 | 359 2 13568 | | 4689 5 7 | 2 3 1689 | 49 4689 168 | :--------------------+------------------+------------------: | 468 9 3468 | 1 7 568 | 345 468 2 | | 68 7 2368 | 3589 256 4 | 1 689 3568 | | 5 1348 123468 | 389 26 689 | 349 7 368 | '--------------------'------------------'------------------'

Finned X-Wing{4}: R67C18 with fin on R4C8 => R6C7<>4

Code: Select all: .-------------------.-----------------.------------------. | 1 2 9 | 4 8 3 | 6 5 7 | | 7 48 48 | 6 1 5 | 2 3 9 | | 3 6 5 | 7 9 2 | 8 1 4 | :-------------------+-----------------+------------------: | 2 1348 1468 | 589 56 1689 | 7 4689 13568 | | 689 138 168 | 589 4 7 | 39 2 13568 | | 4689 5 7 | 2 3 1689 | 49 4689 168 | :-------------------+-----------------+------------------: | 468 9 3 | 1 7 68 | 5 468 2 | | 68 7 268 | 3589 256 4 | 1 689 368 | | 5 148 12468 | 389 26 689 | 349 7 368 | '-------------------'-----------------'------------------'

Empty Rectangle: R7C8(6)-R4C8(6)=R4C56(6)-R6C6(6) => R7C6<>6

Code: Select all: .-------------.----------------.-------------. | 1 2 9 | 4 8 3 | 6 5 7 | | 7 4 8 | 6 1 5 | 2 3 9 | | 3 6 5 | 7 9 2 | 8 1 4 | :-------------+----------------+-------------: | 2 3 4 | 589 56 1689 | 7 68 1568 | | 9 18 16 | 58 4 7 | 3 2 568 | | 68 5 7 | 2 3 168 | 9 4 168 | :-------------+----------------+-------------: | 4 9 3 | 1 7 68 | 5 68 2 | | 68 7 26 | 358 256 4 | 1 9 368 | | 5 18 126 | 389 26 689 | 4 7 368 | '-------------'----------------'-------------'

Website · by **denis_berthier** » Sat Aug 07, 2021 11:56 am

.
I tried the fewest steps algorithm with all-chains-max-length = 6. Considering there's a solution in Z4, this may already be allowing too large chains. But this was more to test my algorithm than anything else. (This new version, not yet published, allows Subsets to be present in the rules without generating unwanted steps.)

The fewest steps I find is 7 (but I did only 3 tries):

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 13 2 9 ! 4 8 13 ! 6 5 7 ! ! 7 1348 1348 ! 6 15 135 ! 2 13 9 ! ! 13 6 5 ! 7 9 2 ! 8 13 4 ! +----------------------+----------------------+----------------------+ ! 2 1348 13468 ! 589 156 15689 ! 7 4689 13568 ! ! 13689 138 1368 ! 589 4 7 ! 359 2 13568 ! ! 14689 5 7 ! 2 3 1689 ! 49 4689 168 ! +----------------------+----------------------+----------------------+ ! 3468 9 3468 ! 1 7 568 ! 345 468 2 ! ! 368 7 2368 ! 3589 256 4 ! 1 689 3568 ! ! 5 1348 123468 ! 389 26 689 ! 349 7 368 ! +----------------------+----------------------+----------------------+

===> STEP #1
finned-x-wing-in-columns: n4{c1 c7}{r6 r7} ==> r7c8 ≠ 4
whip[1]: b9n4{r9c7 .} ==> r6c7 ≠ 4
naked-single ==> r6c7 = 9
hidden-single-in-a-column ==> r8c8 = 9
hidden-single-in-a-block ==> r5c1 = 9

===> STEP #2
naked-pairs-in-a-block: b1{r1c1 r3c1}{n1 n3} ==> r2c3 ≠ 3, r2c3 ≠ 1, r2c2 ≠ 3, r2c2 ≠ 1
whip[1]: b1n1{r3c1 .} ==> r6c1 ≠ 1
whip[1]: b1n3{r3c1 .} ==> r7c1 ≠ 3, r8c1 ≠ 3

===> STEP #3
z-chain[5]: r7c8{n6 n8} - r7c1{n8 n4} - r6n4{c1 c8} - c8n6{r6 r4} - c5n6{r4 .} ==> r7c6 ≠ 6

===> STEP #4
biv-chain[3]: r5c4{n8 n5} - c7n5{r5 r7} - r7c6{n5 n8} ==> r8c4 ≠ 8, r4c6 ≠ 8, r6c6 ≠ 8, r9c4 ≠ 8

===> STEP #5
whip[4]: r6n4{c1 c8} - r6n8{c8 c9} - r4c8{n8 n6} - b5n6{r4c5 .} ==> r6c1 ≠ 6
whip[1]: c1n6{r8 .} ==> r7c3 ≠ 6, r8c3 ≠ 6, r9c3 ≠ 6

===> STEP #6
whip[6]: r7c8{n6 n8} - c6n8{r7 r9} - c6n9{r9 r4} - c6n6{r4 r6} - r6c8{n6 n4} - c1n4{r6 .} ==> r7c1 ≠ 6
hidden-single-in-a-block ==> r8c1 = 6
hidden-single-in-a-row ==> r7c8 = 6
whip[1]: b9n8{r9c9 .} ==> r4c9 ≠ 8, r5c9 ≠ 8, r6c9 ≠ 8

===> STEP #7
biv-chain[4]: r5c7{n3 n5} - r7n5{c7 c6} - b8n8{r7c6 r9c6} - r9c9{n8 n3} ==> r4c9 ≠ 3, r5c9 ≠ 3, r7c7 ≠ 3, r9c7 ≠ 3
stte

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