SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Mon Oct 25, 2021 7:22 am

All times are UTC




Post new topic Reply to topic  [ 5 posts ] 
Author Message
 Post subject: Assassin 68v2 Revisit
PostPosted: Fri Oct 01, 2021 6:30 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 911
Location: Sydney, Australia
Attachment:
a68v2R.JPG
a68v2R.JPG [ 98.27 KiB | Viewed 139 times ]
Assassin 68 v2 Revisit

Another one where the experience on the archive (hyperlink above) doesn't match the SSscore of 1.35 and JSudoku uses just 2 'complex intersections'. So, hopefully its worth a revisit and is challenging enough.
triple click code:
3x3::k:5376:5376:5376:6147:2308:5637:4870:4870:4870:3593:5376:6147:6147:2308:5637:5637:4870:5137:3593:5376:5396:5397:5397:5397:6424:4870:5137:3593:3593:5396:5396:5397:6424:6424:5137:5137:4644:4644:2598:5396:5397:6424:3882:3883:3883:4653:4644:2598:2598:3121:3882:3882:3883:3893:4653:4653:3384:3384:3121:3899:3899:3893:3893:3647:3136:3384:3650:3650:3650:3899:2886:3911:3647:3136:3136:3147:3147:3147:2886:2886:3911:
solution:
+-------+-------+-------+
| 5 7 2 | 8 6 9 | 3 4 1 |
| 4 1 9 | 7 3 5 | 8 6 2 |
| 3 6 8 | 2 1 4 | 9 5 7 |
+-------+-------+-------+
| 2 5 4 | 6 9 7 | 1 3 8 |
| 1 9 6 | 3 5 8 | 7 2 4 |
| 7 8 3 | 1 4 2 | 6 9 5 |
+-------+-------+-------+
| 9 2 1 | 5 8 6 | 4 7 3 |
| 8 4 7 | 9 2 3 | 5 1 6 |
| 6 3 5 | 4 7 1 | 2 8 9 |
+-------+-------+-------+
Cheers
Ed


Top
 Profile  
Reply with quote  
PostPosted: Sat Oct 09, 2021 8:17 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 911
Location: Sydney, Australia
This came out quickly for me. Saw the key step very early. [Many thanks to Andrew for checking my WT]
A68v2R WT:
Preliminaries from SudokuSolver
Cage 14(2) n7 - cells only uses 5689
Cage 15(2) n9 - cells only uses 6789
Cage 12(2) n58 - cells do not use 126
Cage 9(2) n2 - cells do not use 9
Cage 24(3) n12 - cells ={789}
Cage 22(3) n23 - cells do not use 1234
Cage 10(3) n45 - cells do not use 89
Cage 11(3) n9 - cells do not use 9
Cage 14(4) n14 - cells do not use 9

This is an optimised solution so any clean-ups etc are stated.

1. "45" on n7: 1 outie r7c4 + 6 = 2 innies r7c12. Both innies see the outie -> difference cannot be 0 -> no 6 in r7c12 (IOU)

2. "45" on n9 1 outie r7c6 + 4 = 2 innies r7c89
2a. -> no 4 in r7c89 (IOU)

3. "45" on r89: 2 innies r8c37 = 12 (no 1,2,6)

4. "45" on n8: after subtracting the h12(2)r8 -> 2 remaining outies r7c37 + 3 = 1 innie r7c5
4a. -> max r7c37 = 6 (no 6,7,8,9)
4b. and r7c5 from (789)

key step.
5. 15(3)r6c9 with a 6 could be {168/267/456}
5b. but {168/267} blocked by 15(2)n9 needing 6 or 8, 6 or 7
5c. also, 11(3)n9 = {128/137/146/236/245} = one of 5,6,7,8
5d. -> combined cage 15(3)r6c9 and 15(2)n9 can't be [4]{5678}
5. -> no 6 in 15(3)
(alternatively, do 4 innies n9 = 19, then after blocks by 15(2)n9 removed, can't have both 5 & 6 in those innies -> [4]{56} blocked from 15(3))

6. "45" on n8: 3 innies r7c456 = 19 and must have 6 for r7
6a. = {469/568}(no 1,2,3,7)
6b. 6 locked for n8
6c. r6c5 from (34)
6d. h19(3) can't have both 8 & 9, which must go in r7c5 -> r7c46 from {456}

7. "45" on n9: 2 outies r6c9 + r7c6 = 11 = [74/56]

8. 12(3)n8: {345} blocked by r7c46 = two of {456} (Almost Locked Set ALS)
8a. = {129/138/147/237}(no 5)

9. 5 in n8 only in r7c4 + 14(3) -> no 5 in r8c3 since it sees all these (Common Peer Elimination CPE)
9a. -> no 7 in r8c7 (h12(2))

10. 13(3)r7c3 must have 4,5,6 for r7c4
10a. but {256} blocked by none are in r7c3
10b. = {148/157/247/346}(no 9)
10c. 5 in {157} must be r7c4 -> no 5 in r7c3

11. "45" on n7: 2 outies r6c1 + r7c4 = 12 = [84/75/66]

12. 18(3)r6c1: {189/567} blocked by 14(2)n7 [oops, {369} also blocked. Missed that. But don't think it will make a difference.]
12a. and must have 6,7,8 for r6c1
12b. = {279/369/378/468}(no 1,5)

13. "45" on n7: 4 innies r7c123 + r8c3 = 19
13a. = {1279/1378}(no 4)
13b. -> r7c3 = 1
13c. 7 locked for n7
13d. -> r7c4 + r8c3 = 12 = [48/57]
13e. -> r8c7 = (45) (h12(2)r8)
13f. and r6c1 from (78)(outiesn7=12)

14. r7c6 = 6 (hsinglen8)
14a. -> r78c7 = 9 = {45}: both locked for n9 and c7
14b. and r6c9 = 5 (outiesn9=11)
14c. -> r7c89 = 10 = {28/37}(no 9)

15. 9 in n9 only in 15(2) = {69}, 6 locked for c9 and n9, 9 for c9

16. 24(3)r1c4 = {789} -> no 7,8,9 in r2c56 (CPE)
16a. -> r2c6 = 5
16b. -> r1c6 + r2c7 = 17 = {89} only
16c. -> no 8,9 in r2c4 (CPE)
16d. -> r2c4 = 7
16e. -> 8 and 9 locked for r12 in r1c46 + r2c37 (caged x-wings) (or sets of naked pairs!)

17. 9(3)n2 = {36} only: both locked for n2 and c5
17a. -> r67c5 = [48]
17b. -> r7c4 = 5 (h19(3)n8)
17c. -> r78c7 = [45]
17d. and r8c3 = 7 (cage sum)
17e. and r7c89 = 10 = {37} only: both locked for n9, 3 for r7

18. r7c12 = naked pair {29} = 11: both locked for n7
18a. -> r6c1 = 7 (cage sum)

19. naked triple {124} = 7 in r3c456: all locked for r3 and 1,2 for 21(5)
19a. -> r45c5 = 14 = {59}: 9 locked for n5 and c5

20. "45" on r1234: 3 outies r5c456 = 16
20a. but {259} blocked by r4c5 = (59)
20b. must have 5 or 9 for r5c5
20c. = {169/358}(no 2,7)

21. hidden singles 7 in n5 in r4c6, and n8 in r9c5

22. "45" on c89: 2 outies r17c7 = 5 = [32]

23. 15(3)r5c7 = {168/267}(no 3,9)
23a. 6 locked for c7 and n6

24. 25(4)r3c7 = [9718] since can't have both {89} in r34c7 because r2c7 = (89)

pretty straightforward from here with a few cage sums to get through
Cheers
Ed


Top
 Profile  
Reply with quote  
PostPosted: Sun Oct 10, 2021 5:44 pm 
Offline
Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 233
Location: California, out of London
Wow Ed! Very nice Steps 1 - 5! I didn't see that at all :)
Here's how I did it.
Thanks to Andrew for checking it!
Assassin 68v2 Revisit WT:
1. 24(3)r1c4 = {789}
-> 22(3) r1c6 = <769> or <859>
i.e., whichever of (789) is in r2c3 also goes in r1c6 and
whichever of (789) is in r1c4 also goes in r2c7,

A) 22(3) = <769> puts 9(2)n2 = {45} puts 12(2)c5 = {39} puts 21(5)r3c4 = [{123}{78}]
B) 22(3) = <859> puts 9(2)n2 = {36} puts 21(5)r3c4 = [{124}{59}] puts 12(2)c5 = {48}

2. Innies n8 = r7c456 = +19(3)
Innies r89 = r8c37 = +12(2)
Outies n9 = r6c9 + r7c6 = +11(2)
Outies n7 = r6c1 + r7c4 = +12(2)
Innies c6789 = r389c6 = +8(3) = {125} or {134}

Outies r89 = r7c3467 = +16(4)
Since r7c456 = +19(3) -> r7c5 = r7c37 + 3 (I.e., r7c5 is Min 6)
-> 12(2)c5 from [39] or [48]

3. Consider case 1.A). r2c4 = 8, r45c5 = {78} and 12(2)c5 = [39]
Since r7c4 is min 3 this puts max r7c6 = 7 which leaves no place for 8 in n8
-> case 1.B) must be true.

-> 9(2)n2 = {36}, r2c4 = 7, r2c6 = 5
21(5)r3c4 = [{124}{59}]
12(2)c5 = [48]
7 in c5 in r89c5
Also innies c6789 = r389c6 = {134} with 3 in r89c6

4. Remaining outies r789 = r6c19 = +12(2) = {39} or {57}
Since Outies n7 = r6c1,r7c4 = +12(2) -> r7c4 is odd.
-> Remaining Innies n8 = r7c46 = +11(2) = [92] or [56]
But the former puts r6c1 = 3 which leaves no solution for 18(3)r6c1
-> r7c46 = [56]
-> r6c19 = [75]
-> r7c12 = {29}
-> r7c89 = {37}
-> r78c3 = [17]
-> r78c7 = [45]

5. 9 in n8 only in r89c4
-> 24(3)r1c4 = [897] and 22(3)r1c6 = [958]
-> r456c6 = {278}
-> r456c4 = {136}
Outies r1234 = r5c456 = +16(3) must be [358]
-> r4c5 = 9
Also r46c4 = [61]

6. 15(2)n9 = {69}
Outies c89 = r19c7 can only be [32]
-> r89c8 = {18}
-> (Since 19(5)n3 must contain a 1) r1c9 = 1
ALso 15(3)r5c7 must be r6c6 = 2 and r56c7 = [76]
-> 25(4)r3c7 = [9718]
-> 15(3)n6 = {249} and r4c89 = [38]
etc.


Last edited by wellbeback on Sat Oct 16, 2021 6:53 pm, edited 1 time in total.

Top
 Profile  
Reply with quote  
PostPosted: Thu Oct 14, 2021 2:25 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1792
Location: Lethbridge, Alberta, Canada
I finished this on Saturday morning but have only just found time to check my WT and then see how Ed and wellbeback solved it.

Glancing at the archive I see, in small print, that I missed one step back then and again this time. It's Ed's step 4, which he saw slightly differently, and the last part of wellbeback's step 2. It would have simplified my solving path but doesn't appear to be a "game-changer".

My start was very similar to wellbeback's, whereas Ed's solving path was very different.

Here's my walkthrough for Assassin 68V2 Revisited:
Prelims

a) R12C5 = {18/27/36/45}, no 9
b) R67C5 = {39/48/57}, no 1,2,6
c) R89C1 = {59/68}
d) R89C9 = {69/78}
e) 24(3) cage at R1C4 = {789}
f) 22(3) cage at R1C6 = {589/679}
g) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
h) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
i) 14(4) cage at R2C1 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on N2 2 outies R2C37 = 3 outies R3C123 + 10 -> R2C37 = 16,17 = {79/89}, 9 locked for R2, R3C123 = 6,7 = {123/124}, 1,2 locked for R3, N2 and 21(5) cage at R3C4, clean-up: no 7,8 in R12C5
1b. 24(3) cage at R1C4 and 22(3) cage at R1C6 must both contain 9 -> 9 in R1C46, locked for R1
1c. 45 rule on N2 4(2+2) outies R2C37 + R45C5 = 31, R2C37 = 16,17 -> R45C5 = 14,15 = {59/68/69/78}, no 3,4
[Killer pair 3,4 in R12C5 and R3C123 also make these eliminations)
1d. Naked triple {789} in 24(3) cage at R1C4, CPE no 7,8 in R2C6
1e. 22(3) cage at R1C6 = {589/679}
1f. R2C6 = {56} -> no 5,6 in R1C6
1g. Naked triple {789} in R2C347, locked for R2
1h. Killer half-pair in R12C5 and R67C5, 3 locked for C5

2a. 45 rule on C6789 3 innies R389C6 = 8 = {125/134}, 1 locked for C6
2b. 45 rule on C1234 3 innies R389C4 = 15, max R3C4 = 4 -> min R89C4 = 11, no 1
2c. 45 rule on N7 2(1+1) outies R6C1 + R7C4 = 12, no 1,2
2d. 45 rule on N9 2(1+1) outies R6C9 + R7C6 = 11, no 1 in R6C9
2e. 45 rule on R89 2 innies R8C37 = 12 = {39/48/57}, no 1,2,6
2f. 45 rule on C12 2 outies R19C3 = 7 = {16/25/34}, no 7,8,9
2g. 45 rule on C89 2 outies R19C7 = 5 = {14/23}
2h. 19(5) = {12349/12358/12367/12457/13456}, 1 locked for N3

3a. R12C5 = {36/45}, R45C5 (step 1c) = {59/68/69/78}
3b. Consider combinations for R12C5
R12C6 = {36}, locked for N2, 6 locked for C5 => R3C123 = {124} = 7, R45C5 = 14 = {59}
or R12C5 = {45}, locked for C5 and N2 => R3C123 = {123} = 6, R67C5 = {39}, 9 locked for C5, R45C5 = 15 = {78}
-> R45C5 = {59/78}, no 6
3c. 5 in R12C6 = {45} or R45C5 = {59}, locked for C5, clean-up: no 7 in R67C5
3d. Killer pair 3,4 in R12C5 and R67C5, locked for C5
3e. Killer pair 8,9 in R45C5 and R67C5, locked for C5

4a. 45 rule on N1 2 innies R23C3 = 2 outies R4C12 + 10
4b. Min R4C12 = 3 -> min R23C3 = 13, no 3 in R3C3
4c. Max R23C3 = 17 -> max R4C12 = 7, no 7,8 in R4C12

5a. 45 rule on N7 2 innies R7C12 = 1 outie R7C4 + 6 -> no 6 in R7C12 (IOU)
5b. 45 rule on N9 2 innies R7C89 = 1 outie R7C6 + 4 -> no 4 in R7C89 (IOU)

6a. 18(3) cage at R6C1 = {279/378/459/468} (cannot be {189/369/567} which clash with R89C1), no 1
6b. 15(3) cage at R6C9 = {159/249/258/348/357/456} (cannot be {168/267} which clash with R89C9)

7a. R389C4 = 15 (step 2b), R389C6 (step 2a) = {125/134}
7b. 24(3) cage at R1C4 and 22(3) cage at R1C6 -> R2C46 = [75/86]
7c. Consider combinations for R2C46
R2C46 = [75] => R389C6 = {134}
or R2C46 = [86], R12C5 = {45}, R3C4 = 3 => R89C4 = 12 = {57}, 5 locked for N8 => R389C6 = {134}
or R2C46 = [86], R12C5 = {45}, R3C6 = 3 => R389C6 = {134}
-> R389C6 = {134}, locked for C6, clean-up: no 7,8 in R6C9 (step 2d)
7d. 45 rule on N8 3 innies R7C456 = 19 = {289/379/469/478/568}
7e. Hidden killer pair 8,9 in R789C4 and R7C56 for N8, R7C56 cannot contain both of 8,9 (because no 2 in R7C4) -> R789C4 must contain one of 8,9 (cannot be both because of R12C4)
7f. Killer triple 7,8,9 in R12C4 and R789C4, locked for C4, 7 locked for C4, N2 and 24(3) cage at R1C4, no 7 in R2C3, clean-up: no 5 in R6C1 (step 2c)

8a. R389C4 = 15 (step 2b) = {149/158/249/258/348} (cannot be {456} because [456] which clashes with 14(3) cage at R8C4 = [563] and cannot be [465] because 14(3) cage = [671] clashes with R3C456 = [421]), no 6 in R89C4
8b. Killer triple 7,8,9 in R12C4 and R89C4, locked for C4, clean-up: no 3,4 in R6C1 (step 2c)
8c. 14(3) cage at R8C4 = {149/239/248/347/356} (cannot be {158} because 5,8 only in R8C4, cannot be {257} because no 2,5,7 in R8C6)
8d. 1 of {149} must be in R8C5 -> no 1 in R8C6
8e. 12(3) cage at R9C4 = {129/138/147/156/237/246} (cannot be {345} because no 3,4,5 in R9C5)
8f. 2,8 of {138/237} must be in R9C4 -> no 3 in R9C4
8g. R7C456 (step 7d) = {379/478/568} (cannot be {289} because no 2,8,9 in R7C4, cannot be {469} which clashes with 14(3) cage), no 2, clean-up: no 9 in R6C9 (step 2d)
8h. 12(3) cage = {129/147/156/237/246} (cannot be {138} which clashes with R7C456), no 8
8i. 12(3) cage = {129/147/156/237} (cannot be {246} which clashes with R7C456 = {478/568} and clashes with R7C456 = {379} + 14(3) cage then = {248})
8j. R7C456 = {379/478/568} -> R7C5 = {89}, R7C6 = {567}, R6C5 = {34}, clean-up: no 2,3 in R6C9 (step 2d)
8k. R7C456 = {379/568} (cannot be {478} = [487] because R67C5 = [48] clashes with R6C9 + R7C6 = [47], step 2d), no 4, clean-up: no 8 in R6C1 (step 2c)
[With hindsight, having glanced at the archive, 45 rule on R89 4 outies R7C3467 = 16, R7C456 = 19 -> R7C5 = R7C37 + 3 would have got to step 8j more quickly.]

9a. R12C5 = {36/45}, R2C46 (step 7b) = [75/86]
9b. Consider permutations for R67C5 = [39/48]
R67C5 = [39] => 8 in N8 only in R89C4, locked for C4 => R2C4 = 7
or R67C5 = [48] => R12C5 = {36}, 6 locked for N2 => R2C6 = 5
-> R2C46 = [75], clean-up: no 4 in R12C5
[It gets easier from here.]
9c. Naked pair {36} in R12C5, locked for C5, 3 locked for N2 -> R67C5 = [48], R6C9 + R7C6 (step 2d) = [56]
9d. 3 in C6 only in R89C6, locked for N8 -> R7C4 = 5, R6C1 = 7 (step 2c)
9e. R6C1 = 7 -> R7C12 = 11 = {29}, locked for R7 and N7, clean-up: no 5 in R1C3 (step 2f), no 5 in R89C1
9f. R6C9 = 5 -> R7C89 = 10 = {37}, locked for N9, 3 locked for R7, clean-up: no 2 in R1C7 (step 2g), no 8 in R89C9
9g. R19C7 (step 2g) = [32] (cannot be {14} which clashes with R7C7) -> R12C5 = [63], clean-up: no 4,6 in R9C3 (step 2f)
9h. 12(3) cage at R9C4 = {147} (only remaining combination) = [471], R3C6 = 4, 14(3) cage at R8C4 = [923], R1C46 = [89], R2C37 = [98], R89C9 = [69], R89C1 = [86], R3C9 = 7 -> R7C89 = [73], clean-up: no 1 in R1C3 (step 2f)
[Clean-ups for R8C37 (step 2e) were overlooked but that doesn’t matter]
9i. R9C23 = {35} -> R8C2 = 4 (cage sum), R78C3 = [17], R78C7 = [45], R89C8 = [18]
9j. 45 rule on N3 2 remaining innies R2C9 + R3C7 = 11 = [29]
9k. Naked triple {456} in R123C8, 4,6 locked for C8, 4 locked for N3 -> R1C9 = 1
9l. R23C9 = [27] -> R4C89 = 11 = [38], R5C9 = 4
9m. R3C3 = 8 (hidden single in C3)
9n. 45 rule on N1 2 remaining innies R23C1 = 7 = [43] -> R1C123 = [572], R23C2 = [16], R4C12 = 7 = [25]
9o. R56C3 = {36} -> R6C4 = 1 (cage sum)
9p. R4C4 = 6, R4C67 = [71], R3C7 = 9 -> R5C6 = 8 (cage sum)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
PostPosted: Fri Oct 15, 2021 4:41 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1792
Location: Lethbridge, Alberta, Canada
I've now had a look at what difference there would have been to my solving path if I'd seen that step which I missed both originally and in my Revisited walkthrough. It simplified things a bit more than I'd expected, including some of my harder steps. I've changed the middle part; the start and finish are very similar to my previous walkthrough.

Here's my reworked walkthrough for Assassin 68V2 Revisited:
Rework using the step that I missed first time and on the Revisit.

Prelims

a) R12C5 = {18/27/36/45}, no 9
b) R67C5 = {39/48/57}, no 1,2,6
c) R89C1 = {59/68}
d) R89C9 = {69/78}
e) 24(3) cage at R1C4 = {789}
f) 22(3) cage at R1C6 = {589/679}
g) 10(3) cage at R5C3 = {127/136/145/235}, no 8,9
h) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
i) 14(4) cage at R2C1 = {1238/1247/1256/1346/2345}, no 9

1a. 45 rule on N2 2 outies R2C37 = 3 innies R3C456 + 10 -> R2C37 = 16,17 = {79/89}, 9 locked for R2, R3C123 = 6,7 = {123/124}, 1,2 locked for R3, N2 and 21(5) cage at R3C4, clean-up: no 7,8 in R12C5
1b. 24(3) cage at R1C4 and 22(3) cage at R1C6 must both contain 9 -> 9 in R1C46, locked for R1
1c. 45 rule on N2 4(2+2) outies R2C37 + R45C5 = 31, R2C37 = 16,17 -> R45C5 = 14,15 = {59/68/69/78}, no 3,4
[Killer pair 3,4 in R12C5 and R3C123 also make these eliminations)
1d. Naked triple {789} in 24(3) cage at R1C4, CPE no 7,8 in R2C6
1e. 22(3) cage at R1C6 = {589/679}
1f. R2C6 = {56} -> no 5,6 in R1C6
1g. Naked triple {789} in R2C347, locked for R2
1h. Replace by step 3d

2a. 45 rule on C6789 3 innies R389C6 = 8 = {125/134}, 1 locked for C6
2b. 45 rule on C1234 3 innies R389C4 = 15, max R3C4 = 4 -> min R89C4 = 11, no 1
2c. 45 rule on N7 2(1+1) outies R6C1 + R7C4 = 12, no 1,2
2d. 45 rule on N9 2(1+1) outies R6C9 + R7C6 = 11, no 1 in R6C9
2e. 45 rule on R89 2 innies R8C37 = 12 = {39/48/57}, no 1,2,6
2f. 45 rule on C12 2 outies R19C3 = 7 = {16/25/34}, no 7,8,9
2g. 45 rule on C89 2 outies R19C7 = 5 = {14/23}
2h. 19(5) = {12349/12358/12367/12457/13456}, 1 locked for N3

3a. R12C5 = {36/45}, R45C5 (step 1c) = {59/68/69/78}
3b. Consider combinations for R12C5
R12C6 = {36}, locked for N2, 6 locked for C5 => R3C123 = {124} = 7, R45C5 = 14 = {59}
or R12C5 = {45}, locked for C5 and N2 => R3C123 = {123} = 6, R67C5 = {39}, 9 locked for C5, R45C5 = 15 = {78}
-> R45C5 = {59/78}, no 6
3c. 5 in R12C6 = {45} or R45C5 = {59}, locked for C5, clean-up: no 7 in R67C5
3d. Killer pair 3,4 in R12C5 and R67C5, locked for C5
3e. Killer pair 8,9 in R45C5 and R67C5, locked for C5

4a. 45 rule on N1 2 innies R23C3 = 2 outies R4C12 + 10
4b. Min R4C12 = 3 -> min R23C3 = 13, no 3 in R3C3
4c. Max R23C3 = 17 -> max R4C12 = 7, no 7,8 in R4C12

5a. 45 rule on N7 2 innies R7C12 = 1 outie R7C4 + 6 -> no 6 in R7C12 (IOU)
5b. 45 rule on N9 2 innies R7C89 = 1 outie R7C6 + 4 -> no 4 in R7C89 (IOU)

6a. 18(3) cage at R6C1 = {279/378/459/468} (cannot be {189/369/567} which clash with R89C1), no 1
6b. 15(3) cage at R6C9 = {159/249/258/348/357/456} (cannot be {168/267} which clash with R89C9)

[Now the step I missed before]
7a. 45 rule on R89 4 outies R7C3467 = 16, 45 rule on N8 3 innies R7C456 = 19 -> R7C5 = R7C37 + 3 -> R7C5 = {89}, R7C37 = 5,6, no 6,7,8,9 in R7C37, clean-up: no 8,9 in R6C5
7b. R7C456 = {289/379/469/478/568}
7c. 2 of {289} must be in R7C6, 8,9 of {379/469/478/568} must be in R7C5 -> no 8,9 in R7C6, clean-up: no 2,3 in R6C9 (step 2d)
7d. Hidden killer pair 8,9 in R789C4 and R7C5 for N8, R7C5 = {89} -> R789C4 must contain one of 8,9
7e. Killer triple 7,8,9 in R12C4 and R789C4, locked for C4, 7 locked for C4, N2 and 24(3) cage at R1C4, no 7 in R2C3, clean-up: no 5 in R6C1 (step 2c)
7f. From step 3b, R7C5 and R89C5 must contain either 8 and 7 or 9 and 6 -> R7C456 = {289/379/568} (cannot be {469/478}, combo crossover clash), no 4, clean-up: no 8 in R6C1 (step 2c), no 7 in R6C9 (step 2d)
7g. 45 rule on R789 3 outies R7C159 = 16 = {349/367/457} (cannot be {358} because 5,8 only in R6C9), no 8, clean-up: no 3 in R7C6 (step 2d)
7h. R7C159 = {349/457} (cannot be {367} = [736] because R6C1 + R7C4 = [75], step 2c clashes with R6C9 + R7C6 = [65], step 2d), no 6, 4 locked for R6, clean-up: no 6 in R7C4 (step 2c), no 5 in R7C6 (step 2d)

8a. R12C5 = {36/45}, 24(3) cage at R1C4 and 22(3) cage at R1C6 -> R2C46 = [75/86]
8b. Consider permutations for R67C5 = [39/48]
R67C5 = [39] => 8 in N8 only in R789C4, locked for C4 => R2C4 = 7
or R67C5 = [48] => R12C5 = {36}, 6 locked for N2 => R2C6 = 5
-> R2C46 = [75], clean-up: no 4 in R12C5
[It gets easier from here.]
8c. Naked pair {36} in R12C5, locked for C5, 3 locked for N2 -> R67C5 = [48], R3C456 = {124}, 4 locked for R3, clean-up: no 7 in R7C6 (step 2d)
8d. Naked triple {127} in R389C5, 7 locked for C5
8e. R45C5 = {59}, locked for N5
8f. R389C6 (step 2a) = {134}, 3 locked for C6 and N8, clean-up: no 9 in R6C1 (step 6c)
8g. 18(3) cage at R6C1 (step 6a) = {279} (only remaining combination) -> R6C1 = 7, R7C12 = 11 = {29}, locked for R7 and N7, R7C4 = 5, R7C6 = 6 -> R6C9 = 5 (step 2d), clean-up: no 5 in R1C3 (step 2f), no 5 in R89C1
8h. R6C9 = 5 -> R7C89 = 10 = {37}, locked for N9, 3 locked for R7, clean-up: no 2 in R1C7 (step 2g), no 8 in R89C9
8i. R19C7 (step 2g) = [32] (cannot be {14} which clashes with R7C7) -> R12C5 = [63], clean-up: no 4,6 in R9C3 (step 2f)
8j. 12(3) cage at R9C4 = {147} (only remaining combination) = [471], R3C6 = 4, 14(3) cage at R8C4 = [923], R1C46 = [89], R2C37 = [98], R89C9 = [69], R89C1 = [86], R3C9 = 7 -> R7C89 = [73], clean-up: no 1 in R1C3 (step 2f)
[Clean-ups for R8C37 (step 2e) were overlooked but that doesn’t matter]
8k. R9C23 = {35} -> R8C2 = 4 (cage sum), R78C3 = [17], R78C7 = [45], R89C8 = [18]
8l. 45 rule on N3 2 remaining innies R2C9 + R3C7 = 11 = [29]
8m. Naked triple {456} in R123C8, 4,6 locked for C8, 4 locked for N3 -> R1C9 = 1
8n. R23C9 = [27] -> R4C89 = 11 = [38], R5C9 = 4
8o. R3C3 = 8 (hidden single in C3)
8p. 45 rule on N1 2 remaining innies R23C1 = 7 = [43] -> R1C123 = [572], R23C2 = [16], R4C12 = 7 = [25]
8q. R56C3 = {36} -> R6C4 = 1 (cage sum)
8r. R4C4 = 6, R4C67 = [71], R3C7 = 9 -> R5C6 = 8 (cage sum)

and the rest is naked singles.


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 5 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 3 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group