Prelims
a) R12C1 = {17/26/35}, no 4,8,9
b) R1C23 = {29/38/47/56}, no 1
c) R3C12 = {39/48/57}, no 1,2,6
d) R34C7 = {18/27/36/45}, no 9
e) R4C56 = {18/27/36/45}, no 9
f) R5C34 = {49/58/67}, no 1,2,3
g) R5C67 = {29/38/47/56}, no 1
h) R67C3 = {17/26/35}, no 4,8,9
i) R6C45 = {17/26/35}, no 4,8,9
j) R7C89 = {13}
k) 11(3) cage at R2C9 = {128/137/146/236/245}, no 9
l) 24(3) cage at R7C1 = {789}
m) 21(3) cage at R7C4 = {489/579/678}, no 1,2,3
n) 14(4) cage at R7C6 = {1238/1247/1256/1346/2345}, no 9
o) 26(4) cage at R8C9 = {2789/3689/4589/4679/5678}, no 1
Steps resulting from Prelims
1a. Naked pair {13} in R7C89, locked for R7 and N9, clean-up: no 5,7 in R6C3
1b. Naked triple {789} in 24(3) cage at R7C1, locked for N7, clean-up: no 1 in R6C3
1c. 14(4) cage at R7C6 = {1247/1256/2345} (cannot be {1238/1346} because 1,3 only in R8C6), no 8 -> R8C6 = {13}
2a. {456} of 21(3) cage at R7C4 must be in R7C45 (R7C45 cannot be {78/79/89} which clash with R7C12, ALS block) -> no 4,5,6 in R8C4
2b. Killer triple 7,8,9 in R7C12 and R7C45, locked for R7
3a. 45 rule on N3 2 innies R2C8 + R3C7 = 15 = [78/87/96] -> R4C7 = {123}
3b. 45 rule on N7 2 innies R7C3 + R8C2 = 6 = [24/51] -> R6C3 = {36}
3c. 14(4) cage at R7C6 (step 1c) = {1256/2345} (cannot be {1247} = {24}[17] which clashes with R7C3 + R8C2), no 7
3d. 45 rule on N12 2 innies R2C25 = 14 = {59/68}
3e. 45 rule on N1 3 innies R2C23 + R3C3 = 14, min R2C2 = 5 -> max R23C3 = 9, no 9 in R23C3
3f. 45 rule on N1 2 outies R23C4 = 1 innie R2C2 + 4, IOU no 4 in R3C4
3g. 45 rule on N89 2 innies R8C58 = 10 = [19/37]/{28/46}, no 5, no 7,9 in R8C5
3h. 45 rule on R1 2 outies R2C17 = 5 = [14/23/32] -> R1C1 = {567}
3i. 1 in N1 only in R2C1 + R23C3, CPE no 1 in R2C4
3j. 45 rule on R9 2 outies R8C39 = 11 = [29/38/47]/{56}, no 1 in R8C3, no 2,4 in R8C9
3k. 45 rule on N47 2 outies R45C4 = 2 innies R58C2 + 9
3l. Min R58C2 = 3 -> min R45C4 = 12, no 1,2 in R4C4
3m. Max R45C4 = 17 -> max R58C2 = 8, no 8,9 in R5C2
3n. 45 rule on N8 3 innies R7C6 + R8C56 = 9 = {126/135/234}, no 8, clean-up: no 2 in R8C8
4a. 45 rule on R4 3 innies R4C789 = 11 = {128/137/146/236/245}, no 9
4b. 45 rule on R4 1 outie R5C9 = 1 innie R4C7 + 6, R4C7 = {123} -> R5C9 = {789}
4c. 45 rule on R6 1 innie R6C3 = 1 outie R5C1 + 2, R6C3 = {36} -> R5C1 = {14}
4d. 21(4) cage at R6C6 = {1389/1479/1578/2469/2478/2568/3459} (cannot be {1569/2379/3567} which clash with R6C45, cannot be {3468} which clashes with R6C3)
4e. 21(4) cage = {1479/1578/2469/2478/2568/3459} (cannot be {1389} because 21(4) cage combined with R6C45 = {26} clashes with R6C3)
5a. 14(4) cage at R7C6 (step 3c) = {1256/2345}, R7C6 + R8C56 (step 3n) = {126/135/234}
5b. Consider permutations for R7C3 + R8C2 (step 3b) = [24/51]
R7C3 + R8C3 = [24] => R8C7 = 2 => R7C6 + R8C56 = {135}
or R7C3 + R8C3 = [51] => R8C6 = 3 => R7C6 + R8C56 = {135/234}
-> R7C6 + R8C56 = {135/234}, no 6, 3 locked for R8 and N8, clean-up: no 4 in R8C8 (step 3g), no 8 in R8C9 (step 3j)
5c. Hidden killer pair 4,6 in 21(3) cage at R7C4 and 14(4) cage for R7, neither can contain both of 4,6 -> each must contain one of 4,6 -> 21(3) cage = {489/678}, no 5, 8 locked for N8
5d. 4,6 of 21(4) cage must be in R7C67 -> no 4,6 in R8C7
5e. 8 in R9 only in R9C789, locked for N9, clean-up: no 2 in R8C5 (step 3g)
5f. 45 rule on N9 3 innies R7C7 + R8C78 = 15 = {249/267/456}
5g. R8C7 = {25} -> no 2,5 in R7C7
5h. R7C67 contains one of 4,6, R7C7 = {46} -> no 4 in R7C6
[Alternatively R7C36 = {25} (hidden pair in R7).]
5i. R7C6 + R8C56 = {135/234}
5j. Naked triple {134} in R8C256, 4 locked for R8
6a. 45 rule on R6 3 innies R6C123 = 16 = {169/268/349/358} (cannot be {178/259/457} because R6C3 only contains 3,6, cannot be {367} which clashes with R6C45), no 7
6b. R6C3 = {36} -> no 3,6 in R6C12
7a. R2C8 + R34C7 (step 3a) = [781/872/963]
7b. R7C7 + R8C78 (step 5f) = {249/456} (cannot be {267} = [627] which clashes with R2C8 + R34C7) -> R7C7 = 4, R8C8 = {69}, R8C6 = 3 (cage sum), clean-up: no 1 in R2C1 (step 3h), no 7 in R1C1, no 6 in R4C5, no 7 in R5C6, no 8 in R5C7
7c. Naked pair {23} in R2C17, locked for R2
7d. R1C23 = {29/38/47} (cannot be {56} which clashes with R1C1), no 5,6
7e. 21(3) cage at R7C4 = {678} (only remaining combination), 6,7 locked for N8
7f. 9 in R7 only in R7C12, locked for N7
7g. Naked pair {78} in R8C14, 7 locked for R8
7h. 9 in R8 only in R8C89, locked for N9
7i. 1 in N1 only in R23C3, locked for C3 and 18(4) cage at R2C3
8. 45 rule on R45 5(1+4) innies R4C7 + R5C1258 = 15 -> max R5C1258 = 14, no 9 in R5C58
9a. R2C8 + R34C7 (step 3a) = [781/872/963], R5C9 = R4C7 + 6 (step 4b)
9b. Consider placement of 9 in R8
R8C8 = 9 => R2C8 + R3C7 = [781/872]
or R8C9 = 9 => R5C9 = {78}, R4C7 = {12}
-> R2C8 + R3C7 = [781/872], 7,8 locked for N3, R4C7 = {12}, R5C9 = {78}
With hindsight, Ed might have seen this as
45 rule on N3 1 innie R2C8 = 1 outie R4C7 + 6, 45 rule on R4 1 outie R5C9 = 1 innie R4C7 + 6 -> R2C8 = R5C9 = [77/88/99]
9 in R8 only in R8C89 -> R2C8 = R5C9 = [77/88] (cannot be [99]) -> R4C7 = {12}
Alternatively there’s the unusual but direct 45 rule on N3 + R4 (valid since they’re adjacent but don’t overlap) 1 outie R5C9 = 1 innie R2C8 = [77/88/99] …
9c. R34C7 + R5C9 = [728/817] -> naked pair {78} in R3C7 + R5C9, CPE no 7 in R5C7, clean-up: no 4 in R5C7
9d. 11(3) cage at R2C9 = {146/245} (cannot be {236} which clashes with R2C7), no 3, 4 locked for N3
9e. 9 in N3 only in R1C789, locked for R1, clean-up: no 2 in R1C23
9f. 19(4) cage at R1C7 contains 3,9 for N3 = {1369/2359}
9g. Killer pair 5,6 in R1C1 and 19(4) cage, locked for R1
9h. 12(3) cage at R1C4 = {138/147} (cannot be {237} much clashes with R1C23), no 2, 1 locked for R1 and N2
9i. 19(4) cage = {2359} -> 11(3) cage = {146}
9j. R1C1 = 6 (hidden single in R1) -> R2C17 = [23], clean-up: no 8 in R2C5 (step 3d), no 8 in R5C6
9k. R3C12 = {39/57} (cannot be {48} which clashes with R1C23), no 4,8
10a. 1 in N1 only in R23C3
10b. R2C23 + R3C3 (step 3e) = 14 = {149/158}, no 3,7
10c. R2C25 (step 3d) = [59/86/95]
10d. 45 rule on N2 3 innies R2C45 + R3C4 = 18 = {279/369/378/459/468/567}
10e. {459} cannot be [459] which clashes with R2C2 + R23C3 = 9{14} using R2C25, {567} cannot be [657/756] which clashes with R78C4, ALS block) -> no 5 in R2C5, clean-up: no 9 in R2C2
[Cracked. Straightforward from here.]
10f. 9 in N1 only in R3C12 = {39}, locked for R3, 3 locked for N1, clean-up: no 8 in R1C23
10g. Naked pair {47} in R1C23, locked for R1, 4 locked for N1
10h. Naked triple {138} in 12(3) cage at R1C4, 8 locked for N1
10i. R2C23 + R3C3 = {158} -> R23C3 = {18} (cannot be {15} because R23C4 cannot total 12 without 5), 8 locked for C3 and N1, clean-up: no 5 in R5C4
10j. R23C3 = {18} = 9 -> R23C4 = 9 = [45/72]
10k. R2C2 = 5 -> R2C5 = 9
11a. 15(3) cage at R2C6 = {267/456}
11b. 7 of {267} must be in R2C6 -> no 7 in R3C56
11c. R3C7 = 7 (hidden single in R3) -> R4C7 = 2, R5C9 = 8 (step 4b), R8C7 = 5, R1C7 = 9, R5C7 = 6 -> R5C6 = 5, R7C36 = [52] -> R6C3 = 3, R8C2 = 1 (step 3b), R6C7 = 1, R5C1 = 1 (step 4c), clean-up: no 7 in R6C45
11d. Naked pair {26} in R6C45, locked for R6 and N5
11e. 1 in R4 only in R4C56 = {18}, 8 locked for R4 and N5
11f. R5C9 = 8 -> R4C89 = 9 = {45}, locked for R4 and N6
11g. Naked pair {79} in R6C89, locked for R6, 7 locked for N6 -> R6C6 = 4
11h. R5C58 = [73]
11i. R23C6 = [76] -> R3C5 = 2 (cage sum)
and the rest is naked singles.
Login
Register
FAQ
Search
