SudokuSolver Forum

1. C12389+N9 !
a) Outie C12 = R7C3 = 1
b) 4(2) = {13} locked for C2
c) Innies+Outies C1: -4 = R5C2 - R1C1: R5C2 = (245), R1C1 <> 5,7
d) Outie C89 = R3C7 = 9
e) ! Consider placement of 9 in N9 -> R1C1 <> 9:
- i) 9 locked in R8C8+R9C9 @ N9 for D\
- ii) R9C8 = 9 -> 9 locked in R12C2 @ C2 for N1
f) 22(3) = 9{58/67} -> 9 locked for C2+N1; R12C2 <> 6,8 since R1C1 = (68)
g) Innies+Outies C1: -4 = R5C2 - R1C1: R5C2 <> 5
h) 9 locked in 16(3) @ C1 = 9{25/34} for N6 since R5C2 = (24); R45C1 <> 2,4
i) 9 locked in 17(4) @ C3 = 19{25/34} for 17(4) -> 1 locked for R9+N8
j) 9 locked in 12(3) @ N9 = {129} -> R8C8 = 1; 2,9 locked for R9+N9
k) 17(4) = {1349} since R9C345 <> 2,9 -> R8C3 = 9; 3,4 locked for R9

2. C123+N8 !
a) 9(2) @ R8 = [27/36/45]
b) ! 7(2) <> {25} since it's blocked by Killer quad (2359) in R45C1 + 9(2) @ R8
c) Both 9(2) <> {36} since it's a Killer pair of 7(2)
d) Hidden Single: R9C3 = 3 @ N7
e) 17(4) = {1349} -> 4 locked for N8
f) 17(3) = 8{27/36} -> R8C6 = (23), 8 locked for R8
g) 13(2) = {67}/[85]
h) Killer pair (57) locked in R9C1 + 13(2) for N7
i) 9(2) @ R6 = [18/54/72]
j) 2 locked in R78C1 @ C1 for N7

3. C123
a) 11(3) = [28]1/{46}1
b) 8 locked in R78C2 @ C2 for N7
c) Naked pair (24) locked in R78C1 for C1+N7
d) 7(2) = {16} locked for C1+N1
e) 22(3) = {589} -> R1C1 = 8, 5 locked for C2+N1
f) 13(2) = {67} locked for C2+N7
g) R9C1 = 5 -> R8C1 = 4, R7C1 = 2, R6C1 = 7, R7C2 = 8 -> R6C2 = 2, R5C2 = 4

4. C456+N9 !
a) 16(3) = 8{26/35} since R45C3 = (568) -> R5C4 = (23); 8 locked for C3
b) Using R9C45 = (14): Innies+Outies N8: -1 = R9C7 - R7C6: R9C7 = (68), R7C6 = (79)
c) Both 9(2) <> 7,8
d) ! Hidden Killer triple (789) in R9C7 for N9 since 24(4) can have at most two of (789) and R7C6 = (79) -> R9C7 = 8; R6C6 <> 9
e) 24(4) = 59{37/46} -> R7C6 = 9
f) 37(7) must have 4,8,9 -> 8,9 locked for N5; 9 also locked for C5; CPE: R4C4 <> 4
g) 9 locked in 15(3) @ C4 = {249} since R1C3 = (247) -> CPE: R1C56 <> 2,4
h) 1 locked in 19(4) @ R1 = {1567} for 19(4) -> CPE: R1C89 <> 5,6,7

5. R1234
a) Naked triple (234) locked in R1C389 for R1
b) 24(3) = {789} -> 7,8 locked for C8
c) 3 locked in 17(4) @ R1 = {2348} since 1,5,7 only possible @ R2C3 -> R2C9 = 8; 4 locked for N3
d) 13(2) = {67} locked for C9 since R3C9 <> 4,9
e) R3C8 = 7, R3C9 = 6, R4C9 = 7

6. N69
a) 9(2) @ C9 = [45] -> R7C9 = 4, R8C9 = 5
b) 9(2) @ C8 = {36} locked for C8 since R7C8 <> 4,5
c) 15(3) = {159} -> R5C8 = 5; 1 locked for N6
d) 12(3) = 2{37/46} since R56C7 = (2346) -> 2 locked for R5

7. Rest is singles without considering diagonals.

Easy 1.5. I used a small forcing chain.

1. Outies c89 -> r3c7 = 9
-> r34c8 = {78}
Also -> 9 in n9 only in 12(3)n9
-> 12(3)n9 = {129}
-> for 9(2)c8 and 9(2)c9 one is {45} and the other is {36}
-> (78) in n9 in r789c7

2. Outies c12 -> r7c3 = 1
4(2)c2 = {13}
-> r67c2 = {46} or {28}

3. 22(3)n1 contains a 9
-> (D\) at least one of r1c2 and r9c8 is a 9
-> 9 in n7 in r89c3
-> 17(4)n78 contains a 1 in r9c45
-> 12(3)n9 = [1{29}]
-> 17(4)n78 = [93{14}] or [94{13}]

4. (Step 4 deleted - proved unnecessary).

5. 13(2)n7 from {67} or {58}
-> (68) locked in c2 in r6789c2
-> Since 22(9) must contain one of (68) -> r1c1 from (68)
-> 9 in r12c2
-> 9 in c1 in r45c1

6. 8 in c1 either in r7c1 or in r1c1 which puts 5 in r12c2.
Both of these prevent 13(2)n7 from being {58}
-> 13{2)n7 = {67}
-> 9(2)n7 = [45]
-> r9c345 = [3{14}]
Also r67c2 = {28}
-> HS 4 in c2 -> r5c2 = 4
-> r45c1 = {39}
Also r12c2 = {59}
-> r1c1 = 8
Also 7(2)n1 = {16}
-> 4(2)c2 = [31]
Also HS 7 in c1 -> 9(2)r6c1 = [72]
-> r67c2 = [28]
-> r456c3 = {568}
-> r123c3 = {247}

7. 37(7) contains (489)
-> Given other placements for 9 -> 9 locked in n5/c5 in r46c5

8. Given r9c45 = {14} -> r789c6 = +18
-> r7c6 = r9c7 + 1
r9c67 from {68} or {78}
-> r9c7 cannot be 7 (would put 8 in r9c6 and r7c6)
-> 7 in n9 in r78c7
-> r7c6 cannot be 7 -> r9c7 cannot be 6
-> r9c7 = 8
-> r7c6 = 9
-> 17(3)r8c6 = [368] or [278]
Also (given r9c45 = {14}) Outies n89 = r6c68 = +8 can only be {35}
-> 24(4)r6c6 = [39{57}] or [59{37}]

9. 9 in c4 only in r12c4
-> 15(3)r1c3 = [2{49}] or [4{29}]
-> 1 in n2 in the 14(4)
-> HS 1 in r1 -> r1c7 = 1
-> 1 in c9 in r56c9
-> 15(3)n6 from {159} or {168}

10! 1 in n5
Given other placements, 1 in n5 not on diagonals or in r4.
Also given other placements 1 cannot be in r5c4 or r5c6.
-> HS 1 in n5 -> r6c5 = 1
-> r4c5 = 9
-> 9 in n6 only in 15(3)n6 -> 15(3)n6 = {159}
-> r4c89 = {78}
-> (Outies n3) r1c56 = +13 = {67}
-> r123c4 can only be [{49}5]

Easy from here
e.g. since 37(7) contains a 1 it must also contain a 7 which can only go in r5c5

Thanks Afmob for correcting typos and for pointing out when I reached naked singles without using the diagonals.

Prelims

a) R23C1 = {16/25/34}, no 7,8,9
b) R34C2 = {13}
c) R34C9 = {49/58/67}, no 1,2,3
d) R67C1 = {18/27/36/45}, no 9
e) R67C8 = {18/27/36/45}, no 9
f) R78C9 = {18/27/36/45}, no 9
g) R89C1 = {18/27/36/45}, no 9
h) R89C2 = {49/58/67}, no 1,2,3
i) 22(3) cage at R1C1 = {589/679}
j) 24(3) cage at R3C7 = {789}
k) 11(3) cage at R6C2 = {128/137/146/236/245}, no 9
l) 14(4) cage at R2C5 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. 22(3) cage at R1C1 = {589/679}, 9 locked for N1
1b. Naked pair {13} in R34C2, locked for C2

2. 45 rule on C12 1 outie R7C3 = 1, placed for D/, clean-up: no 8 in R6C1, no 8 in R6C8, no 8 in R89C1, no 8 in R8C9
2a. R7C3 = 1 -> R67C2 = 10 = {28/46}, no 5,7

3. 45 rule on C89 1 outie R3C7 = 9, placed for D/, clean-up: no 4 in R4C9, no 4 in R9C2
3a. Naked pair {78} in R34C8, locked for C8, clean-up: no 1,2 in R6C8, no 2 in R7C8

4. 9 in N9 only in 12(3) cage at R8C8 = {129}, locked for N9, clean-up: no 7,8 in R7C9, no 7 in R8C9
4a. 7,8 in N9 only in R789C7, locked for C7
4b. 9 in R7 only in R7C456, locked for N8
4c. 17(3) cage at R8C6 = {278/368/458/467}, no 1

5. Hidden killer triple 7,8,9 in R4C8, R4C9 and 15(3) cage at R5C8 for N6, R4C8 = {78}, 15(3) cage cannot contain more than one of 7,8,9 -> R4C9 = {789}, clean-up: no 7,8 in R3C9
5a. 45 rule on R123 4 outies R4C2489 = 22 = [1489/1579]/[16]{78}/[3289]/[34]{78} -> R4C4 = {2456}

6. 37(7) cage at R4C5 must contain both of 8,9, CPE no 8,9 in R6C6

7. 9 on D\ only in 22(3) cage at R1C1 or 12(3) cage at R8C8, only one of them can have 9 on D\ -> there must be 9 in one of R1C2 + R9C8, CPE no 9 in R9C2, clean-up: no 4 in R8C2
7a. Killer pair 6,8 in R67C2 and R89C2, locked for C2
7b. 22(3) cage = {589/679} -> R1C1 = {68}
7c. Hidden killer pair 2,4 in R5C2 and R67C2 for C2, R67C2 contains one of 2,4 -> R5C2 = {24}

8. 9 in C1 only in R45C1, locked for N4
8a. R5C2 = {24} -> 16(3) cage at R4C1 = {259/349} -> R45C1 = {39/59}
8b. 37(7) cage at R4C5 must contain 9 in R46C5, locked for C5 and N5

9. 1 in C1 only in R23C1 = {16} or R67C1 = [18] -> no 6 in R67C1 (locking-out cages), no 3 in R67C1
9a. Locking-cages killer pair 6,8 in R1C1, R23C1 and R67C1 for C1, no 6 in R89C1, clean-up: no 3 in R89C1
9a. 6 in C1 only in R123C1, locked for N1
9b. Killer pair 5,7 in R89C1 and R89C2, locked for N7, clean-up: no 2,4 in R6C1

10. R89C3 = {39} (hidden pair in N7), locked for C3 and 17(4) cage at R8C3
10a. R89C3 = 12 -> R9C45 = 5 = {14}, locked for R9 and N8, clean-up: no 5 in R8C1
10b. Naked pair {29} in R9C89, locked for R9 and N9 -> R89C3 = [93], clean-up: no 7 in R8C1
10c. R8C8 = 1, placed for D\
10d. 17(3) cage at R8C6 (step 4c) = {278/368}, no 5 -> R8C6 = {23}, 8 locked for R9, clean-up: no 5 in R8C2

11. 45 rule on N8 using R9C45 = 5, 3 remaining innies R789C6 = 18 = {279/369/378} (cannot be {567} because R8C6 only contains 2,3), no 5
11a. R8C6 = {23} -> no 2,3 in R7C6
11b. 9 of {369} must be in R7C6 -> no 6 in R7C6

12. Hidden killer pair 1,3 in R23C1 and R3C2 for N1, R3C2 = {13} -> R23C1 must contain one of 1,3 = {16/34}, no 2,5
12a. 2 in C1 only in R78C1, locked for N7, clean-up: no 8 in R6C2 (step 2a)
12b. 2 in C2 only in R56C2, locked for N4

13. 8 in C2 only in R78C2, locked for N7, clean-up: no 1 in R6C1
13a. 1 in C1 only in R23C1 = {16}, locked for N1 -> R1C1 = 8, placed for D\, R34C2 = [31]
13b. R1C1 = 8 -> R12C2 = 14 = {59}, locked for C2 and N1, clean-up: no 8 in R8C2
13c. Naked pair {67} in R89C2, locked for C2 and N7, clean-up: no 2 in R8C1
13d. R9C1 = 5, placed for D/, R8C1 = 4, R7C2 = 8 -> R6C2 = 2 (cage sum), R5C2 = 4, R67C1 = [72], clean-up: no 5 in R7C9

14. 8 on D/ only in R4C6 + R6C4, locked for N5 and 37(7) cage at R4C5
14a. 8 in N4 only in 16(3) cage at R4C3 = {268/358} -> R5C4 = {23}

15. 22(4) cage at R2C3 = {2578/4567} (cannot be {1678} because 1,8 only in R3C4) -> R23C3 = {27/47}, 7 locked for C3, R34C4 = {56}/[85], 5 locked for C4
15a. 5 in N8 only in R78C5, locked for C5
15b. Max R1C3 = 4 -> min R12C4 = 11, no 1 in R12C4
15c. R9C4 = 1 (hidden single in C4) -> R9C5 = 4

16. 45 rule on N8 using R9C45 = 5, 1 innie R7C6 = 1 outie R9C7 + 1, R7C6 = {79} -> R9C7 = {68}
16a. 7 in C7 only in R78C7, locked for 24(4) cage at R6C6 -> R7C6 = 9, R9C7 = 8
16b. 24(4) cage contains 7,9 = {3579}, no 4,6

17. R3C3 = 4 (hidden single on D\) -> R12C3 = [27]
17a. R23C3 = [74] = 11 -> R34C4 = 11 = {56}, locked for C4, clean-up: no 9 in R4C9
17b. R1C3 = 2 -> R12C4 = 13 = {49}, locked for C4 and N2
17c. Naked pair {56} in R3C49, locked for R3 -> R23C1 = [61]
17d. Naked pair {78} in R4C89, locked for R4 and N6
17e. 6 on D\ only in R4C4 + R5C5, locked for N5, CPE no 6 in R4C7
17f. Killer pair 5,6 in R3C9 and R78C9, locked for C9

18. R6C4 = 8 (hidden single on D/)
18a. R8C5 = 8 (hidden single in N8)
18b. 7 in C4 only in R78C4, locked for N8 -> R9C6 = 6, R8C6 = 3 (cage sum)
18c. R6C6 = 5, placed for D\ -> R2C2 = 9, placed for D\

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

I'll rate my walkthrough for A326X at Easy 1.5 for steps 7 and 9.