SudokuSolver Forum

Hi,

this one should be a bit more difficult than my previous one, whereas TE and chains are not needed. ENJOY !

Assassin 197



3x3::k:3072:4097:4097:4097:1028:4869:4869:4869:2568:2569:3072:4107:6412:1028:4622:4622:2568:3857:2569:4107:4107:6412:6412:2583:4622:2841:3857:2569:2076:2076:6412:7967:2583:2583:2841:3857:3620:3620:2076:7967:7967:7967:2858:2859:2859:5165:2862:4143:4143:7967:4658:2858:2858:4405:5165:2862:2616:4143:4658:4658:3388:3388:4405:5165:2368:2616:2616:2883:4658:3388:2374:4405:2368:2889:2889:2889:2883:4941:4941:4941:2374:

Solution

Thanks manu for another fun puzzle.

In my walkthrough, step 7 was amazingly productive; then step 12b was the only tricky step after which the puzzle was cracked.


Here is my walkthrough for A197

Prelims

a) 12(2) cage at R1C1 = {39/48/57}, no 1,2,6
b) R12C5 = {13}
c) 10(2) cage at R1C9 = {19/28/37/46}, no 5
d) R34C8 = {29/38/47/56}, no 1
e) R5C12 = {59/68}
f) R5C89 = {29/38/47/56}, no 1
g) R67C2 = {29/38/47/56}, no 1
h) 9(2) cage at R8C2 = {18/27/36/45}, no 9
i) R89C5 = {29/38/47/56}, no 1
j) 9(2) cage at R8C8 = {18/27/36/45}, no 9
k) 19(3) cage at R1C6 = {289/379/469/478/568}, no 1
l) 10(3) cage at R2C1 = {127/136/145/235}, no 8,9
m) 10(3) cage at R3C6 = {127/136/145/235}, no 8,9
n) 8(3) cage at R4C2 = {125/134}
o) 11(3) cage at R5C7 = {128/137/146/236/245}, no 9
p) 20(3) cage at R6C1 = {389/479/569/578}, no 1,2
q) 10(3) cage at R7C3 = {127/136/145/235}, no 8,9
r) 11(3) cage at R9C2 = {128/137/146/236/245}, no 9
s) 19(3) cage at R9C6 = {289/379/469/478/568}, no 1

Steps resulting from Prelims
1a. Naked pair {13} in R12C5, locked for C5 and N2, clean-up: no 8 in R89C5
1b. 8(3) cage at R4C2 = {125/134}, 1 locked for N4
1c. R5C89 = {29/38/47} (cannot be {56} which clashes with R5C12

2. 45 rule on R1 3 innies R1C159 = 10 = {127/136/145/235}, no 8,9, clean-up: no 3,4 in R2C2, no 1,2 in R2C8
2a. 5 of {145} must be in R1C1 -> no 4 in R1C1, clean-up: no 8 in R2C2
2b. 2,4,6 only in R1C9 -> R1C9 = {246}, R2C8 = {468}

3. 45 rule on C1234 4 innies R2345C4 = 27 = {3789/4689/5679}, no 1,2, 9 locked for C4
3a. 45 rule on C1234 1 innie R5C4 = 1 outie R3C5 + 2, no 3,5 in R5C4, no 8,9 in R3C5

4. 45 rule on C6789 1 outie R7C5 = 1 innie R5C6 + 1, no 2,9 in R5C6

5. 45 rule on R1234 1 innie R4C5 = 1 outie R5C3 + 6, R4C5 = {789}, R5C3 = {123}

6. 45 rule on R6789 1 innie R6C5 = 1 outie R5C7 + 5, R5C7 = {1234}, R6C5 = {6789}

7. 45 rule on C1 3 outies R258C2 = 20 = {389/479/569/578}, no 1,2, clean-up: no 7,8 in R9C1
7a. 45 rule on C1 3 innies R159C1 = 15 = {258/267/348/456} (cannot be {159/357} which clash with 10(3) cage at R2C1, cannot be {168/249} because R1C1 only contains 3,5,7)
7b. 2,4 only in R9C1 -> R9C1 = {24}, R8C2 = {57}
7c. 6,8 only in R5C1 -> R5C12 = {68}, locked for R5 and N4, clean-up: no 3 in R5C89, no 3,5 in R7C2, no 7,9 in R7C5 (step 4)
7d. R258C2 = {569/578}, 5 locked for C2, clean-up: no 6 in R7C2
7e. 9 in N4 only in R6C123, 9 locked for R6, clean-up: no 4 in R5C7 (step 6)

8. 45 rule on C12 4 innies R1349C2 = 14 = {1238/1247/1346}, no 9

9. 45 rule on R9 3 innies R9C159 = 15 = {249/258/456} (cannot be {159/168/357} because R9C1 only contains 2,4, cannot be {267/348} which clash with 11(3) cage at R9C2), no 1,3,7, clean-up: no 4 in R8C5, no 2,6,8 in R8C8
9a. 9 of {249} must be in R9C5, 2,4 of {258/456} must be in R9C1 -> no 2,4 in R9C5, clean-up: no 7,9 in R8C5
9b. 1 in R9 only in 11(3) cage at R9C2 = {128/137/146}, no 5

10. 45 rule on R9 3 outies R8C258 = 14 = {167/257/347/356}
10a. 3 of {347} must be in R8C8 -> no 4 in R8C8, clean-up: no 5 in R9C9

11. R9C159 (step 9) = {249/258/456}
11a. 5,9 only in R9C5 -> R9C5 = {59}, clean-up: no 5 in R8C5
[Alternatively R9C159 must contain an odd number -> R9C5 must be odd = {59} ...]

12. 5 in R5 only in R5C56, locked for N5
12a. 31(5) cage at R4C5 = {25789/35689/45679} (other combinations don’t contain 5), no 1, 9 locked for N5, clean-up: no 2 in R7C5 (step 4)
12b. Cannot be {45679} because 7{459}6 clashes with R5C89 and 9{457}6 clashes with R89C5
12c. -> 31(5) cage at R4C5 = {25789/35689}, no 4, 8 locked for C5 and N5

13. 4 in R5 only in R5C89 = {47}, locked for R5 and N6 -> R5C4 = 9, R3C5 = 7 (step 3a), R46C5 = [86], R8C8 = 2, R5C56 = [53], R4C4 = 4, R79C5 = [49], R5C7 = 1 (step 6), R5C3 = 2, clean-up: no 3,4 in R3C8, no 7 in R6C2, no 9 in R7C2

14. R2345C4 (step 3) = {4689} (only remaining combination), 6,8 locked for C4 and N2

15. 8(3) cage at R4C2 = {125} (only remaining combination) -> R4C23 = [15], clean-up: no 6 in R3C8

16. 11(3) cage at R5C7 = {128} (only remaining combination), 2,8 locked for R6 and N6, clean-up: no 9 in R3C8

17. R4C6 = 2 (hidden single in R4), R4C1 = 7 (hidden single in R4), clean-up: no 5 in R2C2
17a. 10(3) cage at R3C6 = {235} (only remaining combination) -> R3C6 = 5, R4C7 = 3, R1C4 = 2, R6C9 = 5, clean-up: no 8 in R2C8, no 8 in R3C8, no 6 in R4C8

18. R34C8 = [29], R6C78 = [28], R4C9 = 6, R1C9 = 4, R2C8 = 6, R12C6 = [94], R23C4 = [86]

19. R9C159 (step 9) = {249} (only remaining combination) -> R9C19 = [42], R8C28 = [57], R5C89 = [47]

20. R2C1 = 2 (hidden single in R2), R3C1 = 1 (cage sum), R2C7 = 5 (hidden single in R2), R3C7 = 9 (cage sum), R1C8 = 3, R23C9 = [18], R1C7 = 7, R1C1 = 5, R2C2 = 7, R12C5 = [13], R2C3 = 9, clean-up: no 4 in R6C2

21. R159C1 (step 7a) = {456} (only remaining combination) -> R5C1 = 6, R5C2 = 8, R1C23 = [68], R9C2 = 3, R3C23 = [43]

22. R6C2 = 9, R6C3 = 4 -> R67C4 = 12 = [75]

23. 11(3) cage at R9C2 (step 9b) = {137} (only remaining combination) -> R9C4 = 1, R9C3 = 7

and the rest is naked singles.