Thanks manu for a fun Assassin with an interesting cage pattern!
As usual my walkthrough is how I solved the puzzle. I'll leave it to others to post an optimised walkthrough. I expect that will use the same technique that I used but will probably be quicker in the later stages.
Here is my walkthrough for A196.
Prelims
a) R3C34 = {39/48/57}, no 1,2,6
b) R34C5 = {18/27/36/45}, no 9
c) R3C67 = {19/28/37/46}, no 5
d) R4C23 = {29/38/47/56}, no 1
e) R4C78 = {15/24}
f) R6C23 = {14/23}
g) R67C5 = {39/48/57}, no 1,2,6
h) R6C78 = {59/68}
i) R7C34 = {18/27/36/45}, no 9
j) R7C67 = {19/28/37/46}, no 5
k) 11(3) cage at R1C4 = {128/137/146/236/245}, no 9
l) 19(3) cage at R1C6 = {289/379/469/478/568}, no 1
m) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
n) 11(3) cage at R3C8 = {128/137/146/236/245}, no 9
o) 11(3) cage at R6C1 = {128/137/146/236/245}, no 9
p) 20(3) cage at R6C9 = {389/479/569/578}, no 1,2
1. 45 rule on R34 2 innies R4C46 = 12 = {39/48/57}, no 1,2,6
2. 45 rule on R67 2 innies R6C46 = 9 = {18/27/36/45}, no 9
3. 45 rule on N1 1 outie R4C1 = 1 innie R3C3, no 2,6 in R4C1
4. 45 rule on N3 1 outie R4C9 = 1 innie R3C7, no 9 in R3C7, no 5 in R4C9, clean-up: no 1 in R3C6
5. 45 rule on N9 1 outie R6C9 = 1 innie R7C7 + 2, no 7 in R6C9, no 8,9 in R7C7, clean-up: no 1,2 in R7C6
6. 45 rule on N1 3 innies R3C123 = 19
6a. R3C12 cannot contain R3C123 – R3C34 = 19 – 12 = 7 (otherwise R3C13/R3C23 = R3C34, CCC) -> no 7 in R3C12
6b. R3C123 = 19 = {289/379/469/478/568}
6c. 7 of {379} must be in R3C3 -> no 3 in R3C3, clean-up: no 9 in R3C4, no 3 in R4C1 (step 3)
7. 45 rule on N3 3 innies R3C789 = 11
7a. R3C89 cannot contain R3C789 – R3C67 = 11 – 10 = 1 (otherwise R3C78/R3C79 = R3C67, CCC) -> no 1 in R3C89
7b. R3C789 = 11 = {128/137/146/236/245}
7c. 1 of {128/137} must be in R3C7 -> no 7,8 in R3C7, clean-up: no 2,3 in R3C6, no 7,8 in R4C9 (step 4)
8. 45 rule on N7 1 outie R6C1 = 1 innie R7C3
8a. 45 rule on N7 3 innies R7C123 = 11
8b. R7C12 cannot contain R7C123 – R7C34 = 11 – 9 = 2 (otherwise R7C13/R7C23 = R7C34, CCC) -> no 2 in R7C12
8c. R7C123 = 11 = {128/137/146/236/245}
8d. 2 of {128} must be in R7C3 -> no 8 in R7C3, clean-up: no 8 in R6C1, no 1 in R7C4
9. 45 rule on N9 3 innies R7C789 = 18
9a. R7C89 cannot contain R7C789 – R7C67 = 18 – 10 = 8 (otherwise R7C78/R7C79 = R7C67, CCC) -> no 8 in R7C89
9b. R7C789 = 18 = {279/369/459}, no 1, 9 locked for R7, N9 and 20(3) cage at R6C9, no 9 in R6C9, clean-up: no 3 in R6C5, no 3 in R6C9 (step 5), no 7 in R7C7 (step 5), no 3 in R7C6
9c. 4 of {459} must be in R7C7 -> no 4 in R7C89
9d. 1 in R7 only in R7C123, locked for N7
9e. R7C123 (step 8c) = {128/137/146}, no 5, clean-up: no 5 in R6C1 (step 8), no 4 in R7C4
10. 45 rule on N2 3 innies R3C456 = 15
10a. R3C56 cannot contain R3C456 – R3C34 = 15 – 12 = 3 (otherwise R3C45/R3C46 = R3C34, CCC) -> no 3 in R3C5, clean-up: no 6 in R4C5
10b. R3C45 cannot contain R3C456 – R3C67 = 15 – 10 = 5 (otherwise R3C46/R3C56 = R3C67, CCC) -> no 5 in R3C45, clean-up: no 7 in R3C3, no 7 in R4C1 (step 3), no 4 in R4C5
10c. R3C123 (step 6b) = {289/469/568}, no 3
11. 45 rule on N8 3 innies R7C456 = 16
11a. R7C56 cannot contain R7C456 – R7C45 = 16 – 9 = 7 (otherwise R7C45/R7C46 = R7C34, CCC) -> no 7 in R7C56, clean-up: no 5 in R6C5, no 3 in R7C7, no 5 in R6C9 (step 5)
11b. R7C45 cannot contain R7C456 – R7C67 = 16 – 10 = 6 (otherwise R7C46/R7C56 = R7C67, CCC) -> no 6 in R7C4, clean-up: no 3 in R7C3, no 3 in R6C1 (step 8)
11c. R7C456 = 16 = {268/358/367/457}
11d. 2 of {268} must be in R7C4, 8 of {358} must be in R7C6 -> no 8 in R7C4, clean-up: no 1 in R7C3, no 1 in R6C1 (step 8)
11e. 4 of {457} must be in R7C6 -> no 4 in R7C5, clean-up: no 8 in R6C5
12. 45 rule on R7 3 outies R6C159 = 17 = {278/467} (cannot be {269} which clashes with R6C78), no 9, 7 locked for R6, clean-up: no 2 in R6C46 (step 2), no 3 in R7C5
12a. R7C456 (step 11c) = {268/358/457} (cannot be {367} because 3,7 only in R7C4)
12b. 3,7 of {358/457} must be in R7C4 -> no 5 in R7C4, clean-up: no 4 in R7C3, no 4 in R6C1 (step 8)
13. R34C5 = {18/27}/[63] (cannot be [45] which clashes with R67C5), no 4,5
14. R3C456 (step 10) = 15 = {168/249/267/348}
14a. 1,2 only in R3C5, 8 of {348} must be in R3C5 -> R3C5 = {128}, clean-up: no 2,3 in R4C5
14b. 6,9 only in R3C6, 8 of {345} must be in R3C5 -> no 7,8 in R3C6, clean-up: no 2,3 in R3C7, no 2,3 in R4C9 (step 4)
14c. Killer pair 7,8 in R34C5 and R67C5, locked for C5
15. 7 in C5 only in R46C5, locked for N5, clean-up: no 5 in R4C46 (step 1)
15a. R46C5 = R5C37 (law of leftovers (LOL) for N5, this means these pairs of cages must contain the same two numbers, not just have the same total) -> no 2,3,5,6,9 in R5C37
15b. 2 in 45(9) cage at R4C4 only in R5C456, locked for R5
15c. 7 in 45(9) cage at R4C4 only in R5C37, locked for R5
16. 19(3) cage at R1C6 = {379/568} (cannot be {289/469/478} which clash with R3C456), no 2,4
16a. R3C456 (step 14) = {168/249} (cannot be {267/348} which clash with 19(3) cage), no 3,7, clean-up: no 5,9 in R3C3, no 5,9 in R4C1 (step 3)
16b. 1,2 only in R3C5 -> R3C5 = {12}, clean-up: no 1 in R4C5, no 1 in R5C37 (LOL, step 15a)
16c. 6,9 only in R3C6 -> R3C6 = {69}, clean-up: no 6 in R3C7, no 6 in R4C9 (step 4)
17. Naked pair {48} in R3C34, locked for R3 -> R3C7 = 1, R3C6 = 9, R4C9 = 1 (step 4), R3C5 = 2, R4C5 = 7, R6C5 = 4, R7C5 = 8, clean-up: no 4 in R4C23, no 3,8 in R4C4 (step 1), no 8 in R4C6 (step 1), no 5 in R4C78, no 8 in R5C37 (LOL, step 15a), no 1 in R6C23, no 5 in R6C46 (step 2), no 2 in R7C7
17a. R4C46 = [93], clean-up: no 2,8 in R4C23, no 6 in R6C46 (step 2)
17b. Naked pair {47} in R5C37, locked for R5
17c. Naked pair {18} in R6C46, locked for R6 and N5 -> R6C9 = 6, R7C7 = 4 (step 5), R7C6 = 6, R5C7 = 7, R5C3 = 4, R3C34 = [84], R4C1 = 8
17d. Naked triple {256} in R5C456, locked for R5
18. Naked pair {23} in R6C23, locked for R6 and N4 -> R6C1 = 7, R7C3 = 7 (step 8), R7C4 = 2
18a. Naked pair {13} in R7C12, locked for R7 and N7
18b. Naked pair {59} in R7C89, locked for N9
18c. Naked pair {56} in R3C12, locked for R3 and N1
18d. Naked pair {37} in R3C89, locked for N3
19. 1 in C3 only in R12C3, locked for N1
19a. 14(3) cage at R1C3 = {149} (only remaining combination) -> R2C2 = 4, R12C3 = {19}, locked for C3 and N1
20. R1C2 = 7 (hidden single in N1)
20a. Naked pair {23} in R23C1, locked for C1-> R7C12 = [13], R5C12 = [91], R6C23 = [23]
21. 19(3) cage at R1C6 (step 16) = {568} (only remaining combination) -> R2C5 = 6, R12C6 = {58}, locked for C6 and N2 -> R5C456 = [652], R6C46 = [81]
22. R2C4 = 7 (hidden single in N2)
22a. Naked pair {13} in R1C45, locked for R1 -> R12C1 = [23], R12C3 = [91]
23. R89C6 = {47} = 11 -> R9C5 = 3 (cage sum), R1C45 = [31], R8C5 = 9
24. 15(3) cage at R8C9 = {267} (only remaining combination, cannot be {168} because 1,6 only in R9C8) -> R9C8 = 6, R89C9 = {27}, locked for C9 and N9
25. 18(3) cage in N7 = {468} (only remaining combination) -> R9C1 = 4, R8C12 = [68]
26. 17(3) cage at R1C7 = {269} (only remaining combination) -> R1C7 = 6, R2C78 = {29}, locked for N3
and the rest is naked singles.
Login
Register
FAQ
Search
