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by **Yogi** » Fri Dec 17, 2021 9:04 am

....1..6..3....7....2.........2.3..44......1....7.....654.........8..2..1........

Code: Select all: +---+---+---+ |...|.1.|.6.| |.3.|...|7..| |..2|...|...| +---+---+---+ |...|2.3|..4| |4..|...|.1.| |...|7..|...| +---+---+---+ |654|...|...| |...|8..|2..| |1..|...|...| +---+---+---+

by **Cenoman** » Fri Dec 17, 2021 11:13 am

In three (simple) steps:

Code: Select all: +---------------------+--------------------+----------------------+ | 7 4 59 | 359 1 2 | 3589 6 3589 | | 589 3 1 | 4 58 6 | 7 2 59 | | 589 6 2 | 359 37 578 | 1 4 359 | +---------------------+--------------------+----------------------+ | 59* 1 569* | 2 589 3 | 5689 7 4 | | 4 78-9 37-59 | 6 589 58 | 3589 1 2 | | 2 89* 3569* | 7 4 1 | 569-38 38* 59-38 | +---------------------+--------------------+----------------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 35 37 57 | 4 9 6 | +---------------------+--------------------+----------------------+

1. In r4c13, r6c238: 5 cells, 5 digits (35689), none can be twice; all are there
=> - 38 r6c79, -5 r5c3, -9r5c23; 8 placements

Code: Select all: +--------------------+------------------+-------------------+ | 7 4 59 | 3 1 2 | 59 6 8 | | 589* 3 1 | 4 58 6 | 7 2 59* | | 58 6 2 | 9 7 58 | 1 4 3 | +--------------------+------------------+-------------------+ | 59* 1 569 | 2 589 3 | 5689 7 4 | | 4 78 37 | 6 589 58 | 3589 1 2 | | 2 8-9 356-9 | 7 4 1 | 569 38 59* | +--------------------+------------------+-------------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 5 3 7 | 4 9 6 | +--------------------+------------------+-------------------+

2. Skyscraper (9)r4c1 = r2c1 - r2c9 = r6c9 => -9 r6c23; 8 placements; locked (9)r4c13; 1 placement

Code: Select all: +-------------------+-----------------+------------------+ | 7 4 59 | 3 1 2 | 59 6 8 | | 589* 3 1 | 4 58* 6 | 7 2 59 | | 58* 6 2 | 9 7 58* | 1 4 3 | +-------------------+-----------------+------------------+ | 59# 1 569# | 2 8-5* 3 | 68-5* 7 4 | | 4 7 3 | 6 9 58* | 58* 1 2 | | 2 8 6-5 | 7 4 1 | 569 3 59 | +-------------------+-----------------+------------------+ | 6 5 4 | 1 2 9 | 3 8 7 | | 3 9 7 | 8 6 4 | 2 5 1 | | 1 2 8 | 5 3 7 | 4 9 6 | +-------------------+-----------------+------------------+

3. BUG-lite (58)r2c15, r3c16, r4c57, r5c67 using externals: +5r4c13 => -5 r6c3, r4c57; ste

@Yogi: thanks for the puzzle !

by **yzfwsf** » Fri Dec 17, 2021 11:21 am

After Singles and Locked Candidates, One senior Exocet bring to STTE.

Website · by **denis_berthier** » Fri Dec 17, 2021 3:34 pm

.

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 7 4 59 ! 359 1 2 ! 3589 6 3589 ! ! 589 3 1 ! 4 58 6 ! 7 2 59 ! ! 589 6 2 ! 359 3578 578 ! 1 4 359 ! +-------------------+-------------------+-------------------+ ! 59 1 569 ! 2 589 3 ! 5689 7 4 ! ! 4 789 3579 ! 6 589 58 ! 3589 1 2 ! ! 2 89 3569 ! 7 4 1 ! 35689 38 3589 ! +-------------------+-------------------+-------------------+ ! 6 5 4 ! 1 2 9 ! 38 38 7 ! ! 3 79 79 ! 8 6 4 ! 2 5 1 ! ! 1 2 8 ! 35 357 57 ! 4 9 6 ! +-------------------+-------------------+-------------------+

2 steps in W5:

Code: Select all: whip[5]: r1c3{n9 n5} - r4c3{n5 n6} - r6n6{c3 c7} - r6n5{c7 c9} - b3n5{r1c9 .} ==> r8c3≠9 singles ==> r8c3=7, r8c2=9, r6c2=8, r5c2=7, r6c8=3, r7c8=8, r7c7=3, r5c3=3, r1c9=8, r3c9=3, r1c4=3, r9c4=5, r3c4=9, r9c6=7, r9c5=3, r3c5=7 z-chain[5]: r2n8{c1 c5} - r4n8{c5 c7} - r4n6{c7 c3} - c3n9{r4 r6} - c9n9{r6 .} ==> r2c1≠9 with z-candidates = n9r1c3 n9r2c9 stte

or:

Code: Select all: whip[4]: r4c1{n5 n9} - r2n9{c1 c9} - r6n9{c9 c7} - r6n6{c7 .} ==> r6c3≠5 whip[1]: r6n5{c9 .} ==> r4c7≠5, r5c7≠5 whip[5]: c7n5{r6 r1} - r1c3{n5 n9} - r8n9{c3 c2} - r6n9{c2 c9} - r6n5{c9 .} ==> r6c7≠6 stte

or in Z6, using only reversible chains:

Code: Select all: z-chain[6]: r2n9{c9 c1} - r4c1{n9 n5} - r6n5{c3 c7} - c7n6{r6 r4} - r4n8{c7 c5} - r2c5{n8 .} ==> r2c9≠5 with z-candidates = n5r6c9 n5r2c5 naked-single ==> r2c9=9 z-chain[6]: r6c8{n3 n8} - r6c2{n8 n9} - r8n9{c2 c3} - r1c3{n9 n5} - r1c7{n5 n8} - r7c7{n8 .} ==> r5c7≠3, r6c7≠3 with z-candidates = n3r1c7 n3r7c7 stte

by **P.O.** » Fri Dec 17, 2021 5:32 pm

Code: Select all: after singles and intersections: 7 4 a±5+9 359 1 2 3589 6 3×589 b58-9 3 1 4 58 6 7 2 b5+9 b58-9 6 2 359 3578 578 1 4 359 b5+9 1 569 2 589 3 5689 7 4 4 789 3579 6 589 58 3589 1 2 2 c+89 3×569 7 4 1 35689 d+38 e3+589 6 5 4 1 2 9 38 38 7 3 79 79 8 6 4 2 5 1 1 2 8 35 357 57 4 9 6 /- r2n9{c1 c9} r1c3{n5 n9} 》r6c9{n3n8n9 n5} => r1c9 r6c3 <> 5 \- c1n9{r2r3 r4} - r6c2{n9 n8} - r6c8{n8 n3} intersection: r6n5{c7 c9} => r4c7 r5c7 <> 5 7 4 b5+9 359 1 2 a3+589 6 389 c58-9 3 1 4 58 6 7 2 59 c58-9 6 2 359 3578 578 1 4 359 c5+9 1 569 2 589 3 689 7 4 4 789 3579 6 589 58 389 1 2 2 d8-9 d36-9 7 4 1 da±5×(368)+9 38 a3+589 6 5 4 1 2 9 38 38 7 3 79 79 8 6 4 2 5 1 1 2 8 35 357 57 4 9 6 r6n5{c7 c9} - 》r1c3{n5 n9} - c1n9{r2r3 r4} - r6n9{c2c3 c7} => r6c7 <> 3,6,8 c7n5{r6 r1} - ste.

by **marek stefanik** » Fri Dec 17, 2021 7:52 pm

One cell version of yzfwsf's senior exocet:

Code: Select all: .----------------.---------------.-----------------. | 7 4 a59 | 359 1 2 | 3589 6 3589 | | 589 3 1 | 4 58 6 | 7 2 a59 | | 589 6 2 | 359 37 578 | 1 4 a359 | :----------------+---------------+-----------------: |a59 1 569 | 2 589 3 | 5689 7 4 | | 4 789 3579 | 6 589 58 | 3589 1 2 | | 2 89 3569 | 7 4 1 |a59–368 38 3589 | :----------------+---------------+-----------------: | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 35 37 57 | 4 9 6 | '----------------'---------------'-----------------'

Whichever digit a is true in r4c1 is forced into r1 in b1, c9 in b3 and c7 in r6. –368r6c7, stte

Marek

by **Cenoman** » Fri Dec 17, 2021 9:47 pm

FWIW, playing with writing chains.

Code: Select all: +---------------------+--------------------+----------------------+ | 7 4 59 | 359 1 2 | 3589 6 3589 | | 589 3 1 | 4 58 6 | 7 2 59 | | 589 6 2 | 359 37 578 | 1 4 359 | +---------------------+--------------------+----------------------+ | 59 1 569 | 2 589 3 | 5689 7 4 | | 4 789 3579 | 6 589 58 | 3589 1 2 | | 2 89 3569 | 7 4 1 | 368+59 38 3589 | +---------------------+--------------------+----------------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 35 37 57 | 4 9 6 | +---------------------+--------------------+----------------------+

Searching a solution in one step, I had found this:

Hidden Text: Show

Reading Marek's solution, I tried to write it as an AIC of the same type. The similarity of the embedded chains results from Marek's rationale:
(5)r6c6 = [r23c1 = r4c1 - r6c23 = r6c9 - r23c9 = r1c79] - (5=9)r1c3 - [r23c1 = r4c1 - r6c23 = r6c9 - r23c9 = r1c79] = (9)r6c6 => +59 r6c6; ste
It can be drawn as the following net:

Code: Select all: r6c9 - r23c9 = r1c79 r1c79 = r23c9 - r6c9 || \ / || (5)r6c6 (5=9)r1c3 (9)r6c6 || / \ || r6c23 - r4c1 = r23c1 r23c1 = r4c1 - r6c23 ----------------- => + 59 r6c6; ste

... and written as this other AIC
(5)r6c6 = (r6c9 | r6c23) - (r23c9 & r4c1) = (r1c79 | r23c1) - (5=9)r1c3 - (r1c79 | r23c1) = (r23c9 & r4c1) - (r6c9 | r6c23) = (9)r6c6 => + 59 r6c6; ste

by **eleven** » Sat Dec 18, 2021 12:17 am

You can also see it as an oddagon for both 5 and 9, when starting in r4c1 => only guardians are 59r6c7.

Code: Select all: *-----------------------------------------------------------------* | 7 4 c59 | 359 1 2 | d3589 6 de3589 | | b589 3 1 | 4 58 6 | 7 2 e59 | | b589 6 2 | 359 37 578 | 1 4 e359 | |---------------------+--------------------+----------------------| | a59 1 569 | 2 589 3 | 5689 7 4 | | 4 789 3579 | 6 589 58 | 3589 1 2 | | 2 g89 g3569 | 7 4 1 | *368+59 38 f3589 | |---------------------+--------------------+----------------------| | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 35 37 57 | 4 9 6 | *-----------------------------------------------------------------*

by **rjamil** » Sat Dec 18, 2021 12:35 pm

After looking Cenoman's three (simple) steps solution, trying to share my three simple steps solution path as follows:

Code: Select all: +----------------+---------------+-----------------+ | 7 4 59 | 359 1 2 | 3589 6 3589 | | 589 3 1 | 4 58 6 | 7 2 59 | | 589 6 2 | 359 37 578 | 1 4 359 | +----------------+---------------+-----------------+ | *59 1 *569 | 2 589 3 | 5689 7 4 | | 4 78-9 37-59| 6 589 58 | 3589 1 2 | | 2 8*9 3*569| 7 4 1 |*569-38 38 *59-38| +----------------+---------------+-----------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 35 37 57 | 4 9 6 | +----------------+---------------+-----------------+

1) ALT: 569 @ r6c23 r6c79 r4c13 => -9 @ r5c2 -59 @ r5c3 -38 @ r6c79; eight singles;

Code: Select all: +---------------+------------+--------------+ | 7 4 9*5 | 3 1 2 | 9*5 6 8 | | 589 3 1 | 4 58 6 | 7 2 59 | | 58 6 2 | 9 7 58 | 1 4 3 | +---------------+------------+--------------+ | 59 1 569 | 2 589 3 | 689-5 7 4 | | 4 78 37 | 6 589 58 | 389-5 1 2 | | 2 89 369*5| 7 4 1 | 69*5 38 9*5| +---------------+------------+--------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 5 3 7 | 4 9 6 | +---------------+------------+--------------+

2) Grouped SS: Base 5 @ r16c3 Cover 5 @ r1c7 r6c79 => -5 @ r45c7; two LC Type 2; and

Code: Select all: +--------------+------------+-------------+ | 7 4 59 | 3 1 2 | 59 6 8 | | 58*9 3 1 | 4 58 6 | 7 2 5*9| | 58 6 2 | 9 7 58 | 1 4 3 | +--------------+------------+-------------+ | 5*9 1 569 | 2 89 3 | 68-9 7 4 | | 4 78 37 | 6 589 58 | 389 1 2 | | 2 8-9 36-9| 7 4 1 | 569 38 5*9| +--------------+------------+-------------+ | 6 5 4 | 1 2 9 | 38 38 7 | | 3 79 79 | 8 6 4 | 2 5 1 | | 1 2 8 | 5 3 7 | 4 9 6 | +--------------+------------+-------------+

3) SS: Base 9 @ r2c19 Cover 9 @ r4c1 r6c9 => -9 @ r4c78 r6c23; stte

R. Jamil

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