As usual I've stated placements on the diagonals for anyone doing manual eliminations or solving on paper.
Prelims
a) R1C78 = {18/27/36/45}, no 9
b) R2C23 = {59/68}
c) R3C12 = {15/24}
d) R5C45 = {19/28/37/46}, no 5
e) R6C23 = {14/23}
f) R67C6 = {17/26/35}, no 4,8,9
g) R78C1 = {17/26/35}, no 4,8,9
h) R8C56 = {39/48/57}, no 1,2,6
i) R9C45 = {16/25/34}, no 7,8,9
j) R9C67 = {14/23}
k) 10(3) cage at R4C7 = {127/136/145/235}, no 8,9
l) 24(3) cage at R6C5 = {789}
m) 22(3) cage at R6C7 = {589/679}
n) 19(3) cage at R6C8 = {289/379/469/478/568}, no 1
o) 26(4) cage at R4C1 = {2789/3689/4589/4679/5678}, no 1
p) 14(4) cage at R8C8 = {1238/1247/1256/1346/2345}, no 9
Steps resulting from Prelims
1a. 22(3) cage at R6C7 = {589/679}, 9 locked for C7
1b. 9 in R9 only in R9C123, locked for N7
1c. 24(3) cage at R6C5 = {789}, CPE no 7,8,9 in R8C5, clean-up: no 3,4,5 in R8C6
1d. Naked triple {789} in R7C45 + R8C6, locked for N8, clean-up: no 1 in R6C6
2. R9C45 = {16/25} (cannot be {34} which clashes with R9C67), no 3,4
2a. Combined cage R9C4567 = 12 = {1236/1245}, 1,2 locked for R9
2b. Min R9C89 = 9 (R9C89 cannot be {34/35} which clash with R9C4567) -> max R8C89 = 5, no 5,6,7,8 in R8C89
[I originally used killer pair 1,2 in step 2a but the combined cage is the simplest way to lead into step 2b.]
3. 45 rule on N1 2 innies R13C3 = 11 = {29/38/47} (cannot be {56} which clashes with R2C23), no 1,5,6
4. 45 rule on N3 2 outies R4C68 = 13 = {49/58/67}, no 1,2,3
5. 45 rule on N7 2 outies R68C4 = 7 = {16/25/34}, no 7,8,9
6. 45 rule on N12 1 innie R3C3 = 1 outie R4C5 + 3, no 2,3 in R3C3, R4C5 = {1456}, clean-up: no 8,9 in R1C3 (step 3)
7. 45 rule on N124 2 outies R4C45 = 7 = [16/25/34/61], R4C4 = {1236}
8. 45 rule on R6789 2 innies R6C19 = 12 = {39/48/57}, no 1,2,6
9. 45 rule on D/ 2(1+1) outies R2C7 + R7C2 = 1 innie R5C5
9a. Min R2C7 + R7C2 = 2 -> min R5C5 = 2, clean-up: no 9 in R5C4
10. 45 rule on C789 2 outies R45C6 = 1 innie R9C7 + 10
10a. Min R45C6 = 11, no 1 in R5C6
11. 14(3) cage at R1C1 = {167/239/347} (cannot be {149/257} which clash with R3C12, cannot be {158/356} which clash with R2C23, cannot be {248} which clashes with R13C3), no 5,8
12. 38(7) cage at R1C3 = {1256789/1346789/2345789}, 8,9 locked for N2
13. 19(3) cage at R6C8 = {289/379/469/478/568}
13a. 2,3 of {289/379} must be in R7C89 (R7C89 cannot be {79/89} which clash with R7C45, ALS block), no 2,3 in R6C8
[I saw this 45 much earlier but decided to use the 45 on N12 (step 6) instead. It was only now that I saw the key point, triggered because I realised that it led to step 15; I’d been looking at the hidden killer pair, then spotted that step 14 made it powerful.]
14. 45 rule on N2 2(1+1) outies R1C3 + R4C5 = 8 = [26/35/71] (cannot be [44] because R1C3 + R4C5 “see” all cells in N2), no 4 in R1C3, no 4 in R4C5, clean-up: no 7 in R3C3 (step 3), no 3 in R4C4 (step 7)
15. Hidden killer pair 1,2 in R6C23 and R6C46 for R6, R6C23 contains one of 1,2 -> R6C46 must contain one of 1,2
15a. Killer pair 1,2 in R4C45 and R6C46, locked for N5, clean-up: no 8,9 in R5C45
16. R4C6 + R6C5 = {89} (hidden pair in N5), clean-up: R4C8 = {45} (step 4)
16a. 7 in 24(3) cage at R6C5 must be in R7C45, locked for R7 and N8, clean-up: no 1 in R8C1, no 5 in R8C5
16b. Naked pair {89} in R48C6, locked for C6
17. R17C4 = {89} (hidden pair in C4)
17a. R7C5 = 7 (hidden single in N8), clean-up: no 3 in R5C4
18. 45 rule on C789 3 outies R459C6 = 15, min R4C6 = 8 -> max R59C6 = 7, no 7 in R5C6
19. R4C45 = 7 (step 7), R4C6 + R6C5 = {89} (step 16) = 17
19a. 45 rule on N5 3 remaining innies R5C6 + R6C46 = 11 = {137/146/245} (cannot be {236} which clashes with R4C45)
19b. 3 of {137} must be in R5C6 -> no 3 in R6C46, clean-up: no 5 in R7C6, no 4 in R8C4 (step 5)
19c. 6 of {146} must be in R6C6 -> no 6 in R5C6 + R6C4, clean-up: no 1 in R8C4 (step 5)
19d. 5 of {245} must be in R6C46 (R6C46 cannot be [42] which clashes with R6C23), no 5 in R5C6
19e. 3 in N5 only in R5C56, locked for R5
19f. 5 in N8 only in R8C4 + R9C45, CPE no 5 in R9C23
[I ought to have spotted killer pair 3,4 in R5C45 and R5C6, locked for R5 and N5.]
20. 10(3) cage at R4C7 = {136/145/235} (cannot be {127} because R5C6 only contains 3,4,5), no 7
20a. R5C6 = {34} -> no 3,4 in R45C7
20b. Killer pair 5,6 in R45C7 and 22(3) cage at R6C7, locked for C7, clean-up: no 3,4 in R1C8
21. 3 in N6 only in R46C9, locked for C9
21a. 22(4) cage at R4C9 contains 3 -> remaining three cells total 19, no 1 in 22(4) cage
22. 1 in N6 only in R45C7, locked for C7, clean-up: no 8 in R1C8, no 4 in R9C6
22a. 10(3) cage at R4C7 (step 20) contains 1 = {136/145}, no 2
23. R8C5 = 4 (hidden single in N8), R8C6 = 8, R4C6 = 9, placed for D/, R6C5 = 8, R7C4 = 9, R1C4 = 8, R4C8 = 4 (step 4), clean-up: no 1 in R1C8, no 6 in R5C4, no 4 in R6C1 (step 8)
24. 2,3 in N6 only in 22(4) cage at R4C9 = {2389} (only remaining combination), locked for N6, clean-up: no 5,7 in R6C1 (step 8)
24a. 7 in N6 only in R6C78, locked for R6, clean-up: no 1 in R7C6
25. Naked pair {39} in R6C19, locked for R6, clean-up: no 2 in R6C23
25a. Naked pair {14} in R6C23, locked for R6 and N4, clean-up: no 3,6 in R8C4 (step 5)
25b. Naked pair {25} in R68C4, locked for C4, clean-up: no 5 in R4C5 (step 7), no 2,5 in R9C5
26. Naked pair {16} in R4C45, locked for R4 and N5 -> R4C7 = 5, clean-up: no 4 in R5C4, no 2 in R7C6
26a. Naked pair {16} in R4C45, CPE no 1,6 in R23C4
26b. R5C4 = 7, R5C5 = 3, placed for both diagonals, R5C6 = 4, R5C7 = 1 (hidden single in R5)
27. 22(3) cage at R6C7 = {679} (only remaining combination) -> R7C7 = 6, placed for D\, R6C78 = [76], R8C7 = 9, R4C4 = 1, placed for D\, R4C5 = 6, R9C4 = 6, R9C5 = 1, R8C8 = 2, placed for D\, R8C9 = 1, R6C6 = 5, placed for D\, R7C6 = 3, R6C4 = 2, placed for D/, R9C6 = 2, R9C7 = 3, R8C4 = 5
28. R6C8 = 6 -> R7C89 = 13 = {58}, locked for R7 and N9 -> R9C8 = 7, R9C9 = 4, placed for D\, R1C8 = 5, R1C7 = 4, R3C7 = 8, R2C8 = 1, both placed for D/, R2C7 = 2, R7C23 = [14], R7C1 = 2, R8C1 = 6, R8C2 = 7, placed for D/, R1C9 = 6
and the rest is naked singles.
Login
Register
FAQ
Search
