Afmob wrote:
... but if you want you can look for hidden signs
When I coloured the cages, the pattern looked like a flower.
Afmob wrote:
This one can be solved in a matter of seconds (though minutes is more realistic).
I assume you mean that the breakthrough can be achieved in that time. Congratulations to everyone who does that! Unfortunately I didn't. It took me about 2 hours until I eventually spotted the breakthrough and then about another hour to complete my walkthrough. Still I'm not a quick solver.
I'm surprised at the SS rating. I'll rate A122 at 1.25 the way I solved it. If one gets the breakthrough move early then it's probably Hard 1.0.
Here is my walkthrough. I've left the breakthrough move where I found it. Some of my earlier moves were interesting and might possibly be useful for Afmob's harder version.
Prelims
a) R5C23 = {16/25/34}, no 7,8,9
b) R5C78 = {69/78}
c) 20(3) cage at R2C3 = {389/479/569/578}, no 1,2
d) 20(3) cage at R2C6 = {389/479/569/578}, no 1,2
e) 9(3) diagonal cage at R2C8 = {126/135/234}, no 7,8,9
f) 9(3) cage at R3C8 = {126/135/234}, no 7,8,9
g) R456C1 = {589/679}, 9 locked for C1 and N4
h) R456C9 = {569/578} (cannot be {389/479} which clash with R5C78), 5 locked for C9 and N6
i) 8(3) cage at R6C2 = {125/134}, CPE no 1 in R45C2, clean-up: no 6 in R5C3
j) 21(3) diagonal cage at R6C4 = {489/579/678}, no 1,2,3
k) 11(3) cage at R7C6 = {128/137/146/236/245}, no 9
l) 13(4) remote cage at R2C5 = {1237/1246/1345}, no 8,9, 1 locked for C5
m) 31(5) cage in N3 = {16789/25789/34789/35689/45679}, 9 locked for N3
n) 18(5) cage in N9 = {12348/12357/12456}, 1,2 locked for N9
1. Naked quint {56789} in R5C78 and R456C9, locked for N6
2. 45 rule on C1234 3 innies R159C4 = 7 = {124}, locked for C4
2a. Max R1C4 = 4 -> min R1C56 = 13, no 1,2,3,4 (because R1C456 cannot be 4{49})
2b. Max R9C4 = 4 -> min R9C56 = 11, no 1 in R9C6
3. 45 rule on N4 2 outies R37C2 = 7 = {25/34}/[61], no 1,7,8,9 in R3C2
4. 45 rule on N6 2 outies R37C8 = 11 = [29/38/47/56/65], no 1 in R3C8, no 3,4 in R7C8
5. 45 rule on D\ 3 innies R1C1 + R5C5 + R9C9 = 11 = {128/137/146/236/245}, no 9
6. 45 rule on N2 2 outies R2C37 = 2 innies R23C5 + 12
6a. Min R23C5 = 3 -> min R2C37 = 15, no 3,4,5, no 6 in R2C7
6b. Max R2C37 = 17 -> max R23C5 = 5, no 5,6,7
7. 45 rule on N3 4 innies R23C78 = 14 = {1238/1247/1256/1346} (cannot be {2345} because R2C7 only contains 6,7,8), 1 locked in R2C8 + R3C7, locked for N3 and D/
7a. 6 of {1256/1346} must be in R2C7 -> no 6 in R2C8 + R3C78, clean-up: no 5 in R7C8 (step 4)
7b. 1 in C9 locked in R789C9, locked for N9
7c. 9(3) cage at R3C8 = {135/234}, CPE no 3 in R6C8
8. 9(3) diagonal cage at R2C8 = {126/135}, no 4
8a. 6 of {126} must be in R4C6 -> no 2 in R4C6
9. 45 rule on N8 4 outies R23C5 + R8C37 = 11
9a. Min R23C5 = 3 -> max R8C37 = 8, no 6,7,8,9 in R8C3, no 8 in R8C7
10. 45 rule on N7 1 outie R6C4 = 2 innies R7C2 + R8C3 + 3
10a. Min R7C2 + R8C3 = 3 -> min R6C4 = 6
11. 11(3) cage at R7C6 = {137/146/236/245} (cannot be {128} because no 1,2,8) in R8C7), no 8
12. Hidden killer pair 8,9 in R78C4 and R9C56 for N8, neither can have both of 8,9 -> each must contain one of 8,9
12a. R9C456 = {159/168/249/258/348} (cannot be {267/357/456} which don’t contain 8 or 9), no 7
13. 45 rule on N1 2 innies R2C3 + R3C2 = 1 outie R4C4 + 9
13a. Min R4C4 = 3 -> min R2C3 + R3C2 = 12, no 2 in R3C2, clean-up: no 5 in R7C2 (step 3)
13b. Max R2C3 + R3C2 = 15 -> max R4C4 = 6
14. Hidden killer pair 7,8 in R456C1 and R4C23 for N4 -> R4C23 must contain one of 7,8
14a. 15(3) cage at R3C2 = {168/258/267/348/357} (cannot be {456} which doesn’t contain 7 or 8)
14b. 6 of {168/267} must be in R3C2 -> no 6 in R4C23
15. 45 rule on N5 4 innies R46C46 = 21 = {1569/2568/3459/3468/3567} (other combinations don’t contain at least two of 3,5,6)
15a. 1,2 of {1569/2568} must be in R6C6, 8,9 of {3459/3468} must be in R6C4 -> no 8,9 in R6C6
16. Hidden killer quad 1,2,3,4 in R1C4 + R23C5 + R23C46 for N2 -> R23C46 must contain 3 or 4 -> one of 20(3) cage at R2C3 + 20(3) cage at R2C6 must contain {389/479} and the other must contain {569/578} -> 5 locked in R23C46, locked for N2
17. 45 rule on N3 3 outies R4C678 = 1 innie R2C7 + 4
17a. Min R2C7 = 6 -> min R4C678 = 10, max R4C78 = 7 -> no 3 in R4C6 (because R4C678 cannot be 3{34})
17b. 9(3) diagonal cage at R2C8 (step 8) = {126/135}
17c. 5 of {135} must be in R4C6 -> no 5 in R2C8 + R3C7
18. 45 rule on N1 4 innies R23C23 = 25 = {2689/3589/3679/4579/4678} (cannot be {1789} because no 7,8,9 in R3C2), no 1
Only just spotted an important step!
19. 45 rule on R1 + R9 + C1 + C9 4 innies R19C19 = 10 = {1234} (because total of the outside cages = 170 and is the only combination because R19C19 are common peers)
20. 45 rule on D/ 3 innies R1C9 + R5C5 + R9C1 = 15 = {348} (only remaining combination, cannot be {258/267/357/456} which only contain one of 2,3,4) -> R5C5 = 8, locked for D/ and D\, R1C9 + R9C1 = {34}, locked for D/, CPE no 3,4 in R1C1 + R9C9, clean-up: no 5 in R4C6 (step 8), no 7 in R5C78
20a. Naked pair {12} in R1C1 + R9C9, locked for D\
20b. R4C6 = 6, locked for D/
20c. Naked pair {69} in R5C78, locked for R5 and N6, clean-up: no 1 in R5C3
20d. Naked triple {578} in R456C9, locked for C9
20e. Naked triple {579} in 21(3) diagonal cage at R6C4, 5 locked for N7
20f. Naked pair {12} in R2C8 + R3C7, locked for N3, clean-up: no 9 in R7C8 (step 4)
21. Naked pair {57} in R5C19, locked for R5, clean-up: no 2 in R5C23
21a. Naked pair {34} in R5C23, locked for R5 and N4
22. R5C456 = {128} = 11 -> R46C5 = 13 = {49} (only remaining combination), locked for C5 and N5 -> R6C4 = 7
22a. Naked pair {59} in R7C3 + R8C2, locked for N7
22b. Naked pair {35} in R4C4 + R6C6, locked for D\
23. 13(4) remote cage at R2C5 (prelim l) = {1237} (only remaining combination), locked for C5, 7 locked in R78C5 for N8
23a. R1C5 = 6 -> R1C46 = 11 = [29/47], no 1 in R1C4, no 8 in R1C6
23b. R9C5 = 5 -> R9C46 = 10 = [19/28], no 4 in R9C4, no 2,3,4 in R9C6
23c. R1C4 = 4 (hidden single in C4), R1C6 = 7 (step 23a), R1C9 = 3, locked for D/ -> R9C1 = 4, clean-up: no 8 in R2C7 (step 7), no 3 in R3C2 (step 3), no 8 in R7C8 (step 4)
24. R6C1 = 6 (hidden single in N4), R45C1 = [97] (prelim g), R5C9 = 5, R46C9, = [78], R46C5 = [49]
24a. 8 in R4 locked in R4C23 -> 15(3) cage at R3C2 = {168/258}, no 4, clean-up: no 3 in R7C2 (step 3)
24b. 5 of {258} must be in R3C2 -> no 5 in R4C23
24c. 5 in N4 locked in R6C23, locked for R6 -> R6C6 = 3, R4C4 = 5
25. 20(3) cage at R2C3 = {389} (step 16), 3 locked in R23C4, locked for C4 and N2
25a. Naked pair {12} in R23C5, locked for C5
26. R2C7 = 7 (hidden single in N3), clean-up: no 9 in R23C6 (prelim d)
26a. Naked pair {58} in R23C6, locked for C6 and N2 -> R9C6 = 9, R9C4 = 1 (step 23b), R9C9 = 2, locked for D\, R1C1 = 1, R5C46 = [21]
26b. Naked pair {39} in R23C4, locked for C4 and 20(3) cage -> R2C3 = 8, R23C6 = [58]
27. Naked quad {2359} in R1C23 + R23C1, locked for N1 -> R3C2 = 6, R2C2 = 4, R3C3 = 7, both locked for D\, R5C23 = [34]
28. 2 in R1 locked in R1C23, locked for N1 -> R23C1 = [35], R23C4 = [93], R2C9 = 6, R3C89 = [49], R7C8 = 7 (step 4), R78C5 = [37]
29. Naked triple {124} in R7C269, locked for R7 -> R78C1 = [82]
and the rest is naked singles.