I tried Human Solvable 1 for the first time a few days ago and managed to finish it a couple of days later. Thanks HATMAN for a challenging puzzle!
I enjoyed some of the steps]in the other walkthroughs, breakthroughs and outlines. This puzzle required a lot of chains, either written as such or written as permutation analysis; they even seem necessary to reduce the upper-left corner of the R28C28 "ring" to pairs of combinations. After working through how others solved this puzzle, I've realised that I didn't get enough out of the "ring"; particularly the use of chains in that "ring" to reduce the 17(3) and 10(3) cages in N5 to two combinations each. I think Para must also have used that "ring" for his step 2; it's a pity that Para is no longer active on this site so I can't ask him.
My solving path was more like Afmob's than the other ones.
Prelims
a) 7(2) cage at R1C2 = {16/25/34}, no 7,8,9
b) 10(2) cage at R1C8 = {19/28/37/46}, no 5
c) R2C34 = {49/58/67}, no 1,2,3
d) R2C67 = {39/48/57}, no 1,2,6
e) R34C2 = {49/58/67}, no 1,2,3
f) R34C8 = {39/48/57}, no 1,2,6
g) R67C2 = {59/68}
h) R67C8 = {49/58/67}, no 1,2,3
i) 6(2) cage at R8C1 = {15/24}
j) R8C34 = {59/68}
k) R8C67 = {49/58/67}, no 1,2,3
l) 5(2) cage at R8C9 = {14/23}
m) 10(3) cage at R4C6 = {127/136/145/235}, no 8,9
n) 10(3) cage at R5C7 = {127/136/145/235}, no 8,9
1. R34C2 = {49/67} (cannot be {58} which clashes with R67C2), no 5,8
1a. Killer pair 6,9 in R34C2 and R67C2, locked for C2, clean-up: no 1 in R2C1
2. R8C67 = {49/67} (cannot be {58} which clashes with R8C34), no 5,8
2a. Killer pair 6,9 in R8C34 and R8C67, locked for R8
3. 45 rule on N1 2 innies R2C3 + R3C2 = 13 = {49/67}, no 5,8 in R2C3, clean-up: no 5,8 in R2C4
4. 45 rule on N3 2 innies R2C7 + R3C8 = 10 = {37} (only remaining combination), locked for N3, clean-up: R2C6 = {59}, R4C8 = {59}
4a. 45 rule on N3 2 outies R2C6 + R4C8 = 14 = {59}, CPE no 5,9 in R2C8 + R4C6
4b. Killer pair 7,9 in R2C34 and R2C67, locked for R2, clean-up: no 1 in R1C8
5. 45 rule on N9 2 innies R7C8 + R8C7 = 15 = [69/87/96], R7C8 = {689}, R8C7 = {679}, clean-up: R6C2 = {457}, R8C6 = {467}
6. 45 rule on N7 2 innies R7C2 = R8C3 = 14 = {59/68}
[This is currently just for use with the next step.]
7. Chaining round the R28C28 ring of 2-cell cages, using innies for N1, N3 and N7
R2C34 = {49} => R34C2 (step 3) = {49} => R67C2 = {68} => R8C34 (step 6) = {68} => R8C67 = [49], R67C8 (step 5) = [76]
or R2C34 = {67} => R2C67 = [93] => R34C8 = [75] => R67C8 not [58], R34C2 (step 3) = {67} => R67C2 = {59} => R8C34 (step 6) = {59} => R8C67 = {67} => R67C8 not [76] => R67C8 = [49]
-> R67C8 = [49/76], no 5,8, clean-up: no 7 in R8C7 (step 5), no 6 in R8C6
Also from the chains, no 7 in R3C2, no 6 in R4C2, no 6 in R2C3 (step 3), no 7 in R2C4, no 6,9 in R7C2, no 5,8 in R6C2, no 5,8 in R8C3 (step 6), no 6,9 in R8C4
7a. Naked pair {69} in R7C8 + R8C7, locked for N9
7b. Killer pair 7,9 in R34C8 and R67C8, locked for C8, clean-up: no 1 in R2C9
7c. 45 rule on N9 2 outies R6C8 + R8C6 = 11 = {47}, CPE no 4,7 in R6C6 + R8C8
8. 45 rule on R5 3 innies R5C456 = 21 = {489/579/678}, no 1,2,3
8a. 4 of {489} must be in R5C5 -> no 4 in R5C46
9. 10(3) cage at R4C6 = {127/136/145/235}
9a. 6,7 of {127/136} must be in R5C5 -> no 6,7 in R4C6 + R6C4
10. 17(3) cage at R4C1 = {269/458/467} (cannot be {179/278} which clash with 10(3) cage at R4C6 because of the shared 7 in R5C5, cannot be {368} which clashes with 10(3) cage because of the shared 6 in R5C5, cannot be {359} which clashes with R5C456 because of the shared 5 in R5C5), no 1,3
10a. 5 of {458} must be in R5C5 (cannot be [548/845] which clash with R5C456 because of shared 4 in R5C5), no 5 in R4C4 + R6C6
10b. 8 of {458} must be in R6C6 -> no 8 in R4C4
10c. 6 of {269) must be in R5C5, 6 of {467} must be in R6C6 -> no 6 in R4C4
10d. 6 of {467} must be in R6C6 => R6C2 = 9, R34C2 = [67] => {467} can only be [476]
10e. 17(3) cage = {269/458/467} = [269/458/476/962] -> R4C4 = {249}, R5C5 = {567}
11. R5C456 (step 8) = {579/678}, 7 locked for R5 and N5
11a. 6 of {678} must be in R5C5 (cannot be [678/876] which clashes with 17(3) cage at R4C4 because of shared 7 in R5C5), no 6 in R5C46
11b. 10(3) cage at R5C7 = {136/145/235}
11c. Killer pair 5,6 in R5C456 and 10(3) cage at R5C7, locked for R5
12. 10(3) cage at R4C6 = {127/136/235} (cannot be {145} which clashes with 17(3) cage at R4C4 because of shared 5 in R5C5), no 4 in R4C6 + R6C4
12a. R5C5 = {567} -> no 5 in R6C4
13. R34C2 = {49}/[67], R67C2 = [68/95] -> combined cage R3467C2 = {49}[68]/[67][96] -> R46C2 = [46/79/96]
13a. 14(3) cage at R4C1 = {239/248} (cannot be {149} which clashes with R46C2), no 1, 2 locked for R5 and N4
13b. Killer pair 4,9 in R46C2 and 14(3) cage, locked for N4
14. 1 in R5 only in 10(3) cage at R5C7, locked for N6
14a. 10(3) cage (step 11b) = {136/145}
[Looking a bit more at interactions between cages in N5]
15. Consider permutations for 17(3) cage at R4C1 (step 10e) = {269/458/467} = [269/458/476/962]
17(3) cage = [269/962]
or 17(3) cage = [458] => 10(3) cage at R4C6 = {235}, R5C456 = {579}
or 17(3) cage = [476] => 10(3) cage at R4C6 = {127}, R5C456 = {579}
-> killer pair 2,9 in 17(3) cage, 10(3) cage and R5C456, locked for N5
16. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239}, locked for N4 => R6C2 = 6, R34C2 = [94], R2C3 = 4, R2C4 = 9
or 14(3) cage = {248}, locked for R5 => R5C456 = {579}, locked for N5 => 17(3) cage at R4C4 (step 10e) = [458/476]
-> no 9 in R4C4
16a. 4 must be in R4C2 or R4C4, locked for R4, CPE no 4 in R2C2 using D\
16b. 17(3) cage at R4C1 (step 10e) = {269/458/467} = [269/458/476], no 2 in R6C6
17. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239}, 9 locked for N4
or 14(3) cage = {248}, locked for R5 => R5C456 = {579} => 17(3) cage at R4C1 (step 10e) = [458/476] => R4C4 = 4 => R2C4 = 6 (cannot be {49} because R4C4 “sees” both of R2C4 + R4C2), R2C3 = 7, R3C2 = 6, R6C2 = 9
-> 9 must be in 14(3) cage
or R6C2, locked for N4, clean-up: no 4 in R3C2, no 9 in R2C3, no 4 in R2C4
17a. 9 in R4 only in R4C789, locked for 6
18. 9 in R2 only in R2C46, locked for N2
18a. 17(3) cage at R1C4 = {278/368/458/467}, no 1
18b. 9 in C5 only in R79C5, locked for N8
19. Consider combinations for 14(3) cage at R5C1 (step 13a) = {239/248}
14(3) cage = {239} => 4 in R5 must be in 10(3) cage at R5C7
or 14(3) cage = {248}, locked for N4 => R34C2 = [67], R67C2 = [95], R8C3 = 9, R8C7 = 6, R7C8 = 9, R6C8 = 4
-> 4 must be in 10(3) cage at R5C7 or R6C8, locked for N6
20. R1C2 + R2C1 = [16/25/34/52] (cannot be [43] which clashes with R2C37), no 4 in R1C2, no 3 in R2C1
21. Hidden killer pair 4,8 in R1C9 + R2C8 + R3C7 and R7C3 + R8C2 + R9C1 for D/, R1C9 + R2C8 + R3C7 cannot contain both of {48} (which would clash with 10(2) cage at R1C8), R7C3 + R8C2 + R9C1 cannot contain both of {48} (which would clash with R7C2 + 6(2) cage at R8C1, killer ALS block) -> R1C9 + R2C8 + R3C7 and R7C3 + R8C2 + R9C1 must each contain one of 4,8
21a. Killer pair 4,8 in 10(2) cage at R1C8 and R1C9 + R2C8 + R3C7, locked for N3
21b. Killer pair 4,8 in R7C3 + R8C2 + R9C1, R7C2 and 6(2) cage at R8C1, locked for N7
21c. Hidden killer pair 4,8 in R7C2 + 6(2) cage and R7C3 + R8C2 + R9C2 for N7 -> R7C2 + 6(2) cage must contain one of 4,8 = 5{24}/8{15}, 5 locked for N7
[Although I spotted this hidden killer pair, I missed that there is another hidden killer pair 3,7 on D/. 10(3) cage at R4C6 must contain one of 3,7 -> R7C3 + R8C2 + R9C1 must contain one of 3,7 -> R7C1 + R9C3 must contain one of 3,7.
I’d spotted 4(2+2) outies R1C7 + R3C9 + R7C1 + R9C3 = 15 but couldn’t see how to use this. Maybe the fact that R7C1 + R9C3 must contain one of 3,7, but 4(2+2) outies don’t contain 4,8 might make these outies useful, or it might require a bit more; Afmob also had 1 for N3 only in R1C7 + R3C9.]22. 13(3) cage at R2C5 = {148/157/238/247/256/346}
22a. 45 rule on C5 3 innies R159C5 = 17 = {269/278/359/368/467} (cannot be {179} because 1,9 only in R9C5, cannot be {458} which clashes with 13(3) cage), no 1
22b. 5 of {359} must be in R5C5 -> no 5 in R19C5
22c. 13(3) cage = {148/157/238/247/346} (cannot be {256} which clashes with R159C5)
23. From analysis of the cages in N5, R46C5 = {16/38}/[54], no 5 in R6C5
24. 9 in C5 only in R159C5 (step 22a) = {269/359}
or in 15(3) cage at R6C5 = {159/249} -> 15(3) cage = {159/168/249/258/267/348/357} (cannot be {456} which clashes with R159C5 = {159/249}, locking out cages)
24a. R46C5 (step 23) = {16/38}/[54]
Consider combinations for R46C5
R46C5 = {38} => 15(3) cage cannot be {348} which clashes with R46C5, CCC
or R46C5 = [54] => R6C8 = 7, R7C8 = 6, R8C7 = 9, R8C3 = 6, R8C4 = 8 => 15(3) cage cannot be {348}
-> 15(3) cage = {159/168/249/258/267/357} (cannot be {348})
24b. Consider combinations for R46C5
R46C5 = {38}, locked for N5 => R4C6 + R6C4 = {12} => R5C5 = 7 (cage total) => 17(3) cage at R4C4 (step 10e) = [476] => R4C2 = 7, R3C2 = 6, R6C2 = 9, R7C2 = 5, R8C3 = 9, R8C4 = 5 => 15(3) cage cannot be {258/357}
or R46C5 = [54] => 15(3) cage cannot be {258/357}
-> 15(3) cage = {159/168/249/267} (cannot be {258/357}, no 3, clean-up: no 8 in R4C5 (step 23)
24c. Consider combinations for R46C5
R46C5 = {16}, locked for N5 => R4C6 + R6C4 = {23} => R5C5 = 5 (cage sum) => 15(3) cage cannot be {159}
or R46C5 = [54] -> 15(3) cage cannot be {159}
-> 15(3) cage = {168/249/267} (cannot be {159}), no 5
25. 15(3) cage at R6C5 (step 24c) = {168/249/267}
25a. R159C5 (step 22a) = {359/368} (cannot be {269/278/467} which clash with 15(3) cage), no 2,4,7, 3 locked for C5, clean-up: no 8 in R6C5 (step 23)
26. R46C5 (step 23) = {16}/[54], R5C5 = {56}, killer pair 5,6 locked for C5 and N5
27. 3 in N5 only in 10(3) cage at R4C6, locked for D/
28. 15(3) cage at R6C5 (step 24c) = {249/267} (cannot be {168} which clashes with R46C5 = {16}, CCC), no 1,8, 2 locked for C5 and N8, clean-up: no 6 in R4C5 (step 26)
28a. R6C5 = {46} -> no 4 in R78C5
29. 14(2) cage at R8C3 + 13(2) cage at R8C6 = 27, R8C37 = {69} = 15 -> R8C46 = 12 = [57/84]
29a. 16(3) cage at R9C4 = {169/349/367} (cannot be {178} which clashes with R8C46, cannot be {358} which clashes with R8C4, cannot be {457} which clashes with R8C6), no 5,8
[And suddenly it crumbles …]
30. Killer pair 7,9 in R78C5 and 16(3) cage at R9C4, locked for N8 -> R8C6 = 4, R8C7 = 9, R7C8 = 6, R6C8 = 7, R3C8 = 3, R4C8 = 9, R2C7 = 7, R2C6 = 5, R2C3 = 4, R2C4 = 9, R3C2 = 9 (step 3), R4C2 = 4, R6C2 = 6, R7C2 = 8, R8C3 = 6, R8C4 = 8, R4C4 = 2, placed for D\, R5C4 = 7, R6C5 = 4, clean-up: no 2,3 in R1C2, no 2 in 6(2) cage at R8C1, no 2 in R8C9, no 1 in R9C8
30a. Naked pair {13} in R4C6 + R6C4, locked for N5 and D/ -> R5C5 = 6 (cage sum), placed for both diagonals, R4C5 = 5
30b. Naked pair {15} in 6(2) cage at R8C1, locked for N7
31. R9C1 = 4 (hidden single in N7), placed for D/
32. R1C8 = 4 (hidden single in N3), R2C9 = 6, R2C1 = 2, R1C2 = 5, R2C8 = 8, R2C5 = 1, R3C5 = 7 (cage sum), R2C2 = 3, placed for D\, R78C5 = [92], R9C5 = 3, R1C5 = 8, R9C2 = 1, R8C1 = 5, R8C8 = 1, placed for D\, R3C3 = 8, placed for D\, R6C6 = 9
and the rest is naked singles, without using the diagonals.
Rating Comment.
Afmob wrote:
Rating: 1.75. I used lots of chains and some Hidden Killer pairs.
That comment also applies to my solving path. I don't think my steps were any harder than Afmob's ones so I'll also rate my walkthrough at 1.75.