SudokuSolver Forum

Even though this is at a Paper Solvable level, I’ll start with Prelims to save doing them as I go along. I haven’t bothered to do clean-ups but occasionally I’ve used combinations as if I’d done them.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R23C1 = {19/28/37/46}, no 5
c) R23C6 = {69/78}
d) R23C7 = {18/27/36/45}, no 9
e) R2C89 = {49/58/67}, no 1,2,3
f) R3C89 = {12}
g) R5C56 = {69/78}
h) R6C12 = {59/68}
i) R67C3 = {16/25/34}, no 7,8,9
j) R67C9 = {59/68}
k) R78C2 = {15/24}
l) 17(2) cage at R7C4 = {89}
m) R89C9 = {19/28/37/46}, no 5
n) R9C23 = {69/78}
o) 8(3) cage at R8C4 = {125/134}
p) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9

1. 45 rule on N1 2 outies R23C3 = 16 = {79}, locked for C3, N1 and 24(4) cage at R1C3, no 7,9 in R1C4 -> R8C3 = 8, R7C4 = 9, R9C3 = 6, R9C2 = 9

2. 45 rule on N7 1 remaining innie R7C3 = 3, R6C3 = 4

3. 45 rule on N4 2 remaining innies R4C23 = 8 = [35/62/71]
3a. 45 rule on N1 2(1+1) outies R1C4 + R4C2 = 13 = [67], R4C23 = [71], R1C3 = 2 (cage sum), R5C3 = 5

4. Naked pair {12} in R3C89, locked for R3 and N3
4a. R4C2 = 7 -> R23C2 = 6 = [15]

5. 45 rule on N3 2 outies R1C56 = 6 = {15}, locked for R1 and N2

6. Naked pair {24} in R78C2, locked for C2 and N7
6a. R6C12 = {68}, locked for N4 -> R5C2 = 3, R1C2 = 8, R1C1 = 3
6b. R23C6 = {78}, locked for C6 and N2 -> R5C56 = {69}, locked for R5 and N5 -> R4C12 = [92]
6c. 9 in N2 only in R23C5, locked for C5 -> R5C56 = [69]

7. 13(3) cage at R5C7 = {148}, locked for R5 and N6 -> R5C4 = 7
7a. 14(3) cage at R4C7 = {356}, locked for R4 and N6 -> R6C9 = 9, R7C9 = 5

8. 3 in N3 only in R23C7 = {36}, locked for C7 -> R4C7 = 5
8a. R2C8 = 5 (hidden single in N3), R2C9 = 8, R23C6 = [78], R23C3 = [97]

9. 45 rule on R6789 1 innie R6C4 = 3, R23C4 = [24], R4C3 = 8

10. 8(3) cage at R8C4 must contain 1 -> R9C4 = 5, R8C4 = 1
10a. 8(3) cage = 1{34}, 3,4 locked for R8 and N8 -> R78C2 = [42], R9C6 = 2, R9C5 = 8 (cage sum)

11. R7C56 = [76], R8C7 = 9 -> R6C5 + R7C7 = 7 = [52]

and the rest is naked singles.

the SS score of 0.80 feels a bit high. I only used simple combinations and a few 45s; no killer pairs, etc.

Prelims

a) R1C12 = {29/38/47/56}, no 1
b) R23C1 = {19/28/37/46}, no 5
c) R23C6 = {69/78}
d) R2C89 = {49/58/67}, no 1,2,3
e) R3C89 = {12}
f) R5C56 = {69/78}
g) R6C12 = {59/68}
h) R67C3 = {16/25/34}, no 7,8,9
i) R67C9 = {59/68}
j) R78C2 = {15/24}
k) 17(2) cage at R7C4 = {89}
l) R89C9 = {19/28/37/46}, no 5
m) R9C23 = {69/78}
n) 8(3) cage at R8C4 = {125/134}
o) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9

Steps resulting from Prelims
1a. Naked pair {12} in R3C89, locked for R3 and N3, clean-up: no 8,9 in R2C1
1b. 8(3) cage at R8C4 = {125/134}, 1 locked for R8 and N8, clean-up: no 5 in R7C2, no 9 in R9C9
1c. Killer pair 8,9 in R8C3 and R9C23, locked for N7

2. 45 rule on R6789 1 innie R6C4 = 3, clean-up: no 4 in R7C3

3. 45 rule on N8 3 innies R7C456 = 22 = {589/679}, no 2,3,4, 9 locked for R7 and N8, clean-up: no 5 in R6C9

4. 45 rule on N3 1 outie R1C56 = 6 = {15/24}

5. 45 rule on N7 2 innies R78C3 = 11 = [29/38], R6C3 = {45}

6. 45 rule on N1 2(1+1) outies R1C4 + R4C2 = 13 = {49/58/67}, no 1,2,3

7. 45 rule on N4 3 innies R4C23 + R6C3 = 12 = {147/246} (cannot be {129} because R6C3 only contains 4,5, cannot be {156} which clashes with R6C12) -> R6C3 = 4, R4C3 = {12}, R4C2 = {67}, R7C3 = 3, R8C3 = 8 (step 5), R7C4 = 9, clean-up: R1C4 = {67} (step 6), no 7 in R9C12, no 2 in R9C9
7a. Killer pair 6,7 in R1C4 and R23C6, locked for N2

8. Naked pair {69} in R9C12, locked for R9 and N7, clean-up: no 4 in R8C9

9. 6 in N8 only in R7C56 = {67} (step 3), locked for R7 and 29(5) cage at R6C5, no 6,7 in R6C5 + R8C7, clean-up: no 8 in R6C9
9a. 8 in N8 only in 15(3) cage at R9C4, locked for R9, clean-up: no 2 in R8C9

10. 24(4) cage at R1C3 = {2679} (only remaining combination), no 1,5, 2,9 locked for C3 and N1 -> R4C3 = 1, R4C2 = 7 (step 7), R1C4 = 6 (step 6), R9C23 = [96], R5C3 = 5, clean-up: no 4,5 in R1C1, no 5 in R1C2, no 1 in R2C1, no 9 in R23C6, no 8 in R3C1, no 9 in R6C1
10a. R8C4 = 1 (hidden single in C4)

11. R23C2 = [15] (hidden pair in N1)
11a. Naked pair {24} in R78C2, locked for C2 and N7, clean-up: no 7 in R1C1
11b. R23C1 = {46} (hidden pair in N1), locked for C1 -> R6C12 = [86], R5C2 = 3, R1C12 = [38], R6C9 = 9, R7C9 = 5, clean-up: no 4,8 in R2C8, no 1 in R9C9

12. R8C7 = 9 (hidden single in N9)
12a. 45 rule on N9 2 remaining innies R7C78 = 10 = {28}, locked for R7 and N9 -> R78C2 = [42]
12b. 8(3) cage at R8C4 = {134} (only remaining combination), locked for R8 and N8
12c. Naked pair {67} in R8C89, locked for R8 and N9

13. Naked pair {78} in R23C6, locked for C6 and N2 -> R7C56 = [76], R5C6 = 9, R5C5 = 6,
R45C1 = [92]

14. 14(3) cage at R5C7 = {148} (only remaining combination), locked for R5 and N6 -> R5C4 = 7
14a. 13(3) cage at R4C7 = {356} (only remaining combination), locked for R4 and N6

15. Naked pair {27} in R6C78, locked for R6 and 18(4) cage at R6C5 -> R7C8 = 8, R6C6 = 1 (cage sum)

16. R4C3 = 1, R56C4 = [73], R3C4 = 4 -> R24C4 = 10 = [28], R1C56 = [15]

17. R2C8 = 5 (hidden single in N3), R2C9 = 8

and the rest is naked singles.

I'll rate my walkthrough for Messy One 7 at 0.75. I used one killer pair.