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PostPosted: Tue Feb 02, 2021 8:15 am 
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a44v1.5.JPG
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Note: Broken 21(4) cage at r1289c5

Assassin 44 v1.5 Revisit

Two versions of a44 in the archive (both by Para: he was quite prolific at that time). I don't really like puzzles that grind to a halt early (the V2), so this v1.5 should be the better of the two. Plus, it has quite a few WTs, so we might not need any more on this Revisit. But should be interesting to come at it with fresh eyes. It gets a score of 1.55 (1.70 for the V2). JSudoku uses 1 'complex intersection' (3 for the V2).

triple click code:
3x3::k:4608:4608:4608:4608:5380:5125:5125:5125:4360:5385:5385:5385:2060:5380:6158:6158:4360:4360:3090:3090:3090:2060:3094:3094:6158:4360:5402:4123:3090:5917:4126:4126:4126:6158:5154:5402:4123:5917:5917:3367:3367:3367:5154:5154:5402:4123:5917:3887:4144:4144:4144:5154:4916:5402:4123:5687:3887:3385:3385:1595:4916:4916:4916:5687:5687:3887:3887:5380:1595:3397:3397:3397:5687:4937:4937:4937:5380:5197:5197:5197:5197:
Solution:
+-------+-------+-------+
| 9 3 4 | 2 6 7 | 5 8 1 |
| 8 6 7 | 5 1 9 | 2 3 4 |
| 5 1 2 | 3 4 8 | 7 9 6 |
+-------+-------+-------+
| 3 4 1 | 9 2 5 | 6 7 8 |
| 7 5 8 | 4 3 6 | 9 1 2 |
| 2 9 6 | 7 8 1 | 3 4 5 |
+-------+-------+-------+
| 4 8 3 | 6 7 2 | 1 5 9 |
| 6 7 5 | 1 9 4 | 8 2 3 |
| 1 2 9 | 8 5 3 | 4 6 7 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Fri Feb 05, 2021 9:25 pm 
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Thanks Ed. I'm not going to let you put me off, when I solve Assassin-level puzzles I like to post my new WTs; as usual I haven't looked at any of the original WTs.

Para seemed to like disjoint/toroidal cages. His toroidal puzzles in the Texas Jigsaw Killer archive (other variants forum) seemed particularly hard because it was the jigsaw nonets which were toroidal.

Thanks Ed for pointing out an omission and for correcting typos.
Here's my walkthrough for Assassin 44v1.5 Revisited:
Prelims

a) R23C4 = {17/26/35}, no 4,8,9
b) R3C56 = {39/48/57}, no 1,2,6
c) R7C45 = {49/58/67}, no 1,2,3
d) R78C6 = {15/24}
e) 20(3) cage at R1C6 = {389/479/569/578}, no 1,2
f) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
g) 19(3) cage at R9C2 = {289/379/469/478/568}, no 1
h) 12(4) cage at R3C1 = {1236/1245}, no 7,8,9

1a. 12(4) cage at R3C1 = {1236/1245}, CPE no 1,2 in R1C2
1b. 45 rule on N1 2(1+1) outies R1C4 + R4C2 = 6 = {15/24}/[33], no 6,7,8,9
[I missed 3 in N1 in 18(4) cage at R1C1 or in 12(4) cage at R3C1 blocks [33], an implied forcing chain.]
1c. 45 rule on C123 3 outies R189C4 = 11 = {128/137/146/236/245}, no 9
1d. 45 rule on N9 2(1+1) outies R6C8 + R9C4 = 7 = {16/25/34}, no 7,8,9
1e. 45 rule on C789 3 outies R129C6 = 19 = {289/379/469/478/568}, no 1, clean-up: no 6 in R6C8
1f. Max R9C6 = 6 -> min R12C6 = 13, no 2,3
1g. 45 rule on R1 2 innies R1C59 = 7 = {16/25/34}, no 7,8,9
1h. 45 rule on R9 2 innies R9C15 = 6 = {15/24}
1i. 9 in C4 only in R4567C4
1j. 45 rule on C1234 4 innies R4567C4 = 26 = {2789/3689/4589/4679}, no 1

2a. Hidden killer quad 1,2,4,5 for N8, R78C6 = {15/24}, R9C5 = {1245} -> the remaining cells in N8 can only contain one of 1,2,4,5
2b. R189C4 (step 1c) = {128/137/146/236} (cannot be {245} which requires two of 2,4,5 in R89C4), no 5, clean-up: no 1 in R4C2 (step 1b)
2c. 12(4) cage at R3C1 = {1236/1245}, 1 locked for R3 and N1, clean-up: no 7 in R2C4

3a. R78C6 = {15/24} and R9C15 (step 1h) = {15/24} interact to form combined cage R78C4 + R9C15 = {15/24}, CPE no 2,4,5 in R9C6, clean-up: no 2,3,5 in R6C8 (step 1d)
[Ed pointed out that the CPE also gives no 2,4 in R9C4; fortunately this didn’t significantly affect my solving path.]
3b. R129C6 (step 1e) = {379/469/568} (cannot be {478} because R9C6 only contains 3,6)
3c. R9C6 = {36} -> no 6 in R12C6
3d. R189C4 (step 2b) = {128/137/146/236}
3e. Consider combinations for R129C6
R129C6 = {379}, 7 locked for N2
or R129C6 = {469/568}, R9C6 = 6 => R189C4 = {128/137}, 1 locked for C4
-> R23C4 = {26/35}, no 1,7
3f. R189C4 = {128/137/146} (cannot be {236} which clashes with R23C4)
3g. R4567C4 (step 1j) = {2789/4589/4679} (cannot be {3689} which clashes with R23C4), no 3

[Continuing in that area.]
4a. R189C4 (step 3f) = {128/137/146}
4b. Consider combinations for R7C45 = {49/58/67}
R7C45 = {49/58} => killer quad 1,2,4,5 in R7C45, R78C6 and R9C5, locked for N8 => R189C4 = 1{37}, R8C5 = {89}
or R7C45 = {67} => R189C4 = {128}, R8C5 = 9 (hidden single in N8)
-> R189C4 = {128}/1{37}, no 4,6, no 3 in R1C4, clean-up: no 2,3 in R4C2 (step 1b) and
R8C5 = {89}
4c. Killer pair 2,3 in R189C4 and R23C4, locked for C4
4d. 12(4) cage at R3C1 = {1245} (only remaining combination), 2 locked for R3 and N1, clean-up: no 6 in R2C4
4e. 12(4) cage at R3C1 = {1245}, CPE no 4,5 in R12C2
4f. 3 in N1 only in R1C123, locked for R1, clean-up: no 4 in R1C59 (step 1g)
4g. 20(3) cage at R1C6 = {479/578} (cannot be {569} which clashes with R1C59), no 6, 7 locked for R1
4g. 7 in N1 only in 21(3) cage at R2C1 = {579/678}, no 4, 7 locked for R2
4h. 3 in R1C123, R1C4 = {12} -> 18(4) cage at R1C1 = {349}2/{368}1 (cannot be {358}2 which clashes with 21(3) cage, cannot be {359}1 which clashes with 20(3) cage), no 5
[Continuing those combinations …]
4i. 18(4) cage = {349}2, 4 locked for N1 => R3C123 = {125}, 5 locked for R3 => R23C4 = [53]
or 18(4) cage = {368}1 => 21(3) cage = {579}
-> 5 in R2C134, locked for R2
4j. 21(4) disjoint cage at R1C5 cannot be {1389} because 3,8,9 only in R28C5, R8C5 = {89} -> no 8,9 in R2C5
4k. Max R12C5 = [64] = 10 (cannot be [56] which clashes with R23C4) -> min R89C5 = 11, no 1 in R9C5, clean-up: no 5 in R9C1 (step 1h)

5a. 18(4) cage at R1C1 (step 4h) = {349}2/{368}1
5b. Consider combinations for R189C4 (step 4b) = {128}/1{37}
R189C4 = {128}, 2 locked for C4 => R23C4 = {35}, 5 locked for N2
or R189C4 = 1{37} => 18(4) cage = {368}1, 8 locked for R1 => 20(3) cage = {479}
-> no 5 in R1C6
5c. R129C6 (step 3b) = {379/469}, no 8
5d. 8 in N2 only in R3C56 = {48}, locked for R3, 4 locked for N2
5e. R12C6 = [79] -> R9C6 = 3 (hidden cage sum, step 1e) -> R6C8 = 4 (step 1d)
[The rest is fairly straightforward, except for the final step.]
5f. 21(3) cage at R2C1 = {678}, 6,8 locked for R2 and N1
5g. Naked triple {349} in R1C123, 4,9 locked for R1
5h. Naked pair {58} in R1C78, 5 locked for R1 and N3, clean-up: no 2 in R1C59 (step 1g)
5i. R1C4 = 2 (hidden single in R1) -> R89C4 (step 1c) = 9 = [18], R8C8 = 9, R4C2 = 4 (step 1b)
5j. R7C45 = {67} (hidden pair in N8), locked for R7
5k. R78C6 = {24}, locked for C6 and N8 -> R3C56 = [48], R9C5 = 5 -> R9C1 = 1 (step 1h)
5l. R89C5 = [95] = 14 -> R12C5 = 7 = [61], R1C9 = 1, R7C56 = [67]
5m. R2C4 = 5 (hidden single in R2), R3C4 = 3
5n. R9C1 = 1 -> 22(4) cage at R7C2 = {1489/1579/1678}, no 2,3
5o. R9C4 = 8 -> R9C23 = 11 = {29}/[74]
5p. Killer pair 7,9 in 22(4) cage and R9C23, locked for N7

6a. 45 rule on N6 1 remaining outie R3C9 = 1 innie R4C7 = {67}
6b. R3C8 = 9 (hidden single in N3), R1C9 = 1 -> R2C89 = 7 = [34]
6c. R2C7 = 2
6d. Naked pair {67} in R34C7, locked for C7
6e. 6 in R9 only in R9C89, locked for N9
6f. 20(4) cage at R9C6 contains 3,6 = {2369/3467}
6g. R9C7 = {49} -> no 9 in R9C9

7a. 1 in N9 only in 19(4) cage at R6C8 = 4{159}, 5,9 locked for R7 and N9
7b. R9C67 = [34] -> R9C89 = 13 = {67}, 7 locked for R9 and N9
7c. Naked pair {67} in R39C9, locked for C9
7d. R7C2 = 8, R9C1 = 1 -> R8C12 = 13 = {67}, 6 locked for R8
7e. R8C36 = [54] (hidden pair in R8) -> R7C6 = 2
7f. R8C34 = [51] = 6 -> R67C3 = 9 = [63]
7g. R7C1 = 4 -> R456C1 = 12 = {237} (only remaining combination), locked for C1 and N4

8a. 16(3) cage at R4C4 = {178/259} (cannot be {268/358} because R4C4 only contains 7,9, cannot be {367} which clashes with R4C7, cannot be {169} because 1,6 only in R4C6), no 3,6
8b. R5C46 = [46] (hidden pair in N5) -> R5C5 = 3 (cage sum)
8c. 45 rule on C9 3 remaining innies R789C9 = 19 = [586/937] (cannot be {289} because R9C9 only contains 6,7), no 2
8d. R8C8 = 2 (hidden single in N9)

[Then a sting in the tail, now to fix the final combinations in N6.]
9a. 20(4) cage at R4C8 = {1379/1568}
9b. 6 of {1568} must be in R4C8 -> no 5,8 in R4C8
9c. 16(3) cage at R4C4 (step 8a) = {259} (only remaining combination, cannot be {178} which clashes with R4C78, ALS block) = [925] -> 16(3) cage at R6C4 = [781]
9d. 20(4) cage = {1379} (cannot be {1568} = 6{18}5 because R5C78 = {18} clashes with 23(4) cage at R4C3 ALS block since no 1,8 in R6C2) -> R56C7 = [93], R45C8 = {17}, locked for C8

and the rest is naked singles.


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PostPosted: Sat Feb 06, 2021 5:01 am 
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Ha ha Andrew. I know how difficult it is to put you off. I'll go through your WT later but can see it is very different to how I did it (I did it the same way as Mike in the archive) so your WT is definitely needed here. No WT from me.

Attachment:
a44v2.JPG
a44v2.JPG [ 98.78 KiB | Viewed 5184 times ]
edit: Correct pic now! Thanks Andrew.
However, since the v1.5 was fairly straightforward I had a go at the V2. It is really good with a pretty straight-forward start with much more early progress than the v1.5. Hope I haven't messed up the early part. Still haven't finished the whole yet but think its worth posting.

Assassin 44v2
It gets a score of 1.70 and JSudoku uses 3 'complex intersections'.
Code: Select, Copy & Paste into solver:
3x3::k:4608:4608:4608:4608:4100:5125:5125:5125:4360:5385:5385:5385:2060:4100:4100:3855:4360:4360:3090:3090:3090:2060:3094:3094:3855:4360:5402:4123:3090:5917:4126:4126:4126:3855:5154:5402:4123:5917:5917:3367:3367:3367:5154:5154:5402:4123:5917:3631:4144:4144:4144:5154:4916:5402:4123:5687:3631:3385:3385:1595:4916:4916:4916:5687:5687:3631:3906:3906:1595:3397:3397:3397:5687:4937:4937:4937:3906:5197:5197:5197:5197:
Solution:
+-------+-------+-------+
| 9 3 4 | 2 6 7 | 5 8 1 |
| 8 6 7 | 5 1 9 | 2 3 4 |
| 5 1 2 | 3 4 8 | 7 9 6 |
+-------+-------+-------+
| 3 4 1 | 9 2 5 | 6 7 8 |
| 7 5 8 | 4 3 6 | 9 1 2 |
| 2 9 6 | 7 8 1 | 3 4 5 |
+-------+-------+-------+
| 4 8 3 | 6 7 2 | 1 5 9 |
| 6 7 5 | 1 9 4 | 8 2 3 |
| 1 2 9 | 8 5 3 | 4 6 7 |
+-------+-------+-------+
Cheers
Ed


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PostPosted: Fri Feb 12, 2021 11:02 pm 
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Thanks Ed for also posting the v2 as a Revisit. As you said, a pretty straightforward start, with more progress at that stage than for the v1.5. A different key breakthrough step, a type I haven't used for a long time, but not really much harder than the v1.5.

Here's my walkthrough for Assassin A44v2 Revisited:
Prelims

a) R23C4 = {17/26/35}, no 4,8,9
b) R3C56 = {39/48/57}, no 1,2,6
c) R7C45 = {49/58/67}, no 1,2,3
d) R78C6 = {15/24}
e) 20(3) cage at R1C6 = {389/479/569/578}, no 1,2
f) 21(3) cage at R2C1 = {489/579/678}, no 1,2,3
g) 19(3) cage at R9C2 = {289/379/469/478/568}, no 1
h) 12(4) cage at R3C1 = {1236/1245}, no 7,8,9

1a. 12(4) cage at R3C1 = {1236/1245}, CPE no 1,2 in R1C2
1b. 45 rule on N1 2(1+1) outies R1C4 + R4C2 = 6 = {15/24}/[33], no 6,7,8,9
[I missed 3 in N1 in 18(4) cage at R1C1 or in 12(4) cage at R3C1 blocks [33], an implied forcing chain.]
1c. 45 rule on C123 2 outies R19C4 = 10 = [19/28/37/46], clean-up: no 1 in R4C2
1d. 12(4) cage at R3C1 = {1236/1245}, 1 locked for R3 and N1, clean-up: no 7 in R2C4
1e. 45 rule on N9 2(1+1) outies R6C8 + R9C4 = 7 = {16/25/34}, no 7,8,9
1f. 45 rule on C789 3 outies R19C6 = 10 = {46}/[73/82/91], no 3,5 in R1C6, no 5 in R9C6, clean-up: no 2 in R6C8
1g. 45 rule on R1 2 innies R1C59 = 7 = {16/25/34}, no 7,8,9
1h. 45 rule on R9 2 innies R9C15 = 6 = {15/24}

2a. 15(3) cage at R8C4 = {159/168/249/267/348/357} (cannot be {258} which clashes with R78C6, cannot be {456} which clashes with R7C45)
2b. Hidden killer triple 7,8,9 in R7C45, 15(3) cage and R9C4 for N8, R7C45 and 15(3) cage each contain one of 7,8,9 -> R9C4 = {789}, clean-up: no 4 in R1C4 (step 1c), no 2 in R4C2 (step 1b)
2c. 12(4) cage at R3C1 = {1236/1245}, 2 locked for R3 and N1, clean-up: no 6 in R2C4
2d. 3 of {1236} must be in R4C2 -> no 3 in R3C123
2e. 3 in N1 only in R1C123, locked for R1, clean-up: no 4 in R1C59 (step 1g), no 3 in R4C2 (step 1b), no 7 in R9C4 (step 1c)
2f. 12(4) cage at R3C1 = {1245} (only remaining combination), CPE no 4,5 in R12C2

3a. R78C6 = {15/24} and R9C15 (step 1h) = {15/24} interact to form combined cage R78C4 + R9C15 = {15/24}, CPE no 1,2,4 in R9C6, clean-up: no 6,8,9 in R1C6 (step 1f), no 3,5,6 in R6C8 (step 1e)
3b. 20(3) cage at R1C6 = {479/578} (cannot be {569} because R1C6 only contains 4,7), no 6, 7 locked for R1
3c. 7 in N1 only in 21(3) cage at R2C1 = {579/678}, no 4, 7 locked for R2
3d. Hidden killer pair 1,2 in 15(3) cage at R8C4 and R78C6 for N8, R78C6 contains one of 1,2 -> 15(3) cage (step 2a) must contain one of 1,2 = {159/168/249/267}, no 3
[Step 3a was unnecessary in this version but, having found it for v1.5, I kept it in.]
3e. R9C6 = 3 (hidden single in N8) -> R1C6 = 7 (step 1f), R6C8 = 4 (step 1e), clean-up: no 1 in R2C4, no 5,9 in R3C5, no 5 in R3C6
3f. R1C6 = 7 -> R1C78 = 13 = [49]/{58}, no 9 in R1C7
3g. 45 rule on N6 1 outie R3C9 = 1 remaining innie R4C7 = {356789}, no 4 in R3C9, no 1,2 in R4C7
3h. 45 rule on N8 1 remaining innie R9C4 = 8 -> R1C4 = 2 (step 1c), R4C2 = 4 (step 1b), clean-up: no 5 in R1C59 (step 1g), no 6 in R3C4, no 5 in R7C45
3i. Naked triple {125} in R3C123, 5 locked for R3 and N1 -> R23C4 = [53], clean-up: no 9 in 21(3) cage at R2C1, no 9 in R3C6, no 3,5 in R4C7
3j. Naked pair {48} in R3C56, locked for R3 and N2, clean-up: no 8 in R4C7
3k. Naked triple {678} in 21(3) cage at R2C1, 6,8 locked for R2 and N1
3l. Naked pair {19} in R2C56, locked for R2, 1 locked for N2 -> R1C59 = [61], clean-up: no 7 in R7C4
3m. R1C78 = {58} (hidden pair in N3)
3n. 15(3) cage at R2C7 = {267} (only remaining combination) -> R2C7 = 2, R34C7 = {67}, locked for C7
3o. R1C9 = 1, R2C89 = [34] -> R3C8 = 9 (cage sum)
3p. 6 in N8 only in R78C4, locked for C4
3q. 6 in N8 only in R7C45 = [67] or 15(3) cage (step 3d) = {267} = [672] -> 7 in R78C5 (locking cages), locked for C5 and N8
3r. 4 in N5 only in 13(3) cage at R5C4 = {148/247/346}, no 5,9

4a. 20(4) cage at R9C6 contains 3 = {1379/2369/3467}, no 5
4b. 19(4) cage at R6C8 contains 4 = {1459/2458/3457} (cannot be {1468/2467} which clash with 20(4) cage), no 6, 5 locked for R7 and N9, clean-up: no 1 in R8C6
4c. 45 rule on C9 3 remaining innies R789C9 = 19 = {289/379/568}
4d. 6 of {568} must be in R9C9 -> no 6 in R8C9
4e. R7C789 = {159/357} (cannot be {258} which clashes with R789C9 = {289/568} which each contain two of 2,5,8, CCC (combination crossover clash) which I haven’t used for a long time), no 2,8
[The different key step for this variant; fairly straightforward now until the sting in the tail.]
4f. R9C789 = {269/467} (cannot be {179} which clashes with R7C789), no 1, 6 locked for R9 and N9
4g. 1 in R9 only in R9C15 (step 1h) = {15}, 5 locked for R9
4h. R78C6 = {24} (cannot be [15] which clashes with R9C5), locked for C6 and N8 -> R3C56 = [48], clean-up: no 9 in R7C45
4i. R7C45 = [67] -> R7C789 = {159}, 1,9 locked for R7 and N9
4j. R9C67 = [34] = 7 -> R9C89 = 13 = {67}, 7 locked for R9 and N9
4k. R789C9 = {379/568} (cannot be {289} because R9C9 only contains 6,7), no 2
4l. R8C8 = 2 (hidden single in R8) -> R78C6 = [24]
4m. Naked pair {38} in R8C79, locked for R8
4n. Naked pair {29} in R9C23, 9 locked for N7
4o. Naked pair {67} in R39C9, locked for C9

5a. 45 rule on N4 1 remaining innie R6C3 = 1 outie R7C1 + 2 -> R6C3 = {56}, R7C1 = {34}
5b. 14(3) cage at R6C3 = {158/356} (cannot be {167} because 1,7 only in R8C3, cannot be {347} because R6C3 only contains 5,6), no 4,7
5c. R7C1 = 4 (hidden single in R7) -> R6C3 = 6 -> R78C3 = 8 = [35], R7C2 = 8, R9C15 = [15]
5d. R7C1 = 4 -> R456C1 = 12 = {237} (only possible combination), locked for C1 and N4
5e. Naked pair {19} in R28C5, locked for C5

6a. R5C4 = 4 (hidden single in N5) -> R5C56 = 9 = [36/81]
6b. 16(3) cage at R4C4 = {178/259/358} (cannot be {169} which clashes with R5C6, cannot be {367} which clashes with R4C7, cannot be {268} which clashes with R5C56), no 6
6c. R5C6 = 6 (hidden single in N5) -> R5C5 = 3
6d. 16(3) cage at R4C4 = {178/259}
6e. 7 of {178} must be in R4C4 -> no 1 in R4C4
6f. Similarly for 16(3) cage at R6C4, no 1 in R6C4
6g. Naked pair {79} in R46C4, 9 locked for C4 and N5

7a. 1 in N6 only in 20(4) cage at R4C8 = {1379/1568}
7b. 6 of {1568} must be in R4C8 -> no 5,8 in R4C8
7c. 16(3) cage at R4C4 (step 6d) = {259} (cannot be {178} which clashes with R4C78, ALS block) = [925] -> 16(3) cage at R6C4 = [781]
7d. 20(4) cage = {1379} (cannot be {1568} = 6{18}5 because R5C78 = {18} clashes with 23(4) cage at R4C3 ALS block since no 1,8 in R6C2) -> R56C7 = [93], R45C8 = {17}, locked for C8

and the rest is naked singles.


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PostPosted: Mon Feb 15, 2021 8:39 am 
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I did the start to a45v2 differently to Andrew. Then missed his really great step 4e.

a44 v2 start:
Preliminaries
Cage 6(2) n8 - cells only uses 1245
Cage 8(2) n2 - cells do not use 489
Cage 12(2) n2 - cells do not use 126
Cage 13(2) n8 - cells do not use 123
Cage 21(3) n1 - cells do not use 123
Cage 20(3) n23 - cells do not use 12
Cage 19(3) n78 - cells do not use 1
Cage 12(4) n14 - cells do not use 789

1. "45" on r9: 2 innies r9c15 = 6 = {15/24}

2. 6(2)n8 and h6(2)r9c15 must have different combinations since they share n8
2a. -> naked quad 1,2,4,5 -> no 1,2,4,5 in r9c46

3. "45" on n9: 2 outies r6c8 + r9c6 = 7 = [43/16]

4. "45" on n8: 2 innies r9c46 = 11 = [83]
4a. -> r6c8 = 4 (outies n9=7)
4b. -> r9c23 = 11 = {29/47/56} = 2 or 4 or 5
4c. -> combined cage h6(2)r9c15 + h11(2)r9c23 must have 5: locked for r9 (killer single)

5. "45" on c123: 1 remaining outie r1c4 = 2

6. "45" on n2: 1 remaining innie r1c6 = 7
6a. r1c78 = 13 = [49]/{58}

7. "45" on n1: 1 remaining outie r4c2 = 4
7a. -> r3c123 = {125}: 1,5 locked for r3 and n1
7b. -> r1c123 = 16 = {349} only: all locked for r1, 4 & 9 for n1

8. 8(2)n2 = [53] only

9. 12(2)n2 = {48} only: both locked for n2 and r3

10. r1c78 = {58} only: both locked for n3

11. 17(4)n3 = {1349/1367}(no 2)

12. r2c7 = 2 (hsingle n3)
12a. -> r34c7 = 13 = {67} only: both locked for c7

13. "45" on n3: 1 innie r3c9 = 1 remaining outie r4c7 = {67}

14. r3c8 = 9 (hsingle r3)
14a. -> 17(4)n3 = [1349]
14b. r1c5 = 6

15. r9c789 = 17 = {179/269/467}
15a. -> sp15(3)r7c789: {168/267} blocked
15b. = {159/258/357}(no 6)
15c. must have 5: locked for r7 and n9

16. combined cage sp15(3)r7c789 + sp17(3)r9c789 as {357}+{269} forces both 6(2) in n8 and r9 to be {15} through 13(2)n8
16a. -> sp15(3)r7c789 = {159/258}(no 3,7)

17. 4,6,7 in n9 only in r89
17a. -> {49/67}[2] in 15(3)n8 blocked since it forces 4 into r9 in both r9c1 and r9c789 (see step 15)
17b. -> no 2 in r9c5
17c. -> no 4 in r9c1

18. r39c1 = {125}
18a. -> 16(4)r4c1: {1249/1258/1267/1357/1456/2356} all blocked (Almost Locked Set ALS)
18b. = {1348/2347}(no 5,6,9)
18c. must have 4 -> r7c1 = 4
18d. must have 3: locked for c1 and n4

on from there. Much easier now except for the sting at the end. Pick up Andrew's WT for a very nice way to finally crack it.
Cheers
Ed


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