This puzzle proved to be the opposite for me, with progression possible in big leaps and bounds. Hopefully, I haven't made one of those logic errors that result in a lucky fake breakthrough I've checked the WT through already, so it should be OK (unless I was blind in the same place twice...).Afmob (on A73 V1.5 thread) wrote:...a lot of little moves...
Rating: 1.0 ? Will be interested to hear what the rest of you think.
Edit: Just seen that SS rates this at 1.88!
Assassin 87 Walkthrough
Prelims
a) 10(2) at R1C3 = {19/28/37/46} (no 5)
b) 15(2) at R12C5 = {69/78}
c) 5(2) at R1C6 = {14/23}
d) 11(2) at R23C4, R9C34 and R9C67 = {29/38/47/56} (no 1)
e) 9(2) at R23C6 = {18/27/36/45} (no 9)
f) 12(2) at R34C5 = {{39/48/57} (no 1,2,6)
g) 14(4) at R3C8 = {1238/1247/1256/1346/2345} (no 9)
h) 24(3) at R6C6 = {789}
i) 7(2) at R78C1 = {16/25/34} (no 7..9)
j) 14(2) at R7C9 = {59/68}
k) 13(4) at R8C7 = {1237/1246/1345} (no 8,9); 1 locked for N9
1. Innies N2: R1C46+R3C5 = 10(3) = {127/136/145/235} (no 8,9)
1a. R1C46 cannot sum to 5 due to R1C7
1b. -> no 5 in R3C5
1c. possible permutations are: [127/217]
(Note: [613] blocked because it would force a 4 into both of R1C37)
1d. -> R3C5 = 7
1e. -> R4C5 = 5
1f. R1C46 = {12}, locked for R1 and N2
1g. cleanup: no 3,4,6,7 in R1C3; no 8 in R12C5; no 4,9 in R23C4; no 8 in R23C6
2. Naked pair (NP) at R12C5 = {69}, locked for C5 and N2
2a. cleanup: no 5 in R23C4; no 3 in R23C6
2b. NP at R23C4 = {38}, locked for C4
2c. NP at R23C6 = {45}, locked for C6
2d. cleanup: no 3,8 in R9C3; no 6,7 in R9C7
3. Innies C6789: R58C6 = 10(2) = {19/28/37} (no 6)
3a. -> R58C6 and R67C6 form killer triple (KT) on {789} in C6
3b. -> no 7,8,9 elsewhere in C6
3c. cleanup: no 2,3,4 in R9C7
4. Innies C1234: R58C4 = 11(2) = {29}/{47}/[65] (no 1)
4a. no 6 in R8C4
5. 13(4) at R8C7 = {1237/1246/1345}
5a. -> must have exactly 2 of {234}
5b. only other place for {234} in N9 is R7C8
5c. -> R7C8 = {234} (no 5..9)
6. Outies N36: R14C6+R7C8 = 9(2+1)
6a. R1C6 = {12} -> R4C6+R7C8 must sum to 7 or 8 = [34/62] (only possible permutations)
6b. -> R4C6 = {36}, R7C8 = {24}
7. Innies N9: R7C78+R9C7 = 18(3) = [729/945] (no 8) (only possible permutations)
7a. 9 locked in R79C7 for C7 and N9
7b. cleanup: no 3 in R9C6; no 5 in R78C9
8. Naked pair (NP) at R78C9 = {68}, locked for C9 and N9
9! Innie/Outie (I/O) diff. C9: R67C8 = R19C9 + 8
9a. Max. R67C8 = 13 -> max. R19C9 = 5
9b. -> R19C9 = [31/32/41]
9c. -> R1C9 = {34}; R9C9 = {12}
9d. Min. R19C9 = 4 -> min. R67C8 = 12
9e. -> R67C8 = [84/94]
9f. -> R7C8 = 4; R6C8 = {89}
9g. -> R79C7 = [95] (step 7)
9h. -> R9C6 = 6 (cage sum)
9i. -> R4C6 = 3
9j. -> R1C6 = 2 (step 6)
9k. -> R1C7 = 3 (cage sum); R1C34 = [91]
9l. -> R19C9 = [41] (step 9b); R12C5 = [69]
9m. -> R6C8 = 9 (step 9.)
9n. cleanup: no 7,8 in R58C6 (step 3); no 2 in R9C4; no 3 in R8C1
10. Hidden single (HS) at R3C9 = 9
10a. -> R24C9 = [52] (only possible permutation)
10b. -> R23C6 = [45]
11. Innie N3: R3C8 = 1
11a. -> R4C78 = [46] (only possible permutation)
12. HS in C8/N6 at R5C8 = 5
12a. -> split 9(2) at R56C7 = {18}, locked for C7
13. 18(4) at R3C2 cannot have both of {79} due to cage sum
13a. -> no 7,9 in R4C23
13b. -> R4C23 = {18}, locked for N4
13c. -> split 9(2) at R3C2+R4C4 = [27] (only possible permutation)
13d. cleanup: no 4 in R9C3; no 4 in R58C4 (step 4)
14. R67C6 = [87]
14a. -> R56C7 = [81]
15. R3C7 = 6; R4C1 = 9 (both naked singles)
15a. split 9(2) at R23C1 = [18/63] (only possible permutations)
15b. -> R3C3 = 4 (HS@R3/N1)
16. Innies N7: R7C23+R9C3 = 16(3)
16a. -> R9C3 can't be 2, because {68} in R7C23 blocked by R7C9
16b. -> R9C34 = [74]
16c. -> split 9(2) at R7C23 = {18/36} (no 2,5)
16d. -> R7C23 and R7C9 form KP on {68}, locked for R7
16e. cleanup: no 1 in R8C1
17. 12(3) at R6C4+R7C34 = [615] (only possible permutation)
17a. -> R7C2 = 8 (step 16c)
17b. -> R4C23 = [18]; R78C9 = [68]
17c. cleanup: no 2,6 in R8C1
18. NP at R79C1 = {23}, locked for C1 and N7
18a. cleanup: no 6 in R2C1 (step 15a)
19. HS in C1 at R5C1 = 6
19a. -> split 7(2) at R6C12 = [43] (only possible permutation)
19b. cleanup: no 3 in R7C1
Now only naked singles left.