The New Sudoku Players' Forum

by **P.O.** » Wed Mar 16, 2022 6:52 pm

Code: Select all: . . . . 4 . . 3 . . . . 3 . . 5 . . . . 6 . . 2 . . 7 . 8 2 . . 7 . . . 6 5 . . . . . . 9 1 . 4 . . . . . . . . . . 3 . . 1 . 2 . . . . 9 . . 6 . . . 5 . . 3 . . ....4..3....3..5....6..2..7.82..7...65......91.4..........3..1.2....9..6...5..3..

by **jco** » Wed Mar 16, 2022 8:30 pm

Code: Select all: .--------------------------------------------------------------------. | 5789 1279 15789 | 16789 4 d1568 | 12689 3 128 | | 4789 12479 1789 | 3 16789 168 | 5 24689 1248 | |b34589 1349 6 | 189 d1589 2 | 1489 489 7 | |----------------------+----------------------+----------------------| |a39 8 2 | 1469 1569 7 | 146 456 1345 | | 6 5 7-3 | 1248 128 f1348 | 12478 2478 9 | | 1 379 4 | 2689 25689 e3568 | 2678 25678 2358 | |----------------------+----------------------+----------------------| | 45789 4679 5789 | 24678 3 468 | 24789 1 2458 | | 2 1347 13578 | 1478 178 9 | 478 4578 6 | | 4789 14679 1789 | 5 12678 1468 | 3 24789 248 | '--------------------------------------------------------------------'

1. (3)r4c1 = (3-5)r3c1 = (5)r3c5 - (5)r1c6 = (5-3)r6c6 = (3)r5c6 => -3 r5c3 [4 placements and basics]
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Code: Select all: .--------------------------------------------------------------------. | 5789 1279 1589 | 16789 4 1568 | 2689 3 128 | | 4789 12479 189 | 3 16789 168 | 5 24689 1248 | |c34589 1349 6 | 189 d1589 2 | 489 489 7 | |----------------------+----------------------+----------------------| |b39 8 2 | 1469 169-5 7 | 146 46 a35 | | 6 5 7 | 1248 128 3 | 1248 248 9 | | 1 39 4 | 2689 25689 568 | 2678 2678 35 | |----------------------+----------------------+----------------------| | 45789 4679 589 | 2678 3 468 | 24789 1 248 | | 2 147 3 | 178 178 9 | 478 5 6 | | 4789 14679 189 | 5 12678 1468 | 3 24789 248 | '--------------------------------------------------------------------'

2. (5=3)r4c9 - (3)r4c1 = (3-5)r3c1 = (5)r3c5 => -5 r4c5 [22 placements and basics]
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Code: Select all: .-----------------------------------------------------------. | 589 c27 589 |d79 4 68 |b26 3 1 | | 89 27 1 | 3 e79 68 | 5 26 4 | | 4 3 6 | 1 5 2 | 89 89 7 | |-------------------+-------------------+-------------------| | 3 8 2 | 469 f9-1 7 |a16 46 5 | | 6 5 7 | 48 128 3 | 128 248 9 | | 1 9 4 | 68 28 5 | 2678 2678 3 | |-------------------+-------------------+-------------------| | 579 6 59 | 2 3 4 | 79 1 8 | | 2 1 3 | 78 78 9 | 4 5 6 | | 789 4 89 | 5 6 1 | 3 79 2 | '-----------------------------------------------------------'

3. (1=6)r4c7 - (6=2)r1c7 - (2=7)r1c2 - (7=9)r1c4 - (9)r2c5 = (9)r4c5 => -1 r4c5; ste

Thanks for the puzzle!

by **pjb** » Wed Mar 16, 2022 11:45 pm

I found exactly same as JCO, so to offer something different but by no means shorter:

Code: Select all: 5789 1279 15789 | 6789-1 4 *1568 | 2689-1 3 *128 4789 12479 1789 | 3 6789-1 *168 | 5 2689-4 *1248 345-89 134-9 6 |*189 *1589 2 |*1489 *489 7 ------------------------+-----------------------+--------------------- 39 8 2 | 1469 1569 7 | 146 456 1345 6 5 37 | 1248 128 134-8 | 12478 2478 9 1 379 4 | 2689 25689 35-68 | 2678 25678 35-28 ------------------------+-----------------------+--------------------- 45789 4679 5789 | 2678-4 3 *468 | 2789-4 1 *2458 2 134-7 135-78 |*1478 *178 9 |*478 *4578 6 4789 14679 1789 | 5 2678-1 *1468 | 3 2789-4 *248

SK loop : (89=15)r3c45 - (15=68)r12c6 - (68=14)r79c6 - (14=78)r8c45 - (78=45)r8c78 - (45=28)r79c9 - (28=14)r12c9 - (14=89)r3c78 - loop => 19 eliminations + basics ->

Code: Select all: 5789 1279 15789 | 6789 4 d1568 | 2689 3 128 4789 12479 1789 | 3 6789 d168 | 5 2689 1248 b345 134 6 | 189 c1589 2 | 1489 489 7 ------------------------+----------------------+--------------------- a39 8 2 | 1469 1569 7 | 146 456 1345 6 5 7-3 | 1248 128 d134 | 12478 2478 9 1 79 4 | 2689 2689 35 | 2678 2678 35 ------------------------+----------------------+--------------------- 45789 4679 5789 | 2678 3 d468 | 2789 1 2458 2 134 135 | 1478 178 9 | 478 4578 6 4789 14679 1789 | 5 2678 d1468 | 3 2789 248

(3)r4c1 = (3-5)r3c1 = r3c5 - (5=16834)r12579c6 => -3 r5c3 + basics ->

Code: Select all: 589 7-2 589 | 79 4 68 |a26 3 1 89 e27 1 | 3 d79 68 | 5 6-2 4 4 3 6 | 1 5 2 | 89 89 7 ------------------------+----------------------+--------------------- 3 8 2 | 469 c19 7 |b16 46 5 6 5 7 | 48 128 3 | 128 248 9 1 9 4 | 68 28 5 | 2678 2678 3 ------------------------+----------------------+--------------------- 579 6 59 | 2 3 4 | 79 1 8 2 1 3 | 78 78 9 | 4 5 6 789 4 89 | 5 6 1 | 3 79 2

(2=6)r1c7 - (6=1)r4c7 - (1=9)r4c5 - (9=7)r2c5 - (7=2)r2c2 => -2 r1c2, r2c8; stte

Phil

Website · by **denis_berthier** » Thu Mar 17, 2022 6:29 am

.
SER = 7.3

Code: Select all: Resolution state after Singles (and whips[1]): +-------------------+-------------------+-------------------+ ! 5789 1279 15789 ! 16789 4 1568 ! 12689 3 128 ! ! 4789 12479 1789 ! 3 16789 168 ! 5 24689 1248 ! ! 34589 1349 6 ! 189 1589 2 ! 1489 489 7 ! +-------------------+-------------------+-------------------+ ! 39 8 2 ! 1469 1569 7 ! 146 456 1345 ! ! 6 5 37 ! 1248 128 1348 ! 12478 2478 9 ! ! 1 379 4 ! 2689 25689 3568 ! 2678 25678 2358 ! +-------------------+-------------------+-------------------+ ! 45789 4679 5789 ! 24678 3 468 ! 24789 1 2458 ! ! 2 1347 13578 ! 1478 178 9 ! 478 4578 6 ! ! 4789 14679 1789 ! 5 12678 1468 ! 3 24789 248 ! +-------------------+-------------------+-------------------+ 237 candidates

The puzzle is not only in W5 but also in the much simpler BC5. Having an sk-loop in a puzzle with so low SER, as in pjb's solution is fun, but as also noticed by pjb, it doesn't simplify the solution.

There is indeed at least one 2-step solution in BC5. This is one case where there is no need to increase the length or complexity of individual chains in order to get a shorter path than provided by the simplest-first strategy.

biv-chain[4]: c6n5{r6 r1} - r3n5{c5 c1} - c1n3{r3 r4} - b6n3{r4c9 r6c9} ==> r6c9≠5, r6c6≠3
singles ==> r5c6=3, r5c3=7, r8c3=3, r8c8=5, r4c9=5, r6c9=3, r6c2=9, r4c1=3, r3c2=3
whip[1]: b6n1{r5c7 .} ==> r1c7≠1, r3c7≠1
whip[1]: r3n1{c5 .} ==> r1c4≠1, r1c6≠1, r2c5≠1, r2c6≠1
singles ==> r9c6=1, r8c2=1, r7c6=4, r8c7=4, r2c9=4, r3c1=4, r3c5=5, r6c6=5, r3c4=1, r9c2=4, r7c2=6, r9c5=6, r7c4=2, r7c9=8, r9c9=2, r1c9=1, r2c3=1
whip[1]: b5n6{r6c4 .} ==> r1c4≠6
whip[1]: b7n7{r9c1 .} ==> r1c1≠7, r2c1≠7
whip[1]: r3n8{c8 .} ==> r1c7≠8, r2c8≠8
whip[1]: r3n9{c8 .} ==> r1c7≠9, r2c8≠9
whip[1]: c6n8{r2 .} ==> r1c4≠8, r2c5≠8
biv-chain[5]: r1c2{n7 n2} - r1c7{n2 n6} - r4c7{n6 n1} - r4c5{n1 n9} - b2n9{r2c5 r1c4} ==> r1c4≠7
stte

by **P.O.** » Fri Mar 18, 2022 8:39 am

thank you for your answers, here is my solution :

Code: Select all: 5789 1279 15789 16789 4 c1-568 12689 3 128 4789 12479 1789 3 16789 168 5 24689 1248 a+34589 1349 6 189 b1+589 2 1489 489 7 a±39 8 2 1469 1569 7 146 456 g1×34+5 6 5 e-37 1248 128 d1+348 12478 2478 9 1 379 4 2689 25689 c3+568 2678 25678 2358 45789 4679 5789 24678 3 468 24789 1 g24-58 2 1347 e1+3578 1478 178 9 478 f4+578 6 4789 14679 1789 5 12678 1468 3 24789 248 c1n3{r4 r3} - r3n5{c1 c5} - c6n5{r1 r6} - c6n3{r6 r5} - c3n3{r5 r8} - r8n5{c3 c8} - c9n5{r7 r4} => r4c9 <> 3 singles + intersections 589 27 589 79 4 68 e2+6 3 1 89 c2+7 1 3 b7+9 68 5 d+26 4 4 3 6 1 5 2 89 89 7 3 8 2 469 a+19 7 a±1×6 46 5 6 5 7 48 128 3 128 248 9 1 9 4 68 28 5 2678 2678 3 579 6 59 2 3 4 79 1 8 2 1 3 78 78 9 4 5 6 789 4 89 5 6 1 3 79 2 r4n1{c7 c5} - c5n9{r4 r2} - r2n7{c5 c2} - r2n2{c2 c8} - r1c7{n2 n6} => r4c7 <> 6 ste.

the sk-loop pattern is indeed a surprise.

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