The New Sudoku Players' Forum

by **eleven** » Sun Nov 24, 2024 3:19 pm

Code: Select all: +-------+-------+-------+ | 6 . 2 | . 5 . | . . 3 | | . 1 . | . . . | . 5 . | | 3 . 4 | . . 6 | 7 . . | +-------+-------+-------+ | . 8 . | 1 2 . | . . . | | . . . | . 4 . | . . . | | 2 . . | . . . | . 1 . | +-------+-------+-------+ | . . 3 | . . . | 4 . . | | . 2 . | 8 . . | . 9 . | | 7 . . | . . . | . . 6 | +-------+-------+-------+

ER 9.0

by **jco** » Sun Nov 24, 2024 5:44 pm

Solved the long way, using contradictions in the first 3 steps (SK-loop related).

Code: Select all: ,-----------------------------------------------------------------------------, | 6 7(9) 2 | 479 5 18 | 189 48 3 | | 89 1 789 | 23479 379 23479 | 6 5 <- 24(9) | | 3 5 | 4 | 29 18 6 | 7 *28 1289 | |-----------v-------------+-------------------------+-------------------------| | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 3679 15679 | 35679 4 35789 | 23589 23678 25789 | | 2 34679 5679 | 35679 36789 35789 | 3589 1 ^ 45789 | |-------------------------+-------------------------+-----------|-------------| | 1589 (6)9 3 | 25679 1679 12579 | 4 (28)7 12578 | |(15)4 2 (15)6 -> | 8 1367 13457 |(3)15 9 (7)15 | | 7 (4)9 1589 | 23459 139 123459 | 12358 (28)3 6 | '-----------------------------------------------------------------------------'

1. (9)r2c9 - (9)r2c13 = (9)r1c2 - (9=46)r79c2 - (4|6=15)r8c13 - (1|5=37)r8c79 - (3=28)r79c8
(*) contradiction: cell r3c8 empty => -9 r1c2, -9 r56c2, -9 r2c9, -9 b7p19, -8 r1c7, -8 r3c9, -8r579c8 [3 placements and basics]
---

Code: Select all: ,-----------------------------------------------------------------------------, | 6 7 2 | 49 5 18 | 19 48 3 | | 89 1 89 | 2347 37 2347 | 6 5 24 | | 3 5 4 | 29 18 6 | 7 (2)8 19 | |-------------------------+-------------------------+-------------------------| | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 36 15679 | 3567 4 35789 | 23589 2367 25789 | | 2 346 5679 | 3567 36789 35789 | 3589 1 | 45789 | |-------------------------+-------------------------+-----------v-------------| | 158 *(9)6 3 | 2567 1679 12579 | 4 (7)2 12578 | |1(4)5 2 (6)15 <--| 8 1367 13457 |(15)3 9 (15)7 | | 7 *(9)4 158 | 2345 139 123459 | 12358 (3)2 6 | '-----------------------------------------------------------------------------'

2. (2)r3c8 - (2=37)r79c8 - (3|7=15)r8c79 - (1|5=46)r8c13 - (4|6=9)r79c2
(*) contradiction: two 9s at column 2 => +8 r3c8 [9 placements and basics]
----

Code: Select all: ,--------------------------------------------------------------------, | 6 7 2 | 9 5 8 | 1 4 3 | | 89 1 89 | 347 37 347 | 6 5 2 | | 3 5 4 | 2 1 6 | 7 8 9 | |----------------------+----------------------+----------------------| | 459 8 5679 | 1 2 3579 | 359 367 457 | | 159 36 15679 | 3567 4 3579 | 28 2367 578 | | 2 346 5679 | 3567 8 3579 | 359 1 | 457 | |----------------------+----------------------+----------v-----------| | 158 *(9)6 3 | 57 69 1257 | 4 (7)2 1578 | |(4)15 2 (6)15 <--| 8 367 13457 |(5)3 9 (1)57 | | 7 *(9)4 158 | 345 39 12345 | 28 (3)2 6 | '--------------------------------------------------------------------'

3. (2)r5c8 - (2=73)r79c8 - (3|7=15)r8c79 - (1|5=46)r8c13 - (4|6=9)r79c2
(*)contradiction: two 9s at column 2 => -2 r5c8 [6 placements]
---

Code: Select all: ,--------------------------------------------------------------------, | 6 7 2 | 9 5 8 | 1 4 3 | | 89 1 89 | 347 37 347 | 6 5 2 | | 3 5 4 | 2 1 6 | 7 8 9 | |----------------------+----------------------+----------------------| | 459 8 5679 | 1 2 3579 | 359 367 457 | | 159 36 15679 | 3567 4 3579 | 28 2367 578 | | 2 346 5679 | 3567 8 3579 | 359 1 457 | |----------------------+----------------------+----------------------| | 158 69 3 |(57) 69 1257 | 4 (27) 1578 | | 145 2 156 | 8 367 1347-5 |(35) 9 17-5 | | 7 49 158 | 345 39 12345 | 28 (23) 6 | '--------------------------------------------------------------------'

4. (5=7)r7c4 - (7=235)b9p248 => -5 r7c9, r8c6 [17 eliminations & basics]
---

Code: Select all: ,--------------------------------------------------, | 6 7 2 | 9 5 8 | 1 4 3 | | 9 1 8 | 34 37 47 | 6 5 2 | | 3 5 4 | 2 1 6 | 7 8 9 | |----------------+----------------+----------------| |(4)5 8 (6)9-7| 1 2 359 | 59 36 (47) | | 15 (36) 19 | 7 4 59 | 2 36 8 | | 2 (34) 79 | 6 8 359 | 59 1 47 | |----------------+----------------+----------------| | 8 69 3 | 5 69 2 | 4 7 1 | | 14 2 16 | 8 67 47 | 3 9 5 | | 7 49 5 | 34 39 1 | 8 2 6 | '--------------------------------------------------'

5. (7=4)r4c9 - (4)r4c1 = (4-3)r6c2 = (3-6)r5c2 = (6)r4c3 => -7 r4c3; ste

Thanks for the puzzle!

by **totuan** » Sun Nov 24, 2024 7:53 pm

Code: Select all: *-----------------------------------------------------------------------------* | 6 7-9 2 | 479 5 18 | 189 4-8 3 | | 89 1 789 | 23479 379 23479 | 6 5 249 | | 3 5 4 | 29 18 6 | 7 D(28) 1289 | |-------------------------+-------------------------+-------------------------| | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 367-9 15679 | 35679 4 35789 | 23589 367-28 25789 | | 2 3467-9 5679 | 35679 36789 35789 | 3589 1 45789 | |-------------------------+-------------------------+-------------------------| | 158-9 A6(9) 3 | 25679 1679 12579 | 4 D7(28) 1258-7 | |B4(15) 2 B6(15) | 8 367-1 347-15 |C3(15) 9 C7(15) | | 7 A4(9) 158-9 | 23459 139 123459 | 1258-3 D3(28) 6 | *-----------------------------------------------------------------------------*

Almost like jco’s.
Condition to avoid emty cells:
1- B cannot be 46 (by A emty cell)
2- C cannot be 37 (by D emty cell)
3- B cannot be 15 by C cannot be 37
4- C cannot be 15 by B cannot be 46

(1)&(3) => B must contain digit 4 or 6 => 9r79c2 => r156c2, r7c1, r9c3<>9
(2)&(4) => C must contain digit 3 or 7 => (28)r379c8 => r1c8<>8, r5c8<>28, r7c9<>7, R9c7<>3
(1)&(2)&(3)&(4) => B&C must contain pair(15) => r8c56<>15

ER-7.1 and the rest is not hard – many way to finish

Thanks for nice puzzle!
totuan

by **Cenoman** » Sun Nov 24, 2024 11:21 pm

My first "heavy artillerie" solution:

Hidden Text: Show

Code: Select all: +--------------------------+---------------------------+--------------------------+ | 6 7-9 2 | 479 5 18 | 189 48 3 | | 89 1 789 | 23479 379 23479 | 6 5 249 | | 3 5 4 | 29 18 6 | 7 e28 1289 | +--------------------------+---------------------------+--------------------------+ | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 367-9 15679 | 35679 4 35789 | 23589 23678 25789 | | 2 3467-9 5679 | 35679 36789 35789 | 3589 1 45789 | +--------------------------+---------------------------+--------------------------+ | 158-9 ha69 3 | 25679 1679 12579 | 4 e278 12578 | |gb145 2 gb156 | 8 c1367 c13457 | f135 9 d157 | | 7 ha49 158-9 | 23459 139 123459 | 12358 e238 6 | +--------------------------+---------------------------+--------------------------+

1. (9=46)r79c2 - (4|6)r8c13 = (46-7)r8c56 = r8c9 - (7=283)r379c8 - (3=1|5)r8c7 - (15=4|6)r8c13 - (46=9)r79c2 => -9 r156c2, r7c1, r9c3; lcls, 1 placement

Code: Select all: +----------------------+--------------------------+-------------------------+ | 6 7 2 | 49 5 18 | 19 48 3 | | 89 1 89 | 2347 37 2347 | 6 5 24 | | 3 5 4 | 29 18 6 | 7 28 19 | +----------------------+--------------------------+-------------------------+ | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 36 15679 | 3567 4 35789 | 23589 2367 25789 | | 2 346 5679 | 3567 36789 35789 | 3589 1 45789 | +----------------------+--------------------------+-------------------------+ | 158 c69 3 | 2567 1679 12579 | 4 27 ea158-27 | | c145 2 c156 | 8 367-1 347-15 |db135 9 db157 | | 7 c49 158 | 2345 139 123459 |ea158-23 23 6 | +----------------------+--------------------------+-------------------------+

2. (81)b9p37 = r8c79 - (1=4695)b7p2468 - r8c79 = (58)b9p37 loop => -27 r7c9, -23 r9c7, -1 r8c56, -5 r8c6; lcls, 16 placements

Code: Select all: +-------------------------+---------------------------+--------------------------+ | 6 7-9 2 | 479 5 18 | 189 4-8 3 | | 89 1 789 | 23479 379 23479 | 6 5 249 | | 3 5 4 | 29 18 6 | 7 28# 1289 | +-------------------------+---------------------------+--------------------------+ | 459 8 5679 | 1 2 3579 | 359 3467 4579 | | 159 367-9 15679 | 35679 4 35789 | 23589 367-28 25789 | | 2 3467-9 5679 | 35679 36789 35789 | 3589 1 45789 | +-------------------------+---------------------------+--------------------------+ | 158-9 69^ 3 | 25679 1679 12579 | 4 278* 158-27 | | 145^ 2 156^ | 8 367-1 347-15 | 135* 9 157* | | 7 49^ 158-9 | 23459 139 123459 | 158-23 238* 6 | +-------------------------+---------------------------+--------------------------+

Look at cells r2c8, b79p2468 (tagged '#','^','*'):
1. 9 cells containing 9 digits; none can be there twice => all are there; 15 eliminations, -9 r156c2, b7p19, -27 r7c9, -23 r9c7, -1 r8c56, -5 r8c6, -2 r5c8, -8 r15c8; lcls, 17 placements

Other writings of the same logic:
- Sue de Coq: AALS b9p2468 (*), ALS1 b7p2468(RC 1,5) (^), ALS2 r3c8 (RC 2,8) (#) => same eliminations
- MSLS: 9 cells, r2c8, b79p2468; 9 links, 15r8, 469b7, 37b9, 28c8 => same eliminations

Code: Select all: +---------------------+---------------------+--------------------+ | 6 7 2 | 9 5 8 | 1 4 3 | | 9 1 8 | 347 37 347 | 6 5 2 | | 3 5 4 | 2 1 6 | 7 8 9 | +---------------------+---------------------+--------------------+ | 45 8 5679 | 1 2 3579 | 359 367 457 | | 15 36 159 | 367 4 59 | 2 367 8 | | 2 346 5679 | 367 8 3579 | 359 1 457 | +---------------------+---------------------+--------------------+ | 8 69 3 | a57 69 12 | 4 b27 1-5 | | 145 2 156 | 8 367 347 | b35 9 157 | | 7 49 15 | 345 39 12 | 8 b23 6 | +---------------------+---------------------+--------------------+

3.2. (5=7)r7c4 - (7=235)b9p248 =>-5r7c9; lcls, 11 placements

Code: Select all: +------------------+------------------+-----------------+ | 6 7 2 | 9 5 8 | 1 4 3 | | 9 1 8 | 34 37 47 | 6 5 2 | | 3 5 4 | 2 1 6 | 7 8 9 | +------------------+------------------+-----------------+ | 45 8 67+9 | 1 2 39+5 | 59 36 47 | | 15 36 19 | 7 4 59 | 2 36 8 | | 2 34 79 | 6 8 35+9 | 59 1 47 | +------------------+------------------+-----------------+ | 8 69 3 | 5 69 2 | 4 7 1 | | 14 2 16 | 8 67 47 | 3 9 5 | | 7 49 5 | 34 39 1 | 8 2 6 | +------------------+------------------+-----------------+

4.3. BUG+3:
(9)r4c3|r6c6 == (5)r4c6 - (5=47)r4c19 - r4c3 = (7)r6c3 => -9 r6c3; ste

by **yzfwsf** » Mon Nov 25, 2024 1:33 am

Multi-Fish: 11 Truths:18r1,1258r7,1258r9+r3c8,11 Links:28c8,125b8+r1c67,r7c19,r9c37 => 10 eliminations
r1c7<>9, r7c1<>9, r7c9<>7, r9c3<>9, r9c7<>3, r5c8<>28, r8c5<>1, r8c6<>15
ER:7.1/2.0/2.0

by **eleven** » Mon Nov 25, 2024 11:39 am

No heavy artillerie needed. Some years ago i have called the pattern "blocked SK-links" (recycled here). These links are not hard to spot. At the ends you either have an appropriate 2-digit cell, which can be removed from the rest of the line, or a single digit blocked in 2 cells. Like in SK-loops you can remove the 2 common digits in the rest of the boxes, and in the lines outside the boxes, as totuan showed above.
Here is another ER 9.0 example, which can be solved by kite and skyscraper:

Code: Select all: +-------+-------+-------+ | 4 . . | . 2 . | . . . | | . . 8 | 9 . . | . 1 . | | . 7 . | . . 6 | . . . | +-------+-------+-------+ | . 2 . | . 6 7 | . . . | | . . 5 | 1 . . | . . 3 | | 6 . . | . 4 . | . . . | +-------+-------+-------+ | . . 3 | 4 . . | 8 7 . | | . . . | . . . | . . 4 | | . . . | . 7 1 | . . 5 | +-------+-------+-------+

by **Cenoman** » Mon Nov 25, 2024 9:43 pm

I have edited my post above, using a lighter artillerie

An attempt for the second puzzle:

Code: Select all: +---------------------------+-------------------------+---------------------------+ | 4 13569 169 | 7 2 358 | 3569 35689 89-6 | | 235* 356*^ 8 | 9 35* 4 | 23567^ 1 267^ | | 2359 7 29# | 358 1 6 | 23459 234589 89-2 | +---------------------------+-------------------------+---------------------------+ | 1389 2 b149 | 358 6 7 | 1459 4589 189 | | d789 a489 5 | 1 da89 2-89 | 2467-9 246-89 3 | | 6 1389 c179 | 2358 4 23589 | 12579 2589 12789 | +---------------------------+-------------------------+---------------------------+ | 1259# 1569^ 3 | 4 59 59(-2) | 8 7 1269^# | | 125789 15689 12679# | 23568 3589 23589 | 12369 2369 4 | | 289 4689 2469# | 2368 7 1 | 2369 2369 5 | +---------------------------+-------------------------+---------------------------+

1. Look at impossible pattern (35)r2c125 => 2r2c1|6r2c2 => r13c3 <> 26
r46c3 cannot be 19 : (19)r46c3 - (1|9=26)r13c3; contradiction with the above => 4r4c3 = 7r6c3
Hence (89=4)r5c25 - (4)r4c3 == (7)r6c3 - (7=89)r5c15 => -89 r5c68, -9r5c78 (+2 r5c6, -2 r7c6)

2. Finned XW(6)r7c9 = r7c2 - r2c2 = r2c79 => -6 r1c9
3. Kite (2)r7c9 = r7c1 - r89c3 = r3c3 => -2 r3c9; lclste

Edit - Alternative step #1:

Code: Select all: +---------------------------+-------------------------+---------------------------+ | 4 1359-6 <169 | 7 2 358 | 3569 35689 689 | | <235 <356 8 | 9 <35 4 | 267-35 1 267 | | 359-2 7 <29 | 358 1 6 | 23459 234589 289 | +---------------------------+-------------------------+---------------------------+ | 1389 2 <149 | 358 6 7 | 1459 4589 189 | | <789 <489 5 | 1 <89 2-89 | 2467-9 246-89 3 | | 6 1389 <179 | 2358 4 23589 | 12579 2589 12789 | +---------------------------+-------------------------+---------------------------+ | 1259 1569 3 | 4 59 259 | 8 7 1269 | | 125789 15689 267-19 | 23568 3589 23589 | 12369 2369 4 | | 289 4689 246-9 | 2368 7 1 | 2369 2369 5 | +---------------------------+-------------------------+---------------------------+

1. MSLS: 10 cells r25c125, r1346c3 ('<')
10 links: 35r2, 89r5, 19c3, 26b1, 47b4 => -35 r2c7, -89 r5c68, -9r5c7, -19 r8c3, -9 r9c3, -6 r1c2, -2r3c1

by **eleven** » Mon Nov 25, 2024 11:51 pm

I did not give a proof or detailed explanation for what i said above, it could be made e.g. this way:

Hidden Text: Show

In general, you can have all 4 SK-link candidates in the cells:

The SK links here are [35r2c5] - 35/26r2c12 - 26/19r13c3 - 19/47r46c3 - 47/89r5c12 - [89]r5c5

Code: Select all: +-------------------------+ | a a 1269 | | 2356 2356 a | 35 . . | . . . | a a 1269 | +-------------------------+ | b b 1479 | | 4789 4789 b | 89 . . | . . . | b b 1479 | +-------------------------+ c

There cannot be another 3 or 5 in r2c79, because the links (starting with 26r2c12) would lead to 3 89's in r5
There cannot be another 8 or 9 in r5c678, because the links (starting with 47r5c12) would lead to 3 35's in r2

If c (in r789c3) is 1 (or 9), r46c3 must be 9 (or 1), because 47 leads to 3 89's in r5. But then 19 is missing in r13c3, and we have 3 35's in r2.

If 2 or 6 are in a 'a'-cell in box1: r13c3 must not be the other digit (6 or 2), because it leaves 35 3 times in r2, but then its 19, (and following the loop) leading to 3 89's in r5.
Same for 4 or 7 in the b cells.

(btw the SK loop eliminations could be proved the same way)

So, as soon you have spotted this blocked SK-loop, you can:

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 4 13569 *169 | 7 2 358 | 3569 35689 689 | |*235 *356 8 | 9 *35 4 | 267-35 1 267 | | 359-2 7 *29 | 358 1 6 | 23459 234589 289 | +-------------------------+-------------------------+-------------------------+ | 1389 2 *149 | 358 6 7 | 1459 4589 189 | |*789 *489 5 | 1 *89 2-89 | 2467-9 246-89 3 | | 6 1389 *179 | 2358 4 23589 | 12579 2589 12789 | +-------------------------+-------------------------+-------------------------+ | 1259 1569 3 | 4 59 259 | 8 7 1269 | | 125789 15689 267-19 | 23568 3589 23589 | 12369 2369 4 | | 289 4689 246-9 | 2368 7 1 | 2369 2369 5 | +-------------------------+-------------------------+-------------------------+

Remove 35 from r2c79.
Remove 89 from r5c678.
Remove 19 from r89c3.
Remove 26 from b1p27.
Remove 47 from b4p18.

by **shye** » Tue Nov 26, 2024 1:39 pm

for the second puzzle:

Code: Select all: ,----------------------,--------------------,-----------------------, | 4 13569 *169 | 7 2 358 | 3569 35689 89-6 | |*235 *356 8 | 9 35 4 |#267-35 1 #267 | - 267 | 2359 7 *29 | 358 1 6 | 23459 234589 89-2 | :----------------------+--------------------+-----------------------: | 1389 2 *149 | 358 6 7 | 1459 4589 189 | |*789 *489 5 | 1 89 *89+2 |#467-29 #46-289 3 | - 467 | 6 1389 *179 | 2358 4 23589 | 12579 2589 12789 | :----------------------+--------------------+-----------------------: |*1259 *1569 3 | 4 59 *59-2 | 8 7 #26-19 | -(26) | 125789 15689 #267-19| 23568 3589 23589 | 12369 2369 4 | | 289 4689 #246-9 | 2368 7 1 | 2369 2369 5 | '----------------------'--------------------'-----------------------' | 2467

10 truths (267r2, 467r5, 2467c3)
10 links (r2c79, r5c78, r89c3, 26b1, 47b4)
all other candidates removed. 2r5 is placed
add 26r7
at most one 2|6 in b1, at least one of each in r2c79 & r7c9
-26r13c9
solves with locked pair

XSudo input: Show

by **totuan** » Sat Nov 30, 2024 6:30 am

eleven wrote:I did not give a proof or detailed explanation for what i said above, it could be made e.g. this way:
Hidden Text: Show
In general, you can have all 4 SK-link candidates in the cells:

The SK links here are [35r2c5] - 35/26r2c12 - 26/19r13c3 - 19/47r46c3 - 47/89r5c12 - [89]r5c5
Code: Select all
+-------------------------+ | a a 1269 | | 2356 2356 a | 35 . . | . . . | a a 1269 | +-------------------------+ | b b 1479 | | 4789 4789 b | 89 . . | . . . | b b 1479 | +-------------------------+ c

There cannot be another 3 or 5 in r2c79, because the links (starting with 26r2c12) would lead to 3 89's in r5
There cannot be another 8 or 9 in r5c678, because the links (starting with 47r5c12) would lead to 3 35's in r2

If c (in r789c3) is 1 (or 9), r46c3 must be 9 (or 1), because 47 leads to 3 89's in r5. But then 19 is missing in r13c3, and we have 3 35's in r2.

If 2 or 6 are in a 'a'-cell in box1: r13c3 must not be the other digit (6 or 2), because it leaves 35 3 times in r2, but then its 19, (and following the loop) leading to 3 89's in r5.
Same for 4 or 7 in the b cells.

(btw the SK loop eliminations could be proved the same way)

So, as soon you have spotted this blocked SK-loop, you can:
Code: Select all
+-------------------------+-------------------------+-------------------------+ | 4 13569 *169 | 7 2 358 | 3569 35689 689 | |*235 *356 8 | 9 *35 4 | 267-35 1 267 | | 359-2 7 *29 | 358 1 6 | 23459 234589 289 | +-------------------------+-------------------------+-------------------------+ | 1389 2 *149 | 358 6 7 | 1459 4589 189 | |*789 *489 5 | 1 *89 2-89 | 2467-9 246-89 3 | | 6 1389 *179 | 2358 4 23589 | 12579 2589 12789 | +-------------------------+-------------------------+-------------------------+ | 1259 1569 3 | 4 59 259 | 8 7 1269 | | 125789 15689 267-19 | 23568 3589 23589 | 12369 2369 4 | | 289 4689 246-9 | 2368 7 1 | 2369 2369 5 | +-------------------------+-------------------------+-------------------------+

Remove 35 from r2c79.
Remove 89 from r5c678.
Remove 19 from r89c3.
Remove 26 from b1p27.
Remove 47 from b4p18.

Very nice pattern!
Challenge: can you create puzzles with "almost blocked SK-link"?

Thanks again for sharing it!
totuan

by **eleven** » Sat Nov 30, 2024 10:21 pm

If i made no mistake, using the pattern i could reduce the ER 9.0 to 7.2, but with partially rather complex moves. Maybe you like it

Code: Select all: +-------+-------+-------+ | 7 . 4 | 8 . . | . . 3 | | . 5 . | . . . | . 7 . | | . . 1 | . . . | 4 . . | +-------+-------+-------+ | . . . | 1 . . | . 8 . | | 5 8 . | 3 . 6 | . . . | | . . 2 | . 9 . | . . . | +-------+-------+-------+ | 2 . 3 | . . . | 1 . . | | . 6 . | . . 5 | . 9 . | | . . . | 4 . . | . . 2 | +-------+-------+-------+

by **yzfwsf** » Sun Dec 01, 2024 8:49 am

Code: Select all: ,------------------,---------------------,----------------------, | 7 29 4 | 8 1256 129 | 2569 1256 3 | | 3689 5 689 | 269 12346 12349 | 2689 7 1689 | | 3689 239 1 | 25679 23567 2379 | 4 256 5689 | :------------------+---------------------+----------------------: | 3469 3479 679 | 1 2457 247 | 235679 8 45679 | | 5 8 79 | 3 247 6 | 279 124 1479 | | 1346 1347 2 | 57 9 478 | 3567 13456 14567 | :------------------+---------------------+----------------------: | 2 479 3 | 679 678 789 | 1 456 45678 | | 148 6 78 | 27 12378 5 | 378 9 478 | | 189 179 5789 | 4 13678 13789 | 35678 356 2 | '------------------'---------------------'----------------------'

MSLS:14 Cells r28c3479+b6p134679,14 Links 689r2,78r8,2c4,23c7,14c9,5679b6
14 Eliminations:r1c7,r3c4<>2,r9c7<>3,r7c9<>4,r6c8<>5,r2c15,r6c8<>6,r8c5<>7,r8c15,r2c1<>8,r2c16<>9
skfr: 7.2/1.2/1.2

by **totuan** » Sun Dec 01, 2024 10:51 am

eleven wrote:If i made no mistake, using the pattern i could reduce the ER 9.0 to 7.2, but with partially rather complex moves. Maybe you like it

Yes, thank you!

Code: Select all: *-----------------------------------------------------------------------------* | 7 29 4 | 8 1256 129 | 569-2 B1256 3 | | 3-689 5 C689 |D269 1234-6 1234-9 |C2689 7 C1689 | | 3689 239 1 | 5679-2 23567 2379 | 4 B256 5689 | |-------------------------+-------------------------+-------------------------| | 3469 3479 679 | 1 2457 247 | 235679 8 45679 | | 5 8 79 | 3 247 6 | 279 124 1479 | | 1346 1347 2 | 57 9 8 | 3567 34-56 4567 | |-------------------------+-------------------------+-------------------------| | 2 479 3 | 679 678 79 | 1 A456 5678-4 | | 14-8 6 E78 |E27 123-78 5 |F378 9 F478 | | 189 179 5 | 4 13678 1379 | 678-3 A36 2 | *-----------------------------------------------------------------------------*

ABCDEF-marked cells
(34=56)r79c8-(56=12)r13c8-(12=689)r2c379-(689=2)r2c4-(2=78)r8c34-(78=34)r8c79
=> loop => r1c7<>2, r2c1<>689, r2c56<>69, r3c4<>2, r6c8<>56, r7c9<>4, r8c15<>78, r9c7<>3 and ER-7.2

totuan

by **jco** » Sun Dec 01, 2024 11:58 am

totuan wrote:
Code: Select all
*-----------------------------------------------------------------------------* | 7 29 4 | 8 1256 129 | 569-2 B1256 3 | | 3-689 5 C689 |D269 1234-6 1234-9 |C2689 7 C1689 | | 3689 239 1 | 5679-2 23567 2379 | 4 B256 5689 | |-------------------------+-------------------------+-------------------------| | 3469 3479 679 | 1 2457 247 | 235679 8 45679 | | 5 8 79 | 3 247 6 | 279 124 1479 | | 1346 1347 2 | 57 9 8 | 3567 34-56 4567 | |-------------------------+-------------------------+-------------------------| | 2 479 3 | 679 678 79 | 1 A456 5678-4 | | 14-8 6 E78 |E27 123-78 5 |F378 9 F478 | | 189 179 5 | 4 13678 1379 | 678-3 A36 2 | *-----------------------------------------------------------------------------*

ABCDEF-marked cells
(34=56)r79c8-(56=12)r13c8-(12=689)r2c379-(689=2)r2c4-(2=78)r8c34-(78=34)r8c79
=> loop => r1c7<>2, r2c1<>689, r2c56<>69, r3c4<>2, r6c8<>56, r7c9<>4, r8c15<>78, r9c7<>3 and ER-7.2
totuan

Thanks for sharing the details of the move! I missed the (key!) elimination of (8)r2c1 because I saw the move as

Loop (5|6=12)r13c8 - (1|2=689)r2c379 - (6|9=2)r2c4 - (2=78)r8c34 - (7|8=34)r8c79 - (3|4=56)r79c8 - (5|6=12)r13c8

=> - 69 r2c1, -6 r2c5, -9 r2c6, -2 r1c7, -2 r3c4, -3 r9c7, -4 r7c9, -56 r6c8, -78 r8c15

Writing the move as

Loop (5|6=12)r13c8 - (1|2=689)r2c379 - (6|9|8=2&3)r2c14 - (2=78)r8c34 - (7|8=34)r8c79 - (3|4=56)r79c8 - (5|6=12)r13c8

also does not give that elimination.

Loop eliminations are strange: if instead I had placed a false (8) at r2c4 among the candidates,
then I could write in that chain " -(6|9|8=2)r2c4" and that gives the elimination of (8)r2c1!

EDIT: fixed typo

by **eleven** » Sun Dec 01, 2024 1:22 pm

Yes, as totuan showed in an elegant way, the loop gives the same eliminations as the MSLS found by yzfwsf's solver.

My finish of the puzzle:

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 7 b29 4 | 8 56 c129 | 569 b1256 3 | | 3 5 6 | 29 124 124 | 289 7 189 | | 8 b29 1 | 567 3567 37 | 4 b256 569 | +-------------------------+-------------------------+-------------------------+ | 46 34 79 | 1 2457 247 | 235679 8 45679 | | 5 8 79 | 3 247 6 | 279 124 1479 | | 146 134 2 | 57 9 8 | 3567 34 4567 | +-------------------------+-------------------------+-------------------------+ | 2 47 3 | 679 678 d79 | 1 456 5678 | | 14 6 8 | 2-7 123 5 |a37 9 a47 | | 9 17 5 | 4 13678 137 | 678 36 2 | +-------------------------+-------------------------+-------------------------+

7r8c79 =loop= 12r13c8 & 92r31c2 - (1|2=9)r1c6 - (9=7)r7c6 => -7r8c4

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 7 29 4 | 8 56 e12 | 569 f1256 3 | | 3 5 6 | 9 124 124 | 28 7 f18 | | 8 29 1 | 567 3567 37 | 4 256 569 | +-------------------------+-------------------------+-------------------------+ | 46 34 79 | 1 2457 247 | 235679 8 45679 | | 5 8 79 | 3 247 6 | 279 124 1479 | | 146 134 2 | 57 9 8 | 3567 34 4567 | +-------------------------+-------------------------+-------------------------+ | 2 a47 3 |a67 a678 9 | 1 456 56-8 | |b14 6 8 | 2 c13 5 | 37 9 47 | | 9 c17 5 | 4 13678 d137 | 68 36 2 | +-------------------------+-------------------------+-------------------------+

(8=674)r7c542 - (4=1)r8c1 - (1=37)r8c5,r9c2 - (3|7=1)r9c6 - r1c6 = 18b3p26 => -8r7c9, stte

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