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3x3::k:7169:7169:7169:4610:3587:3587:4100:4100:2309:1798:7169:4610:3335:3335:3587:3587:4100:2309:1798:4610:2056:3849:3849:5386:5386:2315:2315:4610:3084:2056:3853:3853:5386:5386:3598:3598:3343:3084:2056:3853:4880:4880:2065:2065:3598:3343:3343:6162:6162:4880:6675:6675:6675:3604:2069:2069:6162:6162:2070:6675:3604:3604:2839:3096:2585:3354:3354:2070:6675:3611:4380:2839:3096:2585:2585:2333:2333:3611:3611:4380:2839:

it led to a straightforward and fairly quick finish and, more important for me, it avoided messy combination analysis for the 18(4) cage at R1C4 interacting with Innies for N1, which I'd started looking at.

I'll rate my walkthrough for A206 at Easy 1.5 because I used a very short forcing chain. From Ed's introductory comment it's likely that the rating for this puzzle should be a bit lower although possibly using a longer solving path.

Prelims

a) R12C9 = {18/27/36/45}, no 9
b) R23C1 = {16/25/34}, no 7,8,9
c) R2C45 = {49/58/67}, no 1,2,3
d) R3C45 = {69/78}
e) R3C89 = {18/27/36/45}, no 9
f) R45C2 = {39/48/57}, no 1,2,6
g) R5C78 = {17/26/35}, no 4,8,9
h) R7C12 = {17/26/35}, no 4,8,9
i) R78C5 = {17/26/35}, no 4,8,9
j) R89C1 = {39/48/57}, no 1,2,6
k) R8C34 = {49/58/67}, no 1,2,3
l) R89C8 = {89}
m) R9C45 = {18/27/36/45}, no 9
n) 8(3) cage at R3C3 = {125/134}
o) 19(3) cage in N5 = {289/379/469/478/568}, no 1
p) 10(3) cage in N7 = {127/136/145/235}, no 8,9
q) 11(3) cage in N9 = {128/137/146/236/245}, no 9
r) 28(4) cage in N1 = {4789/5689}, no 1,2,3
s) 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. Naked pair {89} in R89C8, locked for C8 and N9, clean-up: no 1 in R3C9
1b. 8(3) cage at R3C3 = {125/134}, 1 locked for C3
1c. 28(4) cage in N1 = {4789/5689}, 8,9 locked for N1
1d. 9 in C9 only in R456C9, locked for N6

2. R2C45 = {49/58} (cannot be {67} which clashes with R3C45), no 6,7
2a. Killer pair 8,9 in R2C45 and R3C45, locked for N2
2b. 14(4) cage at R1C5 = {1238/1247/1256/1346} (cannot be {2345} which clashes with R2C45)

3. 45 rule on N3 2 innies R23C7 = 11 = [29]/{38/47/56}, no 1, no 2 in R3C7
3a. 14(4) cage at R1C5 (step 2b) = {1238/1247/1256/1346}, 1 locked for N2

4. 45 rule on N7 2 innies R78C3 = 15 = {69/78}, clean-up: no 8,9 in R8C4
4a. Hidden killer pair 8,9 in R78C3 and R89C1 for N7, R78C3 contains one of 8,9 -> R89C1 must contain one of 8,9 -> R89C1 = {39/48} (cannot be {57} which doesn’t contain one of 8,9), no 5,7
4b. R23C1 = {16/25} (cannot be {34} which clashes with R89C1), no 3,4

5. 45 rule on N1 3 innies R2C3 + R3C23 = 10 = {136/235} (cannot be {127/145} which clash with R23C1), no 4,7

6. 4,7 in N1 only in 28(4) cage = {4789} (only remaining combination), no 5,6

7. 45 rule on N4 2 innies R4C1 + R6C3 = 1 outies R3C3 + 12
7a. Min R4C1 + R6C3 = 13, no 1,2,3

8. 10(3) cage in N7 = {127/145/235} (cannot be {136} which clashes with R7C12), no 6

9. 45 rule on N9 2(1+1) outies R6C9 + R9C6 = 11 = {29/38/47/56}, no 1 in R6C9 + R9C6

10. 45 rule on R6789 1 innie R6C5 = 1 outie R5C1 + 1, no 9 in R5C1

11. 45 rule on N5 3 innies R4C6 + R6C46 = 11 = {128/137/146/236/245}, no 9

12. 45 rule on N4 4 innies R4C1 + R456C3 = 20 = {1289/1469/1478/1568/2567} (cannot be {1379} because no 4 in R3C3, cannot be {2369/2378/2468} because 8(3) cage at R3C3 cannot contain both of 2,3 or both of 2,4, cannot be {2459/3458/3467} which clash with R45C2), no 3 in R45C3
12a. 6,7,8,9 only in R4C1 + R6C3 -> no 4,5 in R4C1 + R6C3

13. 6 in N1 only in R2C13 + R3C23, CPE no 6 in R4C1

14. 45 rule on N1 2 outies R1C4 + R4C1 = 1 innie R3C3 + 8
14a. Max R3C3 = 5 -> max R1C4 + R4C1 = 13, min R4C1 = 7 -> max R1C4 = 6

[Ed wrote “This one is technically easier than the last couple. No tricks or really advanced moves needed.” Even so I’ve used a short forcing chain which cracks the puzzle; after that it’s straightforward.]

15. Consider placement for 1 in N1
R2C1 = 1 => R3C1 = 6 => R3C45 = {78}, locked for R3
or 1 in R3C123 => no 1 in R3C8 => no 8 in R3C9
-> no 8 in R3C9, clean-up: no 1 in R3C8

16. Hidden killer pair 8,9 in R3C45 and R3C7 for R3, R3C45 must contain one of 8,9 -> R3C7 = {89}, clean-up: R2C7 = {23} (step 3)

17. Combined cage R23C45 = 13(2) + 15(2) = 28(4) = {4789/5689}
17a. 14(4) cage at R1C5 (step 2b) = {1247/1256} (cannot be {1346} which clashes with R23C45), no 3 -> R2C7 = 2, R1C56 + R2C6 = {147/156}, R3C7 = 9 (step 3), clean-up: no 7 in R12C9, no 5 in R3C1, no 6 in R3C45, no 7 in R3C89, no 6 in R5C8

18. Naked pair {78} in R3C45, locked for R3 and N2, clean-up: no 5 in R2C45
18a. Naked pair {49} in R2C45, locked for R2 and N2, clean-up: no 5 in R1C9
18b. R1C4 + R3C6 = {23} (hidden pair in N2)

19. 4 in R3 only in R3C89 = {45}, locked for R3 and N3
19a. 6 in R3 only in R3C12, locked for N1, clean-up: no 1 in R3C1
19b. Killer pair 3,5 in R2C3 and 8(3) cage at R3C3, locked for C3

20. 11(3) cage in N9 = {146/236} (cannot be {137} which clashes with R12C9, cannot be {245} which clashes with R3C9), no 5,7, 6 locked for C9 and N9, clean-up: no 3 in R12C9, no 5 in R9C6 (step 9)
20a. Naked pair {18} in R12C9, locked for C9 and N3, clean-up: no 4 in 11(3) cage in N9, no 3 in R9C6 (step 9)
20b. Naked triple {236} in 11(3) cage, locked for C9 and N9, clean-up: no 8,9 in R9C6 (step 9)

21. 14(3) cage at R6C9 = {149} (only remaining combination) -> R6C9 = 9, R7C78 = {14}, locked for R7 and N9, R9C6 = 2 (step 9), R3C6 = 3, R1C4 = 2, clean-up: no 7 in R7C12, no 6 in R7C5, no 6,7 in R8C5, no 7 in R9C45
21a. Naked pair {57} in R89C7, locked for C7, clean-up: no 1,3 in R5C8
21b. 7 in N3 only in R12C8, locked for C8, clean-up: no 1 in R5C7

22. R2C3 + R3C23 (step 5) = {136} (only remaining combination, cannot be {235} because 3,5 only in R2C3) -> R2C3 = 3, R3C23 = [61], R23C1 = [52], R4C1 = 7 (cage sum), clean-up: no 5 in R45C2, no 3 in R7C2
22a. R5C9 = 7 (hidden single in C9)
22b. R45C3 = {25} (hidden pair in C3), locked for N4

23. R3C67 = [39] = 12 -> R4C67 = 9 = {18} (cannot be {45} which clashes with R4C9), locked for R4, clean-up: no 4 in R5C2

24. 9 in N4 only in R45C2 = {39}, locked for C2 and N4

25. 13(3) cage in N4 = {148} (only remaining combination), locked for N4 -> R6C3 = 6, clean-up: no 9 in R78C3 (step 4), no 4,7 in R8C4
25a. Naked pair {78} in R78C3, locked for C3 and N7 -> R9C3 = 4, R1C3 = 9, clean-up: no 5 in R9C45
25b. R7C1 = 6 (hidden single in C1), R7C2 = 2, R7C9 = 3, R9C9 = 6, R8C9 = 2, clean-up: no 5 in R8C5, no 3 in R9C45
25c. 1 in C1 only in R56C1, locked for N4

26. Naked pair {18} in R9C45, locked for R9 and N8 -> R8C5 = 3, R7C5 = 5, R8C4 = 6, R8C3 = 7, R89C1 = [93], R8C6 = 4
26a. 4 in N6 only in 14(3) cage = {347} (only remaining combination) -> R4C89 = [34], R3C89 = [45], R45C2 = [93], R5C7 = 6, R5C8 = 2, R7C78 = [41], R6C8 = 5, R45C3 = [25]

27. R4C45 = [56] -> R5C4 = 4 (cage sum), R2C45 = [94]
27a. Naked pair {89} in R5C56, locked for R5 and N5 -> R4C6 = 1

and the rest is naked singles.

End of Andrew's step 6 here


7. "45" on r12: 1 outie r3c1 + 3 = 2 innies r1c4 + r2c3
7a. -> no 3 in r1c4 (IOU)

8. 3 in r1 only in r1c56789 -> no 3 in r2c7 (CPE)
8a. no 8 in r3c7 (h11(2)r23c7)

9. "45" on n14: 1 outie r1c4 + 4 = 1 innie r6c3
9a. r1c4 = (245), r6c3 = (689)

Now the hardest one
10. "45" on r12: 3 innies r1c4 + r2c13 = 10
10a. the only way for r1c4 + r2c3 to sum to 9 (and -> have 1 in r2c1) is [45]: however, this is blocked by 13(2)n2 which must have 4/5
10b. -> no 1 in r2c1
10c. no 6 in r3c1

11. 1 in n1 only in r3: locked for r3
11a. no 8 in r3c9

12. 8 in r3 only in 15(2)n2 = {78} only: both locked for r3 and n2

Cracked.