SudokuSolver Forum

1. N12+C6
a) Innie N1 = R3C3 = 1
b) Outies C789 = 1{28/37} -> 1 locked for C6 since R12C6 <> 2,4,6; R9C6 <> 7,8 since R2C6 = (78)
c) 15(2) = {69} locked for R1+N2 since {78} blocked by R2C6 = (78)
d) 16(3) = 5{38/47} -> 5 locked for N2 since {178} blocked by R2C6 = (78)
e) Hidden Single: R1C6 = 1 @ N2 -> R1C7 = 3

2. N124
a) 4(2) @ C1 = {13} locked for C1
b) 6(2) = {24} locked for C1+N4
c) Innies N124 = 15(2+1): R6C2 = (567) since R2C6 >= 7 and R6C1 <= 3
d) Hidden Single: R6C1 = 1 @ N6 -> R7C1 = 3
e) Innies N124 = 14(1+1) = [77/86]
f) 18(5) = 12{348/357/456} -> 2 locked for C4

3. N39 !
a) 30(7) = 12345{69/78} -> 1 locked for N9
b) 11(3) = 2{18/45} -> 2 locked for N3 since R1C89 <> 1,6
c) ! Innies+Outies N3: 8 = R2C6+R4C7 - R3C9: R3C9 <> 6 since R2C6 <> 5,6,9 and R4C7 <> 6
d) 6 locked in 10(2) @ N3 = {46} locked for C8+N3
e) Hidden Single: R2C9 = 1 @ R2
f) 11(3) = {128} -> 2,8 locked for R1+N3

4. R123
a) 4,5,7 locked in R1C123 @ R1 for N1
b) 11(2) = [83/92]
c) 10(2) = [46/73]
d) 5 locked in 23(4) @ R1 = 5{279/378/468} since {3569} blocked by R2C3 = (36); R2C2 <> 9 since 2 only possible there
e) 9 locked in R23C1 @ N1 for C1

5. C123 !
a) 21(3) = {678} locked for N7 since R89C1 <> 4,9 and {57}9 blocked by R1C1 = (57)
b) Innies+Outies N7: 5 = R6C2+R7C4 - R9C3: R7C4 <> 6,7,9 since R6C2 = (67) since R9C3 <> 8
c) ! Innies+Outies N7: 5 = R6C2+R7C4 - R9C3: R6C2 <> 7 since R7C4 = (1458) and R9C3 <> 3,6,7
d) R6C2 = 6
e) 9 locked in 20(3) @ N4 = {389} locked for N4
f) 18(5) = {12357} since R4C23 = (57) -> 5,7 locked for R4+18(5); 3 locked for C4+N2

6. C789+N2
a) 16(3) = {457} locked for N2
b) Outies C789 = 10(2) = [82] -> R2C6 = 8, R9C6 = 2
c) 29(4) = {5789} -> R4C7 = 9; 5,7 locked for N3+C7
d) Innies+Outies N9: R6C9 = R7C3 = (48)
e) 17(3) @ N6 = 8{27/45} -> R6C8 = (57); 8 locked for C7

7. N1789
a) 8 locked in 11(2) @ N1 = {38} -> R3C1 = 8, R3C2 = 3
b) R2C3 = 6 -> R1C3 = 4
c) Innies+Outies N7: -1 = R7C4 - R9C3 -> R7C4 <> 1,5
d) 20(4) = 16{49/58} since 6{24}8 blocked by R7C7 = (48) -> R7C2 = 1
e) 6(2) = {24} -> R8C3 = 2, R8C2 = 4
f) Naked pair (48) locked in R7C47 for R4
g) 9(2) = {36} -> R7C6 = 6, R8C6 = 3
h) 10(2) @ N8 = {19} -> R7C5 = 9, R8C5 = 1
i) R7C3 = 5 -> R7C4 = 8

8. Rest is singles.

Hard 1.0. I used IOD.

1. N124
a) Innie N1 = R3C3 = 1
b) 4(2) @ C1 = {13} locked for C1
c) 6(2) = {24} locked for C1+N4
d) 4(2) @ R1 = {13} locked for R1
e) 18(5) = 12{348/357/456} -> 2 locked for C4+N2

2. N124
a) 18(5) can only have one of (678) -> R4C23 must have one (35)
b) Killer pair (35) locked in 18(5) + 20(3) for N4
c) R6C1 = 1, R7C1 = 3
d) Combining step 2a and 2b: 18(5): R23C4 <> 6,7,8 since R4C23 can only have one of (35)
e) Innies N2 = 14(4) <> 9: R23C4 <> 5 since R2C6 = (578)
f) 29(4) = {5789} -> 9 locked for C7
g) 16(3) <> 3{49/67} since {349} blocked by R23C4 = (234) and {367} blocked by Killer pair (67) of 15(2)
h) 20(3) = 9{38/56} -> 9 locked for N4 since {578} blocked by Killer pair (58) of 18(5)
i) Killer pair (58) locked in 20(3) + 18(5) for N4

3. C456+R9 !
a) 14(2) = [59]/{68}
b) Innies C6789 = 25(4) <> 2 since {2689} blocked by R7C6 = (689)
c) 2 locked in R89C6 @ C6 for N8
d) ! Hidden Killer quad (1234) in R89C6 for C6 since Innies C6789 can only have one of them -> R89C6 = (1234)
e) 25(4) <> 2 since {2689} blocked by R7C6 = (689)
f) 2 locked in 30(7) @ R9 for 30(7)
g) ! Outies C789 = 20(5) = 2{1359/1368/1458/1467/3456}: R7C6 <> 8 since R1289C6 <> 6 and 158{24} blocked by Killer pair (15) of 16(3)
h) 14(2) = [59/86]

4. C789 !
a) Naked quad (5789) locked in R2346C7 for C7
b) ! Hidden Killer pair (89) in 17(3) + 30(7) for N9 since each can only have one of them -> R6C9 <> 8,9
c) Outies N9 = 14(2+2) <> 9 since R6C9 >= 3
d) Innies+Outies N9: 2 = R6C9+R9C6 - R7C7: R7C7 <> 1 since R6C9 >= 3
e) 12(3) <> 8 since R7C7 <> 1,3,8
f) ! Outies R789 = 23(4) = 8{267/357/456} -> R6C7 = 8
g) Cage sum: R7C6 = 6
h) 29(4) = {5789} -> R2C6 = 8

5. N1234
a) Innies N124 = 7(1+1) = [16] -> R1C6 = 1, R6C2 = 6
b) 15(2) = {69} locked for R1+N2
c) R1C7 = 3
d) 11(3) = 2{18/45} -> 2 locked for N3 since R1C89 <> 1,6
e) 10(2) @ N3 = [19]/{46}
f) Innies+Outies N3: R3C9 = R4C7 = (579)
g) 8 locked in 11(2) @ R3 = {38} -> R3C1 = 8, R3C2 = 3
h) 10(2) @ N1 = {46} -> R1C3 = 4, R2C3 = 6

6. R789+N6
a) 12(3) = 3{27/45} -> R6C8 = (57), R8C6 = 3
b) 10(2) = {19} locked for C5+N8
c) 25(4) = {4579} -> R9C3 = 9; 4,5,7 locked for N8
d) 20(4) = {1568} since R7C4 = 8 and [6428] blocked by R7C7 = (24) -> R7C4 = 8, R7C3 = 5, R7C2 = 1
e) 20(3) = {389}

7. Rest is singles.

Hard 1.25. I used a Hidden Killer quad.

I accidentally omitted one of the combinations for 23(4) cage at R1C1 but fortunately bringing forward 45 rule on N7 overcame that problem without much difficulty.

Thanks Afmob for pointing out a couple of typos, suggesting clarification to step 15b and pointing out that I'd reached naked singles after step 16b.
Prelims

a) R12C3 = {19/28/37/46}, no 5
b) R1C45 = {69/78}
c) R1C67 = {13}
d) R23C8 = {19/28/37/46}, no 5
e) R3C12 = {29/38/47/56}, no 1
f) R45C1 = {15/24}
g) R5C78 = {18/27/36/45}, no 9
h) R67C1 = {13}
i) R78C5 = {19/28/37/46}, no 5
j) R78C6 = {18/27/36/45}, no 9
k) R8C23 = {15/24}
l) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
m) 20(3) cage at R5C2 = {389/479/569/578}, no 1,2
n) 21(3) cage at R8C1 = {489/579/678}, no 1,2,3
o) 29(4) cage at R2C6 = {5789}
p) 18(5) cage at R2C4 = {12348/12357/12456}, no 9

Steps resulting from the Prelims
1a. Naked pair {13} in R1C67, locked for R1, clean-up: no 7,9 in R2C3
1b. Naked pair {13} in R67C1, locked for C1, clean-up: no 8 in R3C2, no 5 in R45C1
1c. Naked pair {24} in R45C1, locked for C1 and N4, clean-up: no 7,9 in R3C2

2. 45 rule on N1 1 innie R3C3 = 1, clean-up: no 9 in R1C3, no 9 in R2C8, no 5 in R8C2
2a. 18(5) cage at R2C4 = {12348/12357/12456}, 2 locked for C4 and N2
2b. 2,4 of {12348/12456} must be in R23C4 -> no 6,8 in R23C4
2c. 1 in N4 only in R6C12, locked for R6

3. 45 rule on N2 4 innies R12C6 + R23C4 = 14 = {1238/1247/2345}, no 9
3a. R2C6 = {578} -> no 5,7 in R23C4
3b. 29(4) cage at R2C6 = {5789}, 9 locked for C7

4. 45 rule on N14 2 innies R6C12 = 2 outies R23C4 + 2
4a. R23C4 contains 2 = {23/24} = 5,6 -> R6C12 = 7,8 contains 1 = {16/17} -> R6C1 = 1, R6C2 = {67}, R7C1 = 3, clean-up: no 7 in R8C5, no 6 in R8C6

5. 45 rule on C789 3 outies R129C6 = 11 = {128/137} (cannot be {146/236} because R2C6 only contains 5,7,8, cannot be {245} because R1C6 only contains 1,3) -> R2C6 = {78}, R19C6 = [12/13/31], 1 locked for C6, clean-up: no 8 in R78C6
5a. R12C6 + R23C4 (step 3) = {1238/1247} -> R1C6 = 1, R1C7 = 3, clean-up: no 7 in R23C8, no 6 in R5C8
5b. R78C6 = [45/54/63] (cannot be {27} which clashes with R129C6), no 2,7
5c. R78C5 = {19/28}/[73] (cannot be {46} which clashes with R78C6), no 4,6
5d. 29(4) cage at R2C6 = {5789}, 5 locked for C7, clean-up: no 4 in R5C8
5e. 30(7) cage at R6C9 contains 1, locked for N9

6. R1C45 = {69} (cannot be {78} which clashes with R2C6), locked for R1 and N2, clean-up: no 4 in R2C3
6a. 9 in C6 only in R456C6, locked for N5

7. 11(3) cage at R1C8 = {128/245} (cannot be {146} because 1,6 only in R2C9), no 6,7, 2 locked for N3, clean-up: no 8 in R23C8
7a. 1 of {128} must be in R2C9 -> no 8 in R2C9
7b. Killer pair 1,4 in 11(3) cage and R23C8, locked for N3
7c. 7 in R1 only in R1C123, locked for N1, clean-up: no 4 in R3C2

8. 45 rule on N3 3 innies R23C7 + R3C9 = 21 = {579} (cannot be {678} = {78}6 which clashes with R2C6), locked for N3, clean-up: no 1 in R2C8
8a. Naked pair {46} in R23C8, locked for C8 and N3
8b. Naked pair {28} in R1C89, locked for R1 and N3 -> R2C9 = 1, clean-up: no 2,8 in R2C3
8c. Naked triple {457} in R1C123, locked for N1, clean-up: no 6 in R3C12
8d. R3C8 = 6 (hidden single in R3) -> R2C8 = 4
8e. 2 in N1 only in R23C2, locked for C2, clean-up: no 4 in R8C3
8f. 1 in N9 only in R9C78, locked for R9

9. 5 in N1 only in 23(4) cage at R1C1 = {2579/3578/4568} (cannot be {3569} which clashes with R2C6)
9a. 2 of {2579} must be in R2C2 -> no 9 in R2C2
9b. 9 in N1 only in R23C1, locked for C1

10. 21(3) cage at R8C1 = {678} (only possible combination, cannot be {489} because 4,9 only in R9C2, cannot be {579} = {57}9 which clashes with R1C1), locked for N7
10a. R1C1 = 5 (hidden single in C1)
10b. 7 in C1 only in R89C1, locked for N7

11. 9 in N4 only in 20(3) cage at R5C2 = {389/569}, no 7

12. 45 rule on N7 2 outies R6C2 + R7C4 (both in 20(4) cage at R6C2) = 1 remaining innie R9C3 +5
12a. R9C3 = {2459} -> R6C2 + R7C4 = 7,9,10,14 = [61/64/68] (cannot be [77], R6C2 + R7C4 cannot total 9) -> R6C2 = 6, R7C4 = {148}, R9C3 = {259}, R9C2 = 8
12b. Naked pair {23} in R23C2, locked for C2 and N1, R2C3 = 6 -> R1C3 = 4, R1C2 = 7
12c. Naked triple {259} in R789C3, locked for C3 and N7
12d. R5C2 = 9 (hidden single in N4)

13. R4C2 = 5, R4C3 = 7 (hidden single in C4) -> 18(5) cage at R2C4 = {12357} -> R23C4 = {23}, locked for C4 and N2
13a. 16(3) cage at R2C5 = {457} (only remaining combination), locked for N2 -> R2C6 = 8, R4C7 = 9
13b. Naked pair {57} in R23C7, locked for C7 and N3 -> R3C9 = 9, R3C1 = 8 -> R3C2 = 3, clean-up: no 2 in R5C8
13c. R129C6 (step 5) = {128} (only remaining combination) -> R9C6 = 2, clean-up: no 8 in R78C5

14. R3C9 = 9 -> R4C89 + R5C9 = 10 = {127/136/145/235}, no 8
14a. 8 in R4 only in R4C45, locked for N5

15. 17(3) cage at R6C7 must contain an odd number -> R6C8 = {357}
15a. 45 rule on N6 3 remaining innies R6C789 = 17
15b. R6C7 contains an even number, R6C8 contains an odd number -> R6C9 must be even = {48}
15c. 45 rule on N6 1 remaining outie R7C7 = 1 remaining innie R6C9 -> R7C7 = {48}
15d. R6C789 = 17 = {278/458}, no 3, 8 locked for R6 and N6 -> R56C3 = [83], clean-up: no 1 in R5C78
15e. 17(3) cage at R6C7 = {278/458}, 8 locked for C7
15f. R4C8 = 1 (hidden single in N6)
15g. R9C7 = 1 (hidden single in C7)

16. 20(4) cage at R6C2 = 6{149/158} (cannot be 6{248} which clashes with R7C7), no 2
16a. R8C3 = 2 (hidden single in N7) -> R8C2 = 4, R7C2 = 1, clean-up: no 5 in R7C6, no 9 in R8C5
16b. Naked pair {48} in R7C47, locked for R7, R7C6 = 6 -> R8C6 = 3, R8C5 = 1 -> R7C5 = 9, R7C3 = 5 -> R7C4 = 8 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough for A320 at 1.0 to Hard 1.0. I also used IOD, but for a different nonet.

Thanks Afmob for pointing out a flaw in my re-work, hope it's now right after adding a couple of sub-steps at the start of step 10.
Prelims

a) R12C3 = {19/28/37/46}, no 5
b) R1C45 = {69/78}
c) R1C67 = {13}
d) R23C8 = {19/28/37/46}, no 5
e) R3C12 = {29/38/47/56}, no 1
f) R45C1 = {15/24}
g) R5C78 = {18/27/36/45}, no 9
h) R67C1 = {13}
i) 14(2) cage at R6C7 = {59/68}
j) R78C5 = {19/28/37/46}, no 5
k) R8C23 = {15/24}
l) 11(3) cage at R1C8 = {128/137/146/236/245}, no 9
m) 20(3) cage at R5C2 = {389/479/569/578}, no 1,2
n) 21(3) cage at R8C1 = {489/579/678}, no 1,2,3
o) 29(4) cage at R2C6 = {5789}
p) 18(5) cage at R2C4 = {12348/12357/12456}, no 9

Steps resulting from the Prelims
1a. Naked pair {13} in R1C67, locked for R1, clean-up: no 7,9 in R2C3
1b. Naked pair {13} in R67C1, locked for C1, clean-up: no 8 in R3C2, no 5 in R45C1
1c. Naked pair {24} in R45C1, locked for C1 and N4, clean-up: no 7,9 in R3C2

2. 45 rule on N1 1 innie R3C3 = 1, clean-up: no 9 in R1C3, no 9 in R2C8, no 5 in R8C2
2a. 18(5) cage at R2C4 = {12348/12357/12456}, 2 locked for C4 and N2
2b. 2,4 of {12348/12456} must be in R23C4 -> no 6,8 in R23C4

3. 45 rule on N2 4 innies R12C6 + R23C4 = 14 = {1238/1247/2345}, no 9
3a. 5,7 of {1247/2345} must be in R2C6 -> no 5,7 in R23C4
3b. 29(4) cage at R2C6 = {5789}, 9 locked for C7, clean-up: no 5 in R7C6

4. 1 in N4 only in R6C12, locked for R6
4a. 45 rule on N14 2 innies R6C12 = 2 outies R23C4 + 2
4b. R23C4 contains 2 = {23/24} = 5,6 -> R6C12 = 7,8 contains 1 = {16/17} -> R6C1 = 1, R6C2 = {67}, R7C1 = 3, clean-up: no 7 in R8C5
4c. 9 in N4 only in 20(3) cage at R5C2 = {389/569}, no 7

5. 45 rule on N3 3(1+2) outies R12C6 + R4C7 = 1 innie R3C9 + 9
5a. Min R12C6 + R4C7 = 1{57} = 13 -> min R3C9 = 4

6. 11(3) cage at R1C8 = {128/146/236/245} (cannot be {137} because 1,3 only in R2C9), no 7
6a. Min R1C89 = 6 -> max R2C9 = 5

7. 45 rule on N7 2 outies R6C2 + R7C4 = 1 remaining innie R9C3 + 5
7a. Max R6C2 + R7C4 = 14, min R6C2 = 6 -> max R7C4 = 8
7b. R6C2 + R7C4 cannot total 9 -> no 4 in R9C3

8. 45 rule on N78 3 remaining innies R789C6 = 1 outie R6C2 + 5
8a. Max R6C2 = 7 -> max R789C6 = 12, min R7C6 = 6 -> max R89C6 = 6, no 6,7,8,9 in R89C6
8b. R6C2 = {67} -> R789C6 = 11,12 = {128/146/236/129/156/246} (cannot be {138} which clashes with R1C6, cannot be {245/345} because R7C6 only contains 6,8,9)
[First time through I accidentally omitted one of the combinations for R789C6. I’ve had to do some re-work but have kept to my original steps as much as possible.]

9. 45 rule on C6789 4 innies R3456C6 = 25 = {1789/3589/3679/4579/4678} (cannot be {2689} which clashes with R7C6), no 2
9a. 2 in C6 only in R89C6, locked for N8, clean-up: no 8 in R78C5
9b. R789C6 (step 8b) contains 2 = {128/236/129/246}, no 5
9c. R12C6 + R23C4 (step 3) = {1238/1247/2345}
9d. R3456C6 = {1789/3589/3679/4579/4678} -> R12789C6 = {12359/12368/12467/23456} (cannot be {12458} because R12C6 + R23C4 only contains one of 1,5)
9e. 6 of {12368} must be in R7C6 -> no 8 in R7C6, clean-up: no 6 in R6C7
9f. Naked quad {5789} in R2346C7, locked for C7, 7 also locked for 29(4) cage at R2C6, no 7 in R2C6, clean-up: no 1,2,4 in R5C8
9g. R12C6 + R23C4 (step 3) = {1238/2345}, 3 locked for N2

10. 29(4) cage at R2C6 and 14(2) cage at R6C7, R2346C7 = {5789} = 29 -> R27C6 = 14
10a. 45 rule on C6 using R3456C6 = 25 (step 9), R27C6 = 14, 3 remaining innies R189C6 = 6 = {123}, locked for C6
10b. Max R7C7 + R8C6 = 9 and 12(3) cage cannot be [363] -> no 2,3 in R6C8

11. 45 rule on R789 4 remaining outies R6C2789 = 23 = {2579/2678/3569/3578/4568} (cannot be {2489} because R6C2 only contains 6,7, cannot be {3479} because R6C7 only contains 5,8)
11a. Min R6C278 = 15 -> max R6C9 = 8
11b. 2,3 of {2579/2678/3569/3578} must be in R6C9, 6 of {4568} must be in R6C2 -> no 6,7 in R6C9

12. R12C6 + R23C4 (step 9g) = {1238/2345} -> R12C6 = [18/35] -> R1234C7 = 1{789}/3{579}
12a. 45 rule on N3 4 innies R123C7 + R3C9 = 24 = 1{89}6/3{579} (cannot be 3{89}4/3{78}6 because R1234C7 only contain one of 3,8), no 4,8 in R3C9, 9 locked for N3, clean-up: no 1 in R2C8

13. R12C6 = [18/35], R123C7 + R3C9 (step 12a) = 1{89}6/3{579}
13a. Consider placements for 5 in R3
5 in R3C12 = {56}, locked for R3 => R123C7 + R3C9 = 3{579}
or 5 in 16(3) cage at R2C2, locked for N2 => R12C6 = [18] => R123C7 + R3C9 = 3{579}
or 5 in R3C79 => R123C7 + R3C9 = 3{579}
-> R123C7 + R3C9 = 3{579} -> R1C7 = 3, R23C7 + R3C9 = {579}, locked for N3, R12C6 = [18], clean-up: no 2 in R1C3, no 7 in R1C45, no 2 in R3C8, no 6 in R5C8
13b. Naked pair {69} in R1C45, locked for R1 and N2, clean-up: no 4 in R2C3
13c. R2C9 = 1 (hidden single in N3) -> R1C89 = 10 = {28}, locked for R1 and N3, clean-up: no 2 in R2C3
13d. Naked pair {46} in R23C8, locked for C8,
13e. Naked triple {457} in R1C123, locked for N1, clean-up: no 6 in R3C12

14. R23C4 = {23} (hidden pair in N2), 3 locked for C4
14a. 18(5) cage at R2C4 = {12357} (only remaining combination) -> R4C23 = {57}, locked for R4 and N4 -> R4C7 = 9, R6C2 = 6
14b. Naked pair {57} in R23C7, locked for C7 and N3 -> R3C9 = 9, R3C1 = 8, R6C7 = 8 -> R7C6 = 6, R4C6 = 4, R45C1 = [24], clean-up: no 2 in R3C2, no 1 in R5C7, no 5 in R5C8, no 4 in R78C5
14c. Naked pair {23} in R89C6, locked for N8, clean-up: no 7 in R7C5
14d. Naked pair {19} in R78C5, locked for C5 and N8 -> R1C45 = [96]

15. Naked triple {579} in R56C6 + R6C4, locked for N5, R6C5 = 2 (cage sum)
15a. Naked pair {57} in R6C48, locked for R6 -> R6C6 = 9, R6C3 = 3, R2C3 = 6 -> R1C3 = 4, clean-up: no 2 in R8C2
15b. 6 in N7 only in 21(3) cage at R8C1 = {678} -> R9C2 = 8, R89C1 = {67}, 7 locked for C1 and N7

16. 25(4) cage at R8C4 = {4579} (only remaining combination) -> R9C3 = 9, R7C4 = 8 (hidden single in N8)

17. 45 rule on R6789 1 remaining innie R6C4 = 7
17a. R6C8 = 5 -> R7C7 + R8C6 = 7 = [43]

and the rest is naked singles.

I'll rate my walkthrough for A320H at 1.5 for steps 12 and 13