Prelims
a) R23C6 = {18/27/36/45}, no 1
b) R3C12 = {29/38/47/56}, no 1
c) R34C5 = {18/27/36/45}, no 1
d) R3C89 = {49/58/67}, no 1,2,3
e) R5C34 = {39/48/57}, no 1,2,6
f) R5C67 = {89}
g) R67C5 = {15/24}
h) R7C12 = {29/38/47/56}, no 1
i) R78C6 = {18/27/36/45}, no 9
j) R7C89 = {29/38/47/56}, no 1
k) 19(3) cage at R1C2 = {289/379/469/478/568}, no 1
l) 8(3) cage at R1C8 = {125/134}
m) 10(3) cage at R4C7 = {127/136/145/235}, no 8,9
n) 11(3) cage at R8C1 = {128/137/146/236/245}, no 1
o) 10(3) cage at R8C8 = {127/136/145/235}, no 8,9
Steps resulting from Prelims
1a. R34C5 = {18/27/36} (cannot be {45} which clashes with R67C5), no 4,5
1b. Naked pair {89} in R5C67, locked for R5, clean-up: no 3,4 in R5C34
1c. Naked pair {57} in R5C34, locked for R5
1d. 8(3) cage at R1C8 = {125/134}, 1 locked for N3
2. 45 rule on N6 3 innies R5C7 + R6C78 = 22 = {589/679}, 9 locked for N6, CPE no 9 in R7C7
3. 45 rule on N1 1 outie R1C4 = 1 innie R1C1 + 5 -> R1C1 = {1234}, R1C4 = {6789}
4. 45 rule on N3 1 innie R1C9 = 1 outie R1C6 + 2, no 8,9 in R1C6, no 2 in R1C9
5. 13(3) cage at R4C9 = {148/238/247/346} (cannot be {157/256} which clash with R5C7 + R6C78), no 5
6. 45 rule on N4 3 innies R5C3 + R6C23 = 14 = {158/167/257/347/356} (cannot be {149/239/248} because R5C3 only contains 5,7), no 9
7. 45 rule on C6789 3(1+2) innies R4C6 + R19C9 = 20
7a. Max R19C9 = 17 -> min R4C4 = 3
7b. Max R1C9 + R4C6 = 17 (both on D/) -> min R9C9 = 3
8. 23(4) disjoint cage R19C19, max R1C1 = 4 -> min R1C9 + R9C19 = 19, no 1 in R9C1
9. 45 rule on N7 2 innies R7C3 + R9C1 = 1 outie R9C4 + 8, IOU no 8 in R7C3
10. 45 rule on N6 2 outies R6C6 + R7C7 = 1 innie R5C7 + 1, IOU no 1 in R6C6
11. 45 rule on N4 2 outies R6C4 + R7C3 = 1 innie R5C3 + 5, IOU no 5 in R6C4
[Maybe this is Ed’s one-trick pony step …?]
12. R4C6 + R19C9 = 20 (step 7) -> R9C1 + R19C9 cannot total 20 (almost overlapping cages because R9C1 “sees” all of R4C6 + R19C9; if R9C1 + R19C9 totalled 20 then R4C6 and R9C1 would have the same value) -> no 3 in R1C1, clean-up: no 8 in R1C4 (step 3)
13. 1 in N1 only in R1C1 + R123C3
13a. 45 rule on N1 4 innies R1C1 + R123C3 = 15 = {1239/1248/1347} (cannot be {1257} which clashes with R5C3, cannot be {1356} because 20(4) cage at R1C3 cannot be {356}6), no 5,6
13b. R3C12 = {29/47/56} (cannot be {38} which clashes with R1C1 + R123C3), no 3,8
14. 15(3) cage at R8C7 cannot have 9 in R9C6 (R89C7 cannot be {15} which clashes with 10(3) cage at R8C8, cannot be {24} which clashes with combined 21(5) cage at R7C8) -> no 9 in R9C6
14a. 9 in C6 only in R456C6, locked for N5
[Or more likely this is Ed’s one-trick pony step …?]
15. 45 rule on C89 5(3+2) innies R456C8 + R19C9 = 35
15a. Max R19C9 = 17 -> min R456C8 = 18
15b. Min R456C7 = [185] = 14, 13(3) cage at R4C9 -> max R456C8 = 18
15c. From steps 15a and 15b, R456C8 = 18 -> R19C9 = 17 = {89}, locked for C9, clean-up: R1C6 = {67} (step 4), no 4,5 in R3C8, no 2,3 in R7C8
15d. R19C9 = 17 -> R19C1 = 6 = [15/24/42]
15e. R19C9 = 17 -> R4C6 = 3 (step 7), placed for D/, clean-up: no 6 in R23C6, no 6 in R3C5, no 6 in R78C6
15f. R456C8 = 18, 13(3) cage at R4C9 -> R456C7 = 14 = [185], R5C6 = 9, clean-up: no 8 in R3C5
15g. R6C8 = 9 (hidden single in N6), clean-up: no 4 in R3C9, no 2 in R7C9
15h. R4C7 = 1 -> R45C8 = 9 = [63/72]
15i. R6C78 = [59] = 14 -> R6C6 + R7C7 = 9 = [27/63/72]
16. R4C6 = 3 -> R4C4 + R5C5 = 11 = [56/74]
16a. Naked pair {57} in R45C4, locked for C4 and N5; clean-up: no 2 in R1C1 (step 3), no 2 in R3C5, no 1 in R7C5, no 2 in R7C7 (step 15i), no 4 in R9C1 (step 15d)
16b. Killer pair 6,7 in R4C4 + R5C5 and R6C6 + R7C7, locked for D\
16c. 6 on D\ only in R5C5 + R6C6, locked for N5, clean-up: no 3 in R3C5
16d. Killer pair 1,2 in R34C5 and R67C5, locked for C5
17. R1C69 = [68/79], killer pair 6,9 in R1C4 and R1C69, locked for R1
18. 45 rule on N2 3 innies R1C46 + R3C5 = 16 = {169} (only remaining combination) -> R3C5 = 1, R4C5 = 8, R1C46 = [96], R1C9 = 8, placed for D/, R9C9 = 9, placed for D\, R1C1 = 4 (step 3), placed for D\, R5C5 = 6, placed for D/, R4C4 = 5 (step 16), placed for D\, R5C34 = [57], R6C6 = 2, placed for D\, R6C5 = 4, R7C5 = 2, R6C4 = 1, placed for D/, clean-up: no 7,8 in R23C6, no 7 in R3C12, no 5 in R3C9, no 9 in R7C1, no 7,9 in R7C2, no 7 in R78C6
19. R1C1 = 4, R19C9 = [89] = 17 -> R9C1 = 2 (cage sum), placed for D/, clean-up: no 9 in R3C2
20. Naked pair {38} in R2C2 + R3C8, locked for N1 and D\ -> R7C7 = 7, R8C8 = 1, clean-up: no 4 in R7C2, no 4 in R7C89
21. Naked pair {67} in R3C89, locked for R3, clean-up: no 5 in R3C12
21a. R3C12 = [92] -> R3C7 = 4, R2C8 = 5, both placed for D/, R23C6 = [45], R789C6 = [187]
22. R1C6 + R3C7 = [64] = 10 -> R12C7 = 12 = [39]
23. R8C2 = 7 -> R8C1 + R9C2 = 4 = [31]
and the rest is naked singles, without using the diagonals.
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