SudokuSolver Forum

3x3::k:3584:3584:10753:2562:2562:2819:2819:10753:6148:4101:2822:2822:10753:10753:10753:10753:6148:6148:4101:3591:10753:3592:4617:4617:4617:10753:6148:4101:3591:3591:3592:3592:3082:4617:3595:3595:4101:7948:7948:3085:3085:3082:4617:5134:3595:7948:7948:4623:4623:4623:3082:6160:5134:5134:7948:3345:4623:9234:4623:6160:6160:9234:5134:7948:3345:4627:4627:9234:9234:9234:2836:2836:4627:4627:4627:9234:5653:5653:5653:9234:2836:

1. n89
36(7) contains a 9
22(3) contains a 9
-> 9 nowhere else in n89
-> 24(3) = [9{78}]
-> 9 in r9c56
-> HS 9 in 36(7) -> r7c8 = 9
-> 9 in r123c9

2. Innies - Outies r12 -> r3c389 = r2c1 + 22
-> Either r2c1 = 1 and r3c389 = {689}, or r2c1 = 2 and r3c389 = {789}
-> Whichever of (12) is in r2c1 must go in 42(8) in r1c8

3. 9 in 42(8) in r13c3 or r2c456 -> 11(2)n1 not (29)
Both (45) in 42(8) in r13c3 or r2c4567
-> 11(2)n1 not {47} or {56}
-> 11(2)n1 = {38}
-> 14(2)n1 = {59}
-> r3c89 = [89]
-> r3c3 from (67)

Alternatively - The two values (not 3) in r13c3 can only go in r2 in r2c89.
-> 3 in r2 only in r2c23.
-> 11(2)n1 = {38} ...

4. Trying r2c1 = 2, r1c8 = 2, and r3c3 = 7 puts (78) in r1c456 for which there is no solution
Alternatively - Given r37c8 = [89] -> Innies c89 = r19c8 = +4. Must be r19c8 = [13].

-> r2c1 = 1
-> r1c8 = 1
-> r3c3 = 6
-> Only place for 6 in n2 -> 10(2)r1 = {46}
-> Only place for 8 in n2 -> 11(2)r1 = [83]
-> r7c67 = [78]
Also HS 4 in 42(8) -> r2c7 = 4
Also 6 in r2c89
-> 24(4)n3 = {2679}
-> r3c7 = 5

5. Innies n689 = r45c7 + r7c5 + r8c4 = +8
-> r45c7 = max +5 and since r123c7 = [345] -> Can only be r45c7 = {12}

-> 18(5)r3c5 = [735]{12}
-> HS 7 in 42(8) -> r1c3 = 7
-> 24(4)n3 = [2{67}9]
Also r3c12 = {24}
Also r3c4 = 1

6. r89c7 = {67}
-> 22(3) = [{69}7]
-> r8c7 = 6

Also given r456c7 = [{12}9] -> r7c9 = 1
-> 11(3)n9 = [2{45}]
-> r9c8 = 3

7. Given other placements -> innies n8 = r7c5 + r8c4 = +5
Cannot be [14] (1 already in r7) or [41] (Leaves no place for 1 in n7)
-> r7c5 = 2
-> r8c4 = 3

8. r3c2 from (24)
-> 14(3)r3c2 does not contain a 6
-> 6 in n4 in r456c1 or r56c2
-> HS 6 in n7 -> r7c2 = 6
-> r8c2 = 7
-> HS 9 in n7 -> r8c1 = 9
-> r1c12 = [59]
-> HS 9 in n4 -> r4c3 = 9

Also 18(5)r8c3 = {12348}
-> r7c13 = [35]

-> 16(4)c1 = [12{67}]
-> r34c2 = [41]
-> r6c3 = 3
-> r6c45 = [71]
-> 12(3)n5 = {246}
-> 12(2)n5 = [93]
-> r4c45 = {58}

9. Given r7c9 = 1 and r6c7 = 9 -> 20(4)n6 must contain an 8
-> r6c9 = 8
-> HS 8 in c1 -> r9c1 = 8
-> NS r6c1 = 4

etc.

1. R789+N6 !
a) ! 9 locked in 22(3) + 36(7) for N89 (Caged X-Wing)
b) 24(3) = {789} -> R6C7 = 9; 7,8 locked for R7
c) 22(3) = 9{58/67} -> 9 locked for R9+N8
d) Hidden Single: R7C8 = 9 @ N7
e) Innies N89 = 6(2+1) <> 5,6,7,8 -> R7C9+R8C4 <> 4 and 6(2+1) must have 1 -> CPE: R7C4 <> 1
f) Innies N689 = 8(2+2) <> 5,6,7,8

2. R123+N6 !
a) Innies+Outies R12: 22 = R3C389 - R2C1 -> R2C1 = (12); R3C389 = 23/24(3) = 89{6/7} -> 8,9 locked for R3; CPE: R2C7 <> 8
b) Killer pair (67) locked in 18(5) + R3C389 for R3
c) Both 11(2) <> {56} since it's a Killer pair of 14(2)
d) 18(5) @ N6 = 125{37/46} -> 5 locked for R3
e) ! Killer quad (1234) locked in R23C1+R3C2 + 11(2) for N1
f) 42(8) = {12456789} -> CPE: R2C89 <> 1,2,4 and R2C23 <> 9
g) Innies R1 = 10(3) <> 8,9: R1C89 <> 5,6,7 since R1C3 >= 5

3. R123 !
a) R2C4567 <> 7 since it sees all 7 of N1
b) R3C8 <> 6 since it sees all 6 of R2
c) ! Hidden Killer pair (37) in 24(4) @ R2 since 11(2) can only have one of them
d) 9 locked in 24(4) @ C9 = 9{267/348/357} <> 1
e) Innies R1 = 10(3): R1C8 <> 4 since R1C39 >= 7
f) 42(8) = {12456789} -> 4 locked for R2
g) 11(3) @ N1 = {38} locked for R2+N1
h) 14(2) = {59} locked for R1+N1
i) 10(2) <> 1
j) Hidden Single: R1C8 = 1 @ R1, R2C1 = 1 @ R2, R3C8 = 8 @ 42(8)

4. R123+C9
a) Innie C89 = R9C8 = 3
b) Naked pair (67) locked in R13C3 @ N1 for C3+42(8)
c) 6 locked in 24(4) @ R2 = {2679} for N3 -> R1C9 = 2; 7 locked for N3
d) Killer pair (67) locked in 10(2) + R1C3 for R1
e) 11(2) @ R1 = {38} -> R1C7 = 3, R1C6 = 8
f) 10(2) = {46} locked for R1+N2
g) R7C6 = 7, R7C7 = 8, R7C9 = 1
h) 20(4) = 18{47/56} -> R6C9 = 8
i) 11(3) = {245} -> R8C8 = 2; 4,5 locked for C9+N9
j) 22(3) = {679} sine R9C7 = (67) -> R9C7 = 7; 6 locked for N8+R9

5. C123+N5
a) 18(5) = {12348} -> 2,4,8 locked for N7; 2 also locked for R9; 3 locked for R8
b) 13(2) = {67} -> R7C2 = 6, R8C2 = 7
c) Hidden Single: R8C1 = 9 @ N7, R4C3 = 9 @ C3
d) R1C1 = 5, R7C1 = 3, R7C3 = 5
e) 16(4) = {1267} -> R3C1 = 2; 6,7 locked for N4
f) R3C2 = 4 -> R4C2 = 1
g) Hidden Single: R6C3 = 3 @ N4
h) 18(5) @ N4 = {12357} -> R7C5 = 2; 1,7 locked for R6+N5
i) 8 locked in 14(3) @ R4 @ N5 = {158} for N5 since R3C4 = (13) -> R3C4 = 1; 5,8

6. Rest is singles.

1.25. I used a Caged X-Wing and a Killer quad.

1e) Grouped Killer pair (78) locked in 36(7) + 22(3) + R7C67 for N89; 36(7) can only have one of (78) -> 36(7) = 34569{18/27}
1f) Caged Killer pair (56) locked in 36(7) + 22(3) + 11(3) for N89
1g) Innies N89 = 6(2+1) -> R7C9+R8C4 <> 4 and 6(2+1) must have 1 -> CPE: R7C4 <> 1

Prelim's courtesy of SudokuSolver
Preliminaries
Cage 14(2) n1 - cells only uses 5689
Cage 12(2) n5 - cells do not use 126
Cage 13(2) n7 - cells do not use 123
Cage 10(2) n2 - cells do not use 5
Cage 11(2) n1 - cells do not use 1
Cage 11(2) n23 - cells do not use 1
Cage 24(3) n689 - cells ={789}
Cage 22(3) n89 - cells do not use 1234
Cage 11(3) n9 - cells do not use 9
Cage 18(5) n78 - cells do not use 9
Cage 18(5) n236 - cells do not use 9
Cage 18(5) n4578 - cells do not use 9
Cage 42(8) n123 - cells ={12456789}

1. 22(3)r9c5 = {589/679}: must have 9 -> 9 locked for r9
1a. and 36(7)r7c4 = {1236789/1245789/1345689/2345679}; must have 9 -> 9 locked for n89 in those two cages: no 9 in r7c679 (Caged X-wing)

2. 24(3)r6c7 = {789}: must have 9 -> r6c7 = 9
2a. r7c67 = {78} only: both locked for r7
2b. no 2 in r1c6
2c. no 5,6 in r8c2

3. Hidden single 9 in n9 -> r7c8 = 9
3a. no 4 in r8c2

4. "45" on r12: 1 innie r2c1 + 22 = 3 outies r3c389 -> r3c389 = 23/24 = {689/789}(no 1,2,3,4,5): must have both 8 & 9 -> 8 and 9 both locked for r3
4a. and r2c1 from (12)

5. r13c3 sees all of r2 apart from r2c89 -> r13c3 must both repeat there (Clone)
5a. no 3 in r13c3 -> no 3 in r2c89

6. 3 in r2 only in 11(2)n1 = {38} only: both locked for r2 and n1
6a. -> 14(2)n1 = {59} only: both locked for r1 and n1
6b. no 1 in 10(2)r1c4
6c. no 2,6 in 11(2)r1c6

7. "45" on r1: 3 innies r1c389 = 10 = {127/136}(no 4,8)

8. 42(8)r1c3 = {12456789}: must have 8 -> r3c8 = 8
8a. must have 4,5,9 which are only in r2: all locked for r2

9. "45" on c89: 2 remaining innies r19c8 = 4 = [13] only permutation

10. Hidden single 1 in r2 -> r2c1 = 1

11. "45" on r12: 2 remaining outies r3c39 = 15 = [69] only permutation

12. "45" on r1: 2 remaining innies r1c39 = 9 = {27} only: both locked for r1 and no 2,7 in r2c7 (it sees both r1c39: CPE)
12a. 11(2)r1c6 = [83] only permutation
12b. 10(2)n2 = {46} only: 4 locked for n2

13. 42(8)r1c3 must have 4 -> r2c7 = 4
13a. and 42(8) must have 5 which is only in n2: 5 locked for n2

The other two WTs have beautiful mop-ups from here. No need for another.

Thanks Afmob for your detail corrections.

Prelims

a) R1C12 = {59/68}
b) R1C45 = {19/28/37/46}, no 5
c) R1C67 = {29/38/47/56}, no 1
d) R2C23 = {29/38/47/56}, no 1
e) R5C45 = {39/48/57}, no 1,2,6
f) R78C2 = {49/58/67}, no 1,2,3
g) 24(3) cage at R6C7 = {789}
h) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
i) 22(3) cage at R9C5 = {589/679}
j) 18(5) cage at R3C5 = {12348/12357/12456}, no 9
k) 18(5) cage at R6C3 = {12348/12357/12456}, no 9
l) 18(5) cage at R8C3 = {12348/12357/12456}, no 9
m) 42(3) cage at R1C3 = {12456789}, no 3

1. 22(3) cage at R9C5 = {589/679}, 9 locked for R9
1a. 36(7) cage at R8C4 must contain 9 -> caged X-Wing for 9 in 36(7) cage and 22(3) cage, no other 9 in N89
1b. Naked pair {78} in R7C67, locked for R7 and 24(3) cage at R6C7 -> R6C7 = 9, clean-up: no 2 in R1C6, no 5,6 in R8C2
1c. R7C8 = 9 (hidden single in N9), clean-up: no 4 in R8C2
1d. 9 in R8 only in R8C12, CPE no 9 in R5C2

2. 42(3) cage at R1C3 = {12456789}, CPE no 9 in R2C123, clean-up: no 2 in R2C23

3. R1C67 = {38/47}/[92] (cannot be {56} which clashes with R1C12), no 5,6 in R1C67
3a. R2C23 = {38/47} (cannot be {56} which clashes with R1C12), no 5,6 in R2C23

4. 45 rule on R1 3 innies R1C389 = 10 = {127/136/145/235}, no 8,9
4a. 3 of {136} must be in R1C9 -> no 6 in R1C9
4b. 9 in C9 only in 24(4) cage at R1C9 in R23C9
4c. Caged X-Wing for 9 in 42(8) cage at R1C3 and 24(4) cage for R23, no other 9 in R23

5. 45 rule on N89 3(2+1) innies R7C59 + R8C4 = 6
5a. Min R7C59 = 3 -> max R8C4 = 3
5b. Min R7C5 + R8C4 = 3 -> max R7C9 = 3
5c. Min R7C9 + R8C4 = 2 -> max R7C5 = 4
5d. R7C59 + R8C4 must contain 1, CPE no 1 in R7C4

6. Hidden killer triple 7,8,9 in R8C1, R8C2 and 18(5) cage at R8C3 for N7, R8C2 = {789}, 18(5) cage cannot contain more than one of 7,8 -> R8C1 = {789}, 18(5) cage = {12348/12357}, no 6
6a. R78C2 = {49/67} (cannot be [58] which clashes with 18(5) cage), no 5 in R7C2, no 8 in R8C2
6b. Killer pair 4,7 in R78C2 and 18(5) cage, locked for N7
6c. 6 in N7 only in R7C123, locked for R7

7. 45 rule on N6 2 remaining innies R45C7 = 1 outie R7C9 + 2
7a. Max R7C9 = 3 -> max R45C7 = 5, no 5,6,7,8 in R45C7

8. 45 rule on N5 2 innies R6C45 = 1 outie R3C4 + 7, IOU no 7 in R6C5

9. 45 rule on N5 4(3+1 for step 9a, 2+1+1 for step 9b) outies R3C4 + R67C3 + R7C5 = 11
9a. Min R67C3 + R7C5 = 6 -> max R3C4 = 5
9b. Min R3C4 + R7C35 = 4 -> max R6C3 = 7

10. 45 rule on R89 2 innies R8C12 = 1 remaining outie R7C4 + 12
10a. 9 in R8 only in R8C12 = [89/97] = 16,17 -> R7C4 = {45}
10b. R7C24 + R8C12 = [4589/6497], 4 locked for R7
10c. 4 in N8 only in R79C4 + R8C56, locked for 36(7) cage at R7C4, no 4 in R8C7 + R9C8
10d. 4 in N9 only in 11(3) cage at R8C8 = {146/245}, no 3,7,8

[Only just spotted …]
11. 45 rule on R12 3 outies R3C389 = 1 innie R2C1 + 22
11a. Max R3C389 = 24 -> max R2C1 = 2
11b. R2C1 = {12} -> R3C389 = 23,24 = {689/789}, 8 locked for R3
11c. 18(5) cage at R3C5 = {12357/12456}, 5 locked for R3
11d. Killer pair 6,7 in R3C389 and 18(5) cage, locked for R3
11e. Killer quad 1,2,3,4 in R23C1, R2C23 and R3C2, locked for N1

12. R1C389 (step 4) = {127/136/145/235}
12a. R1C3 = {567} -> no 5,6,7 in R1C89

13. 42(8) cage at R1C3 = {12456789}, CPE no 1,2,4 in R2C89
13a. 6 of 42(8) cage must be in R13C3 + R2C4567 (R13C3 + R2C4567 cannot contain both of 7,8 with would clash with R2C23), no 6 in R3C8

14. 45 rule on C89 3 remaining innies R139C8 = 12
14a. Min R3C8 = 7 -> max R19C8 = 5, no 5,6,7,8 in R9C8
14b. 7,8 in N9 only in R789C7, locked for C7, clean-up: no 3,4 in R1C6

15. 24(4) cage at R1C9 contains 9 = {1689/2589/2679/3489/3579/4569}
15a. Hidden killer pair 5,6 in R89C7 and 11(3) cage for N9, 11(3) cage contains one of 5,6 -> R89C7 must contain one of 5,6
15b. Hidden killer pair 5,6 in R23C7 and R89C7 for C7, R89C7 contains one of 5,6 -> R23C7 must contain one of 5,6
15c. Hidden killer pair 5,6 in R23C7 and 24(4) cage for N3, R23C7 contains one of 5,6 -> 24(4) cage must contain one of 5,6 = {1689/2589/2679/3579} (cannot be {3489} which doesn’t contain 5 or 6, cannot be {4569} which contains both of 5,6), no 4
15d. R1C9 = {123} -> no 3 in R2C89
[Cracked. The rest is fairly straightforward.]

16. 3 in R2 only in R2C23 = {38}, locked for R2 and N1, clean-up: no 6 in R1C12
16a. Naked pair {59} in R1C12, locked for R1 and N1, clean-up: no 1 in R1C45, no 2 in R1C7
16b. Naked pair {67} in R13C3, locked for C3 and 42(8) cage at R1C3, no 6,7 in R2C4567 + R3C8 -> R3C8 = 8
16c. R3C8 = 8 -> R19C8 = [13] (step 14)
16d. Naked pair {78} in R17C6, locked for C6
16e. R2C1 = 1 (hidden single in R2)
16f. R3C9 = 9 (hidden single in R3)
16g. Naked pair {24} in R3C12, locked for R3
16h. 9 in C3 only in R45C3, locked for N4

17. 16(4) cage at R2C1 contains 1 = {1258/1267/1348/1357/1456} (cannot be {1357} because R3C1 only contains one of 2,4)
17a. R3C1 = {24} -> no 2,4 in R45C1

18. R1C389 (step 4) = {127/136}
18a. R1C45 = {28/46} (cannot be {37} which clashes with R1C389), no 3,7 in R1C45
18b. 3 in R1 only in R1C79, locked for N3

19. Naked triple {567} in R2C89 + R3C7, locked for N3
19a. 4 in N3 only in R12C7, locked for C7
19b. 18(5) cage at R3C5 (step 11c) = {12357} (only remaining combination) -> R3C5 = 7, R13C3 = [76], R1C6 = 8 -> R1C7 = 3, R1C9 = 2, R23C7 = [45], R3C6 = 3 -> R3C4 = 1, clean-up: no 5 in R5C4

20. Naked pair {12} in R45C7, locked for C7 and N6, R7C9 = 1
20a. Naked triple {678} in R789C7, locked for N9
20b. Naked pair {45} in R89C9, locked for C9 and N9 -> R8C8 = 2, R8C4 = 3, R7C5 = 2, clean-up: no 9 in R5C5

21. 14(3) cage at R4C8 = {347/356}, no 8
21a. 4,5 only in R4C8 -> R4C8 = {45}
21b. R6C9 = 8 (hidden single in N6)

22. R6C45 = R3C4 + 7 (step 8)
22a. R3C4 = 1 -> R6C45 = 8 = [71] (cannot be [53] which clashes with R7C2), clean-up: no 5 in R5C5
22b. R6C45 + R7C5 = [712] = 10 -> R67C3 = 8 = {35}, locked for C3 -> R2C23 = [38]

23. 12(3) cage at R4C6 = {246} (only remaining combination), locked for C6 and N5, clean-up: no 8 in R5C45
23a. R5C45 = [93]
23b. Naked pair {58} in R4C45, locked for R4 -> R4C8 = 4, R4C9 = 3 (hidden single in N6), R5C9 = 7 (cage sum)

24. R4C3 = 9 (hidden single in C3) -> R34C2 = 5 = [41], R4C67 = [62], R234C1 = [127] = 10 -> R5C1 = 6 (cage sum)
24a. R5C2 = 8 (hidden single in R5)

and the rest is naked singles.

It was hard to decide what rating to give my walkthrough. I'll go for Hard 1.25; I think the way hidden killer pairs are linked together in step 15 makes it more than a regular 1.25.