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) R89C9 = {19/28/37/46}, no 5
l) R9C23 = {69/78}
m) 11(3) cage at R8C8 = {128/137/146/236/245}, no 9
1. Naked pair {12} in R3C89, locked for R3 and N3, clean-up: no 8,9 in R2C1
2. 45 rule on R6789 1 innie R6C4 = 3, clean-up: no 4 in R7C3
3. 45 rule on N3 1 outie R1C56 = 6 = {15/24}
3a. 35(7) cage at R1C5 must contain at least one of 6,7
3b. R2C89 = {49/58} (cannot be {67} which clashes with 35(7) cage), no 6,7 in R2C89
4. 45 rule on N1 2(1+1) outies R1C4 + R4C2 = 13 = {49/58/67}, no 1,2,3
5. 45 rule on N7 2 innies R78C3 = 11 = [29/38/56/65], clean-up: no 6 in R6C3
6. 45 rule on N4 3 innies R4C23 + R6C3 = 12 = {129/147/246} (cannot be {156} which clashes with R6C12), no 5,8, clean-up: no 5,8 in R1C4 (step 4), no 2 in R7C3, no 9 in R8C3 (step 5)
6a. 9 of {129} must be in R4C2, no 9 in R4C3
7. R78C3 (step 5) = [38/56/65]
7a. Killer pair 6,8 in R78C3 and R9C23, locked for N7
8. 45 rule on R9 2 innies R9C19 = 1 outie R8C8 + 4, IOU no 4 in R9C1
9. 45 rule on C123 2 innies R48C3 = 1 outie R1C4 + 3
9a. R1C4 = {4679} -> R48C3 = 7,9,10,12 -> no 6 in R4C3 (because no 1,3,4 in R8C4)
10. 45 rule on C12 1 innie R9C2 = 1 outie R5C3 + 4, R9C2 = {6789} -> R5C3 = {2345}
[I can see a complex clash in N1 to make the following elimination, but prefer this way …]
11. Consider combinations for R4C23 + R6C3 (step 6) = {129/147/246}
R4C23 + R6C3 = {129/147}, 1 locked for C3
or R4C23 + R6C3 = {246} => R4C2 = 6, R1C4 = 7 (step 4) => 24(4) cage at R1C3 cannot be {1689} (only combination for 24(4) containing 1)
-> no 1 in R12C3)
[With hindsight, an alternative way is 24(4) cage at R1C3 cannot be {1689} because {168}9 clashes with R78C3 and {189}6 clashes with R4C23 + R6C3 = 7{14} using step 4 -> no 1 in R12C3.
I’d originally seen the first half of that, but had blocked {189}6 by the combined cage R1C12 + R23C1 which must contain at least one of 8,9 because of the interactions between R1C12 and R23C1.]
12. 1 in R1 only in R1C56 = {15} (step 3), locked for R1, N2 and 35(7) cage at R1C5, no 5 in R23C7, clean-up: no 6 in R1C12
12a. 5 in N3 only in R2C89 = {58}, locked for R2 and N3, clean-up: no 7 in R3C6
12b. 2,8 in R1 only in R1C123, locked for N1
12c. R1C12 cannot contain both of 2,8 -> R1C3 = {28} (hidden killer pair 2,8 for N1)
[Afmob pointed out that this also implies R1C12 = {29/38}.]
13. 24(4) cage at R1C3 = {2679/3489/3678/4578} (cannot be {2589} which contains both of 2,8, other combinations don’t contain 2 or 8)
13a. 24(4) cage = {2679/3678} (cannot be {3489} which clashes with R1C12, cannot be {4578} which clashes with R78C3), no 4,5, clean-up: no 9 in R4C2 (step 4)
14. R3C2 = 5 (hidden single in N1), clean-up: no 9 in R6C1, no 1 in R78C2
14a. Naked pair {24} in R78C2, locked for C2 and N7, clean-up: no 7,9 in R1C1
14b. R3C2 = 5 -> R24C2 = 8 = [17], R1C4 = 6 (step 4), clean-up: no 4 in R1C1, no 9 in R23C6, no 9 in R3C1, no 8 in R9C3
14c. 6 in N3 only in R23C7, locked for C7
14d. R23C1 = {46} (hidden pair in N1), locked for C1, clean-up: no 8 in R6C2
15. R23C6 = [78], clean-up: no 7,8 in R5C5
15a. Naked pair {69} in R5C56, locked for R5 and N5
[With hindsight, I could have done naked quad {6789} in R23C6 and R5C56, CPE no 6,7,8,9 in R6C6 earlier, but it wouldn’t have achieved much.]
16. R3C3 = 7 (hidden single in N1), clean-up: no 8 in R9C2
16a. Naked pair {69} in R9C23, locked for R9 and N7, clean-up: no 1,4 in R8C9
16b. 13(3) cage at R7C1 = {157} (only remaining combination), locked for C1 and N7 -> R6C1 = 8, R6C2 = 6, R78C3 = [38], R6C3 = 4, R5C123 = [235], R4C13 = [91], R1C1 = 3, R1C2 = 8, R12C3 = [29], R9C23 = [96], clean-up: no 6,8 in R7C9, no 2 in R9C9
16c. Naked pair {59} in R67C9, locked for C9 -> R2C89 = [58], clean-up: no 2 in R8C9, no 1 in R9C9
17. 6 in N6 only in 14(3) cage at R4C7 = {356} (only remaining combination) -> R4C7 = 5, R67C9 = [95]
18. R35C9 = [21] (hidden pair in C9), R3C8 = 1
18a. Naked pair {27} in R6C78, locked for R6, N5 and 18(4) cage at R6C6, no 2,7 in R7C8
19. R5C4 = 7 (hidden single in R5)
19a. 25(6) cage at R2C4 = {123478} (only remaining combination) -> R234C4 = [248], R23C1 = [46], R23C5 = [39], R23C7 = [63], R5C56 = [69]
20. 11(3) cage at R8C8 = {128/137/146} (cannot be {236} which clashes with R89C9) -> R9C7 = 1, R9C4 = 5, R9C1 = 7, R78C1 = [15], clean-up: no 3 in R8C9
20a. R9C4 = 5 -> R9C56 = 10 = [82]
21. R78C4 = [91], R8C3 = 8 -> R8C56 = 7 = [43], R78C2 = [42]
22. R7C56 = [76], R7C78 = [28], R8C7 = 9, R6C5 = 5 (cage sum)
and the rest is naked singles.
Login
Register
FAQ
Search
