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1. C789+N2
a) Innies N23 = 31(2+2) <> 1,2,3,4; R1C45 <> 5 and R3C7 = (89) since R3C4 <= 7
b) Innies N3 = 14(3): R2C7 <> 6,7,8,9 since R3C7 >= 8
c) 10(3): R3C3+R4C4 = (1234) since R3C4 >= 5
d) Innies+Outies C9: 7 = R23C8 - R1C9 -> R23C8 <> 7 (IOU @ N3)
e) Innies+Outies C9: -8 = R23C9 - R1C8 -> R23C9 <> 8 (IOU @ N3)
f) Innies+Outies R9: 2 = R8C78 - R9C9 -> R8C78 <> 2 (IOU @ N9)
g) Innies+Outies R9: -9 = R9C78 - R8C9 -> R9C78 <> 9 (IOU @ N9)

2. R789
a) 9 locked in 14(2) @ R9 = {59} locked for R9+N8
b) Innies+Outies C1: 7 = R78C2 - R9C1 -> R78C2 <> 7 (IOU @ N7)
c) Innies+Outies C1: -7 = R78C1 - R9C2 -> R78C1 <> 7 (IOU @ N7)
d) 8(2) = {17/26}
e) Killer pair (12) locked in 8(2) + 5(2) for R9
f) 8 locked in Innies R9 = 18(3) = 8{37/46} for N9
g) Outies R9 = 11(3) <> 9

3. C789 !
a) ! Hidden Killer triple (789) in 9(2) @ C9 since Innies C9 = 16(3) <> 8 and 13(2) can only have one of them -> 9(2) = [18/27]
b) Outies R9 = 11(3): R8C78 <> 1 since R8C9 = (12) and R8C78 <> 8
c) 20(4) = 34{58/67} -> 3,4 locked for N9
d) 7(2) = {16/25}
e) 3 locked in Innies C9 = 16(3) = 3{49/67} for N3
f) 8(2) = [17/26/53]
g) 7 locked in Innies C9 @ N3 = 16(3) = {367} locked for C9+N3
h) R9C9 = 8 -> R8C9 = 1
i) 13(2) = {49} locked for N6
j) 9 locked in Innies N9 = 16(3) = {259} locked for R7
k) Innies N69 = 10(2) = [19/82]

4. C789 !
a) Killer pair (12) locked in Innies N3 + Innies N69 for C7
b) ! Hidden Killer pair (29) in Innies N3 = 14(3) = 4{19/28} -> 4 locked for C7+N3
c) 5 locked in R123C8 @ N3 for C8
d) Hidden Single: R7C9 = 5 @ N9 -> R6C9 = 2
e) 8(2) = {17} locked for C8+N6
f) R4C7 = 8, R3C7 = 9, R7C7 = 2
g) 5(2) = {14} locked for R1

5. C123
a) Innies N14 = 8(2) = [17/35]
b) 19(3) = 8{47/56} -> 8 locked for D/; R6C4+R7C3 = (468)
c) 12(2) = {39/57}
d) Innies C1 = 15(3) <> 9 since 9{15/24} blocked by Killer pair (59) of 12(2) and (24) of 5(2)
e) 22(4) = {3568} locked for N7
f) 8(2) = {17} locked for R9+N7
g) 5(2) = {23} -> R9C3 = 2, R9C4 = 3
h) 19(3) = {478} since R7C3 = 4 -> R7C3 = 4, R6C3 = 7, R6C4 = 8
i) Innie N14 = R3C3 = 1
j) R4C4 = 4 -> R3C4 = 5, R9C7 = 6, R8C8 = 3

6. C456+N1
a) Innies N23 = 17(2) = {89} -> R1C4 = 9, R1C5 = 8
b) 12(2) = {57} locked for C1+N1
c) 25(4) = {2689} -> R1C3 = 6, R1C2 = 2, R2C2 = 9, R2C3 = 8
d) R1C8 = 5 -> R1C9 = 3
e) 24(4) = {2679}

7. Rest is singles without considering diagonals.

1.25 - Hard 1.25. I used a Hidden Killer triple.

Prelims

a) R12C1 = {39/48/57}, no 1,2,6
b) R1C67 = {14/23}
c) R1C89 = {17/26/35}, no 4,8,9
d) R2C45 = {17/26/35}, no 4,8,9
e) R34C1 = {14/23}
f) R45C8 = {17/26/35}, no 4,8,9
g) R45C9 = {49/58/67}, no 1,2,3
h) R56C1 = {49/58/67}, no 1,2,3
i) R56C2 = {18/27/36/45}, no 9
j) R67C9 = {16/25/34}, no 7,8,9
k) R89C9 = {18/27/36/45}, no 9
l) R9C12 = {17/26/35}, no 4,8,9
m) R9C34 = {14/23}
n) R9C56 = {59/68}
o) 10(3) cage at R3C3 = {127/136/145/235}, no 8,9
p) 19(3) cage at R6C3 = {289/379/469/478/568}, no 1

1. 45 rule on N1 3 innies R3C123 = 8 = {125/134}, 1 locked for R3 and N1

2. 6 in N1 only in 25(4) cage at R2C1 = {2689/3679/4678}, no 5

3. 45 rule on R9 3 innies R9C789 = 18 = {279/378/459/468} (cannot be {189/369/567} which clash with R9C56), no 1, clean-up: no 8 in R8C9
3a. 45 rule on R9 3 outies R8C789 = 11 = {128/137/146/236/245}, no 9

4. 45 rule on N23 4(2+2/3+1) innies R1C45 + R3C47 = 31
4a. Max R1C45 = 17 -> min R3C47 = 14 must contain one of 8,9 -> R3C7 = {89}
4b. Min R3C47 = 14 -> min R3C4 = 5
4c. R1C45 + R3C47 = 31 = 22+9/23+8 -> R1C45 + R3C4 = {589/679/689}, no 1,2,3,4, 9 locked for R1 and N2, clean-up: no 3 in R2C1
4d. 5 of {589} must be in R3C4 -> no 5 in R1C45
4e. 9 in R3 only in R3C789, locked for N3

5. 10(3) cage at R3C3 = {127/136/145/235}
5a. R3C4 = {567} -> no 5,6,7 in R3C3 + R4C4

6. 45 rule on N3 3 innies R123C7 = 14
6a. Min R3C7 = 8 -> max R12C7 = 6, no 6,7,8 in R2C7

7. 45 rule on N69 2 innies R47C7 = 10 = {19/28/37/46}, no 5

8. 45 rule on C1 3 innies R789C1 = 15
8a. Hidden killer pair 1,2 in R34C1 and R789C1 for C1, R34C1 contains one of 1,2 -> R789C1 must contain one of 1,2 = {159/168/249/258/267}, no 3, clean-up: no 5 in R9C2

9. R89C9 = [18]/{27/36} (cannot be {45} which clashes with R45C9 + R67C9, killer ALS block), no 4,5
9a. R9C789 (step 3) = {378/468} (cannot be {279} which clashes with R89C9 = {27} CCC, cannot be {459} because no 4,5,9 in R9C9), no 2,5,9, 8 locked for R9 and N9, clean-up: no 2 in R4C7 (step 7), no 7 in R8C9, no 6 in R9C56
9b. Naked pair {59} in R9C56, locked for R9 and N8, clean-up: no 3 in R9C2
[Alternatively for step 9a 45 rule on R9 2 innies R9C78 = 1 outie R8C9 + 9, IOU no 9 in R9C89, etc. Where there’s a CCC there’s usually an IOU, and vice versa. This also applies for step 11.]

10. 9 in N9 only in R7C78, locked for R7, CPE no 9 in R56C7
10a. 45 rule on N9 3 innies R7C789 contains 9 = 16 = {169/259} (cannot be {349} which clashes with R9C789), no 3,4,7, clean-up: no 3,6,7 in R4C7 (step 7), no 3,4 in R6C9

11. 45 rule on C9 3 innies R123C9 = 16 = {169/259/349/367} (cannot be {178/268/358} which clash with R1C89, CCC, cannot be {457} which clashes with R45C9), no 8
11a. 4 in C9 only in R123C9 = {349} or R45C9 = {49} -> R123C9 = {349/367} (cannot be {169/259} locking-out cages), no 1,2,5, 3 locked for C9 and N3, clean-up: no 2 in R1C6, no 6,7 in R1C8, no 6 in R89C9
11b. Killer pair 1,2 in R7C789 and R8C9, locked for N9

12. R123C7 = 14 (step 6) = {149/158/248}
12a. R123C9 (step 11) = {367} (only remaining combination, cannot be {349} because R1C89 + R23C9 = [5349] clashes with R123C7), locked for C9 and N3 -> R9C9 = 8, placed for D\, R8C9 = 1, clean-up: no 4 in R2C1, no 5 in R45C9, no 6 in R7C78 (step 10a), then no 4,9 in R4C7 (step 7)
12b. Naked pair {49} in R45C9, locked for N6
12c. Naked triple {259} in R7C789, locked for R7 and N9
12d. R123C7 = {149/248} (cannot be {158} which clashes with R4C7), no 5, 4 locked for C7 and N3
12e. Killer pair 1,2 in R123C7 and R47C7, locked for C7
12f. Killer pair 8,9 in R3C7 and R47C7, locked for C7
12g. 5 in C7 only in R56C7, locked for N6 -> R67C9 = [25], clean-up: no 3,6 in R45C8, no 7 in R5C2
12h. Naked pair {17} in R45C8, locked for C8 and N6 -> R4C7 = 8, R3C7 = 9, placed for D/, R7C7 = 2, placed for D\, clean-up: no 3 in R1C6, no 7 in R1C9
12i. Naked pair {14} in R1C67, locked for R1, clean-up: no 8 in R2C1
12j. Killer pair 3,5 in R12C1 and R3C123, locked for N1

13. 10(3) cage at R3C3 = {136/145}, no 7, 1 locked for D\, CPE no 1 in R4C3
13a. R3C7 = 9 -> R1C45 + R3C47 (step 4c) = 22+9 -> R1C45 + R3C4 = {589/679}
13b. R3C4 = {56} -> no 6 in R1C45

14. R789C1 (step 8a) = {168/258/267} (cannot be {159} which clashes with R12C1, cannot be {249} which clashes with R34C1), no 4,9
14a. R8C3 = 9 (hidden single in N7)
14b. 19(3) cage at R6C3 = {478/568}, no 3
14c. 45 rule on N7 2 remaining innies R79C3 = 6 = [42], 4 placed for D/, R9C4 = 3, clean-up: no 5 in R2C5, no 6 in R9C12
14d. Naked pair {17} in R9C12, locked for R9 and N7 -> R9C78 = [64], R8C8 = 3, placed for D\, R3C3 = 1, R4C4 = 4, placed for D\, R3C4 = 5 (cage sum), R45C9 = [94], clean-up: no 9 in R2C1, no 3 in R2C5, no 9 in R6C1, no 5 in R6C2
14e. Naked pair {57} in R12C1, locked for C1 and N1 -> R9C1 = 1, placed for D/
14f. Naked pair {68} in R78C1, locked for C1 and N7 -> R8C2 = 5, placed for D/, R56C1 = [94]

15. R1C9 = 3 (hidden single in R1), placed for D/ -> R1C8 = 5, R1C1 = 7, placed for D\

16. Naked pair {89} in R1C45, locked for R1 and N2 -> R12C3 = [68], R2C2 = 9, placed for D\, R2C8 = 2, placed for D/, clean-up: no 6 in R2C45
16a. Naked pair {17} in R2C45, locked for R2 and N2

17. R5C5 = 6, R4C6 = 7, R6C4 = 8, R1C45 = [98]
17a. R8C3 = 9 -> R7C45 + R8C4 = 15 = {267} (only remaining combination) -> R7C45 = [67]

and the rest is naked singles, without using the diagonals.


My walkthrough would have been a bit easier if I'd looked for more CCCs/IOUs; they would have made the clash in step 12a unnecessary. I only found two CCCs; Afmob found six IOUs.

I'll rate my walkthrough for A323X at Easy 1.5. I used locking-out cages.