SudokuSolver Forum

Assassin 118


SSolver 3.2.1 Rating: 1.29


An easier version 0.9


SSolver 3.2.1 Rating: 0.92

Thanks JC for this fun Killer! You really had to look for Hidden Cages to solve this one and spotting and using some Killer subsets helped too.

A118 Walkthrough:

1. R1234
a) Innies = 22(3) = 9{58/67} -> 9 locked for R4+N4
b) Innies N1 = 11(2) = [56/74/83/92]
c) 12(2): R1C4 <> 8,9
d) Innies N3 = 10(2) <> 5; R3C7 <> 1
e) Outies N3 = 11(3)

2. R6789
a) 12(2) @ R6C3: R7C3 <> 3
b) Innies N7 = 12(2): R7C3 <> 1,2,6,9
c) Innies N9 = 8(2) <> 4,8,9
d) Outies N7 = 15(3)
e) Innies R6789 = 14(3)

3. R456
a) Using Outies N3 and Innies R6789: Innies N6 = 20(3) <> 1,2
b) Using Outies N7 and Innies R1234: Innies N4 = 8(3) = 1{25/34}
-> 1 locked for R5+N4
c) Innies N47 = 10(2) <> 5
d) Innies N36 = 9(2) <> 9; R6C7 <> 7,8

4. R123 !
a) ! 12(2) <> {57} because 8(2) @ R1 and 14(2) must have two of (567)
b) Innies N1 = 11(2): R3C3 <> 4,6
c) 4 locked in 18(3) @ N1 = 4{59/68}
d) Outies N1 = 10(3): R34C4 <> 3,4 because R1C4 = (34)
e) 9(3) = 1{26/35} -> 1 locked for C4
f) 9(3): R34C4 <> 2 because R3C3 = (23)

5. N47
a) Innies N47 = 10(2) <> {28} since it's a Killer pair of Innies N1
b) 12(2) @ N4 <> {39} because it's a Killer pair of Innies N1
c) Innies N7 = 12(2) <> 3
d) OUties N7 = 15(3) <> 5{37/46} because those combos blocked by Killer pairs (35,45) of Innies N4
e) 15(3) <> 5{37/46} because R6C3 = R7C2 (Innies+Outies N7)

6. C123+R9 !
a) 12(2) @ R9 <> {57} since two of (567) already at both 8(2) @ R9
b) Outies C12 = 12(3) <> 7 because {147} blocked by Killer pair (47) of 12(2) @ N4
and {237} blocked by R3C3 = (23)
c) 8(2) @ R2C2: R2C2 <> 1
d) Outies C12 = 12(3) = {129/138/246/345} because R9C3 <> 1,5,6
e) ! Killer pair (23) locked in Outies C12 + R3C3 for C3
f) Innies N47 = 10(2) <> 7
g) 7 locked in 12(2) @ R6C3 @ C3 -> 12(2) = {57} locked for C3
h) 8(2) @ R2C2 <> 3
i) Innies N7 = 12(2) = {57} locked for R7+N7
j) 15(3) = 2{58/67} because R7C2 = (57) -> 2 locked for R6+N6; R6C12 <> 5,7

7. R456
a) Innies N4 = 8(3) = {134} locked for R4
b) 2 locked in 36(7) @ R5 for N5 -> 36(7) = 279{1368/1458/3456}
-> 7 locked for R5
c) Innies N36 = 9(2) = [54/63/81]
d) Innies N6 = 20(3) = {569} locked for R5+N6
e) Hidden Single: R4C3 = 9 @ 36(7)
f) Innie N47 = R5C3 = 1
g) R1C3 = 8 -> R1C4 = 4

8. R123
a) Innie N1 = R3C3 = 3
b) R9C3 = 4 -> R9C2 = 8
c) 14(2) = {59} locked for R1+N3
d) Innies N3 = 10(2) = {28/46}

9. C789
a) 10(2) = {28} locked for C7 since (46) is a Killer pair of Innies N36
b) Innies N9 = 8(2) = {17} because (35) is a Killer pair of Innies N36
-> R7C7 = 1, R9C7 = 7
c) Innies R6789 = 14(3) = {347} locked for R6+N6
d) 13(3) = 1{39/48} -> R67C6 = [84/93]
e) Innies N3 = 10(2) = {28} locked for R3+N3

10. N25
a) Hidden pair (34) in R4C56 for N5 -> R4C56 = {34} locked for 22(4)
b) 22(4) = 34{69/78}; R2C6 <> 7
c) Outies N12 = 12(3) = {345} -> R4C4 = 5
d) Cage sum: R3C4 = 1
e) Hidden Single: R6C5 = 1 @ N5, R6C4 = 6 @ N5, R6C6 = 9 @ N5
f) Cage sum: R7C6 = 3
g) 17(4) = {1268} -> 2,8 locked for C4+N8

11. N9
a) 11(2) = [38/92] because (56) is a Killer pair of 8(2) @ R9C8
b) 4 locked in 18(3) = 4{59/68}

12. Rest is singles.

Rating: 1.25. I used Killer triples.

For a while I thought v0.9 was almost as hard as v1, if not harder.

But then I worked out this 10-short-step walkthrough, with some very tidy analysis.


I'll give it a rating of 1.0 (easy), with the trickiest moves (pointing cells, cage blocking) in steps 3-5.

_________________
ADYFNC HJPLI BVSM GgK Oa m

My idea for this cage template

_________________
Jean-Christophe
"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." Sherlock Holmes.

I finished A118 yesterday evening but I only went through Afmob's walkthrough today.

There are plenty of Hidden Cages in this cage pattern, many of which were very helpful for solving A118.

I'll rate my solution as 1.25. It's probably a bit more difficult than Afmob's but not sufficiently so to rate it as Hard 1.25.

Here is my walkthrough. Thanks Afmob for pointing out that I should have given "no 5" in step 20a; it has therefore been deleted from step 25b.

Prelims

a) R1C12 = {17/26/35}, no 4,8,9
b) R1C34 = {39/48/57}, no 1,2,6
c) R1C78 = {59/68}
d) R2C23 = {17/26/35}, no 4,8,9
e) R34C7 = {19/28/37/46}, no 5
f) R67C3 = {39/48/57}, no 1,2,6
g) R8C78 = {29/38/47/56}, no 1
h) R9C23 = {39/48/57}, no 1,2,6
i) R9C67 = {17/26/35}, no 4,8,9
j) R9C89 = {17/26/35}, no 4,8,9
k) 9(3) cage at R3C3 = {126/135/234}, no 7,8,9
l) 11(3) cage at R3C8 = {128/137/146/236/245}, no 9
m) 36(7) cage at R4C3 must contain 9
n) 31(5) cage in N8 must contain 9, locked for N8

1. 45 rule on R1 3 innies R1C569 = 11 = {128/137/146/236/245}, no 9

2. 9 in R1 locked in R1C3478
2a. Combined cage R1C3478 = 26 = {3689/4589} (cannot be {4679} which clashes with R1C78}), no 7, 8 locked for R1, clean-up: no 5 in R1C34
2b. R1C569 (step 1) = {137/146/236/245}
2c. Killer pair 3,4 in R1C34 and R1C569, locked for R1, clean-up: no 5 in R1C12

3. 45 rule on N1 2 innies R13C3 = 11 = [83/92], clean-up: no 8,9 in R1C4

4. 45 rule on N1 3 outies R134C4 = 10 = {136/145} (cannot be {235} because 9(3) cage at R3C3 cannot be {225}), no 2, 1 locked for C4
4a. R1C4 = {34} -> no 3,4 in R34C4
[If preferred, step 4 can be done in two separate steps using R134C4 = {136/145/235} and then 9(3) cage at R3C3 to eliminate 2 from R34C4.]

5. 4 in N1 locked in 18(3) cage = {459/468}, no 1,2,3,7

6. 45 rule on R1234 3 innies R4C123 = 22 = {589/679}, 9 locked for R4 and N4, clean-up: no 1 in R3C7, no 3 in R7C3

7. 45 rule on N12 3 outies R4C456 = 12 = {138/147/246/345} (cannot be {156} which clashes with R4C123, cannot be {237} because R4C4 only contains 1,5,6)
7a. R4C4 = {156} -> no 1,5,6 in R4C56

8. 45 rule on N47 2 innies R45C3 = 10 = [64/73/82/91], no 5, no 6,7,8 in R5C3

9. 45 rule on N36 2 innies R56C7 = 9 = {18/27/36/45}, no 9

10. 45 rule on N3 2 innies R3C78 = 10 = {28/37/46}/[91], no 5 in R3C8

11. 45 rule on N7 2 innies R7C23 = 12 = [39]/{48/57}, no 1,2,6,9 in R7C2

12. 45 rule on N9 2 innies R79C7 = 8 = {17/26/35}, no 4,8,9 in R7C7

13. 45 rule on N12 2 innies R23C6 = 1 outie R4C4 + 10 -> min R23C6 = 11, no 1

14. 45 rule on N7 3 outies R6C123 = 15, R4C123 (step 7) = 22 -> R5C123 = 8 = {125/134}, 1 locked for R5 and N4, clean-up: no 8 in R6C7 (step 9)

15. 45 rule on N3 3 outies R4C789 = 11
15a. 45 rule on R6789 3 innies R6C789 = 14 -> R5C789 = 20 = {389/479/569/578}, no 2, clean-up: no 7 in R6C7 (step 9)

16. R6C123 = 15 (step 14) = {258/267/348} (cannot be {357/456} which clash with R4C123)
16a. 7 of {267} must be in R6C3 -> no 7 in R6C12

17. 20(4) cage at R5C1 = {1379/1469/2567/3458/3467} (cannot be {1289} because no 5 in R45C3, cannot be {1478/1568} which clash with R4C123, cannot be {2369/2378/2459/2468} which clash with R5C123)
17a. R4C12 cannot be {59} -> no 8 in R4C3 (step 6), clean-up: no 2 in R5C3 (step 8)

18. 45 rule on C12 3 outies R289C3 = 12 = {129/138/156/246/345} (cannot be {147} which clashes with R45C3, cannot be {237} which clashes with R3C3), no 7, clean-up: no 1 in R2C2, no 5 in R9C2
18a. 9 of {129} must be in R9C3 -> no 9 in R8C3

19. 45 rule on C89 2 innies R18C8 = 1 outie R2C7 + 7, IOU no 7 in R8C8, clean-up: no 4 in R8C7
[The same result is achieved with 45 rule on C89 2 outies R28C7 = 1 innie R1C8 + 4, IOU no 4 in R8C7, clean-up: no 7 in R8C8]

20. 45 rule on N89 3 outies R6C456 = 16, R4C456 = 12 (step 7) -> R5C456 = 17
[Alternatively R45C3 = 10 (step 8), R56C7 = 9 (step 9) -> R5C456 = 17]
20a. R5C456 = {269/278/368/467} (cannot be {359/458} which clash with R5C123), no 5
20b. 36(7) cage at R4C3 = {1236789/1245789/1345689/2345679} with 9 in R4C3 or R5C456 -> R45C3 = [73/91] (cannot be [64] which clashes with R5C456 = {269}), no 6 in R4C3, no 4 in R5C3
20c. R5C456 (step 20a) = {269/278/368} (cannot be {467} because R45C3 cannot be [93]), no 4
20d. R5C789 (step 15a) = {479/569/578} (cannot be {389} which clashes with R5C456), no 3, clean-up: no 6 in R6C7 (step 9)

21. Killer triple 7,8,9 in R1C3, R4C3 and R67C3, locked for C3, clean-up: no 3,4 in R9C2

22. R4C456 (step 7) = {138/147/345} (cannot be {246} which clashes with R5C456}, no 2,6

23. 2 in R4 locked in R4C789, locked for N6, clean-up: no 7 in R5C7 (step 9)
23a. R4C789 = 11 (step 15) = {128/236/245}, no 7, clean-up: no 3 in R3C7, no 7 in R3C8 (step 10)

24. 45 rule on R9 3 innies R9C145 = 17 = {179/269/359/458} (cannot be {278/368/467} which are blocked by the two 8(2) cages)
24a. Hidden killer pair 8,9 in R9C145 and R9C2 -> R9C2 must have one of 8,9 -> R9C23 = [84/93], no 5,7

25. 6 in C3 locked in R28C3
25a. R289C3 (step 18) = {246} (only remaining combination, cannot be {156} because R9C3 only contains 3,4) -> R9C3 = 4, R9C2 = 8, R28C3 = {26}, locked for C3 -> R3C3 = 3, R5C3 = 1, R1C3 = 8 (step 3), R1C4 = 4, R4C3 = 9 (step 8), clean-up: no 6 in R1C78, no 6 in 18(3) cage in N1 (step 5), no 5,7 in R2C2, no 6 in R3C4 (step 4), no 7 in R3C7 (step 10), no 5 in R4C1 (step 6), no 3 in R4C7, no 8 in R5C7 (step 9), no 3 in R7C2 (step 11)
25b. R5C456 (step 20c) = {278/368}, 8 locked for R5 and N5
25c. 9 in R5 locked in R5C89, locked for N6

26. Naked pair {26} in R2C23, locked for R2 and N1
26a. Naked pair {17} in R1C12 , locked for R1
26b. Naked pair {59} in R1C78, locked for R1 and N3, clean-up: no 1 in R3C8 (step 10), no 1 in R4C7
26c. Naked pair {15} in R34C4, locked for C4

27. R4C456 (step 22) = {147/345}, 4 locked for R4 and N5, clean-up: no 6 in R3C7, no 4 in R3C8 (step 10), no 5 in R4C89 (step 23a)

28. R6C123 (step 16) = {258/267} (cannot be {348} because R6C3 only contains 5,7}, no 3,4, 2 locked for R6 and N4, clean-up: no 5 in R5C12 (step 14)
28a. 5 of {258} must be in R6C3 -> no 5 in R6C12

29. Naked pair {34} in R5C12, locked for R5, clean-up: no 6 in R5C456 (step 25b), no 7 in R5C89 (step 15a), no 5 in R6C7 (step 9)
29a. Naked triple {278} in R5C456, locked for N5, clean-up: no 1 in R4C4 (step 27)
29b. R34C4 = [15], clean-up: no 8 in R4C1 (step 6)

30. Naked pair {67} in R4C12, locked for R4 and N4 -> R6C123 = [825], R7C23 = [57], R2C23 = [62], R8C3 = 6, R5C12 = [67], R1C12 = [71], clean-up: no 4 in R3C7, no 6 in R3C8 (step 10), no 5 in R8C78, no 1,3 in R9C7 (step 12), no 5,7 in R9C6

31. Naked pair {34} in R4C56, locked for R4, N5 and 22(4) cage at R2C6
31a. Naked triple {169} in R6C456, locked for R6

32. Naked pair {28} in R3C78, locked for R3 and N3
32a. Naked pair {28} in R34C7, locked for C7, clean-up: no 6 in R79C7 (step 12) , no 3,9 in R8C8, no 2,6 in R9C6
32b. 6 in N3 locked in R13C9, locked for C9, clean-up: no 2 in R9C8

33. R5C7 = 6 (hidden single in C7), R6C7 = 3 (step 9), R7C7 = 1, R9C7 = 7 (step 12), R9C6 = 1, R2C7 = 4, R8C7 = 9, R8C8 = 2, R1C78 = [59], R3C78 = [28], R4C7 = 8, R4C89 = [12], R5C89 = [59], R8C12 = [13], R5C12 = [34], R3C2 = 9, R23C1 = [54], clean-up: no 6 in R9C8, no 3 in R9C9
33a. R9C89 = [35], R2C8 = 7, R123C9 = [316], R6C89 = [47], R7C8 = 6

34. 45 rule on N2 2 remaining innies R23C6 = 15 = [87], R3C5 = 5, R5C6 = 2, R1C56 = [26], R6C6 = 9, R6C45 = [61], R7C6 = 3 (cage sum), R4C56 = [34], R2C45 = [39], R8C6 = 5, R9C5 = 6

35. 45 rule on N8 2 remaining innies R78C4 = 10 = [28]

and the rest is naked singles

That's a very interesting concept although I wouldn't have called it a Hint. I went through my walkthrough again and Afmob's one after reading the concept and I can't see how it could help to reach the breakthrough any quicker. However that doesn't detract from it being an interesting cage pattern concept.

Thanks J-C for another fun puzzle.

I thought the same at first.

This made better use of the interactions between the hidden cages than in my solution.

I had to work a bit harder so I'll rate my solution as Hard 1.0; that may even be a bit too low.

Here is my walkthrough for V0.9.

Prelims

a) R1C12 = {18/27/36/45}, no 9
b) R1C34 = {29/38/47/56}, no 1
c) R1C78 = {69/78}
d) R2C23 = {69/78}
e) R34C7 = {19/28/37/46}, no 5
f) R67C3 = {18/27/36/45}, no 9
g) R8C78 = {18/27/36/45}, no 9
h) R9C23 = {49/58/67}, no 1,2,3
i) R9C67 = {14/23}
j) R9C89 = {29/38/47/56}, no 1
k) 35(7) cage at R4C3 must contain 5

1. 45 rule on R1 3 innies R1C569 = 10 = {127/136/145/235}, no 8,9

2. 45 rule on N1 2 innies R13C3 = 5 = [23/32/41], clean-up: R1C4 = {789}

3. 45 rule on N9 2 innies R79C7 = 8 = [53/62/71], clean-up: no 1 in R9C6

4. 45 rule on N3 2 innies R3C78 = 9 = {18/27/36}/[45], no 9, no 4 in R3C8, clean-up: no 1 in R4C7

5. 45 rule on N7 2 innies R7C23 = 10 = {28/37/46}/[91], no 5, no 1 in R7C2, clean-up: no 4 in R6C6

6. 45 rule on N47 2 innies R45C3 = 7 = {16/25} (cannot be {34} which clashes with R13C3)
6a. Killer pair 1,2 in R13C3 and R45C3, locked for C3, clean-up: no 7,8 in R67C3, no 2,3,8,9 in R7C2 (step 5)
6b. Killer pair 5,6 in R45C3 and R67C3, locked for C3, clean-up: no 9 in R2C2, no 7,8 in R9C2

7. 45 rule on N36 2 innies R56C7 = 7 = {16/25/34}
7a. R45C3 = 7, R56C7 = 7 -> R5C456 = 21 = {489/579/678}, no 1,2,3
7b. 4,5,6 locked in 35(7) cage at R4C3 = {1245689/1345679/2345678}
[Here I missed CPE no 4 in R5C89.]

8. 45 rule on N89 3 outies R6C456 = 11 = {128/137/146/236/245}, no 9

9. Hidden triple {789} in R289C3, clean-up: no 9 in R9C2
[And here I missed 5 in C3 locked in R456C3, locked for N4 which would have simplified analysis of R6C123 and 18(3) cage at R6C1.]

10. 45 rule on C89 3 outies R128C7 = 20 = {389/479/569/578}, no 1,2, clean-up: no 7,8 in R8C8

11. 1,2 in N7 locked in 22(5) cage = {12379/12469/12568} (cannot be {12478} which clashes with R7C23)
11a. R9C23 = [49/58] (cannot be [67] which clashes with 22(5) cage), no 6,7

[At this stage I spotted that because there are two 12(3) hidden cages in R5 (see steps 14 and 15) this might limit how they can be paired. Initially I incorrectly thought that there were only two such pairs but on checking I found that there are three pairs so at least one pair has to be eliminated.]

12. 45 rule on N7 3 outies R6C123 = 17 = {359/368/458} (cannot be {179/278} because R6C3 only contains 3,5,6, cannot be {269} which clashes with R45C3, cannot be {467} because 18(3) cage at R6C1 would be {47}7), no 1,2,7
12a. Killer pair 5,6 in R45C3 and R6C123, locked for N4

13. 7 in N4 locked in 21(4) cage = {1479/2379/2478}

14. 45 rule on R1234 3 innies R4C123 = 16, R6C123 (step 12) = 17 -> R5C123 = 12
14a. R5C123 = {129/246} (cannot be {138} because 21(4) cage doesn’t contain both of 3,8, cannot be {147} which clashes with R5C456, cannot be {156} because 5,6 only in R5C3, cannot be {237} because no 3 in R5C3 leading to clash with 21(4) cage, cannot be {345} because 21(4) cage doesn’t contain both of 3,4), no 3,5,7,8, 2 locked for R5 and N4, clean-up: no 5 in R6C7 (step 7)

15. 45 rule on N3 3 outies R4C789 = 16, 45 rule on R6789 3 innies R6C789 = 17 -> R5C789 = 12
15a. 3 in R5 locked in R5C789, locked for N6, clean-up: no 7 in R3C7, no 2 in R3C8 (step 4), no 4 in R5C7 (step 7)
15b. R5C789 = {138/345}, no 6,7,9, clean-up: no 1 in R6C7 (step 7)

16. 7 in R5 locked in R5C456 for N5
16a. R5C456 (step 7a) = {579/678}, no 4
16b. 35(7) cage at R4C3 (step 7b) = {1345679/2345678} -> R56C7 = [34] (hidden pair in cage), clean-up: no 6 in R3C7, no 3,5,6 in R3C8 (step 4), no 6,7 in R4C7, no 5 in R5C89 (step 15b), no 5 in R7C7 (step 3), no 5,6 in R8C8, no 2 in R9C6

17. Naked pair {18} in R5C89, locked for R5 and N6, clean-up: no 2 in R3C7, no 7 in R3C8 (step 4), no 6 in R4C3 (step 6), no 9 in R5C12 (step 14a), no 6 in R5C456 (step 16a)

18. Naked pair {24} in R5C12, locked for N4 -> R5C3 = 6, R4C3 = 1 (step 6), clean-up: no 4 in R1C3 (step 2), no 7 in R1C4, no 3,9 in R4C12 (step 13), no 3 in R67C3, no 4,7 in R7C2 (step 5)
18a. R67C3 = [54], R7C2 = 6, R9C2 = 5, R9C3 = 8, R7C7 = 7, R9C7 = 1 (step 3), R9C6 = 4, R3C7 = 8, R3C8 = 1, R4C7 = 2, R5C89 = [81], clean-up: no 3,4 in R1C1, no 7 in R1C8, no 7 in R2C2, no 9 in R2C3, no 2 in R8C8, no 3,6 in R9C89
18b. R2C23 = [87], R4C12 = [87], R8C3 = 9, clean-up: no 1,2 in R1C12

19. 9 in C7 locked in R12C7, locked for N3 -> R1C8 = 6, R12C7 = [95], R8C7 = 6, R8C8 = 3, R1C1 = 5, R1C2 = 4, R1C4 = 8, R1C3 = 3, R3C3 = 2, R3C12 = [69], R2C1 = 1, R5C12 = [42], R6C12 = [93], R6C89 = [76], R8C2 = 1

20. Naked pair {29} in R9C89, locked for R9 and N9 -> R7C89 = [58], R8C9 = 4, R4C89 = [95], R9C89 = [29], R2C8 = 4

21. R3C3 = 2 -> R34C4 = 10 = [46/73]
21a. R4C5 = 4 (hidden single in R4), R3C4 = 4 (hidden single in R3), R4C4 = 6, R4C6 = 3, R9C5 = 6 (hidden single in R9), R2C6 = 6 (hidden single in R2), R3C6 = 5 (cage sum)

22. 45 rule on N8 3 remaining innies R7C46 + R9C4 = 16 = {259} (only remaining combination) -> R8C4 = 5, R7C46 = {29}, locked for R7 and N8 -> R789C1 = [327], R7C5 = 1, R9C4 = 3
22a. R5C5 = 5 (hidden single in R5)

23. R8C4 = 5 -> R6C45 + R7C4 = 12 = {129} (only remaining combination), no 8

and the rest is naked singles

Using JC's cage template tips, here is another walkthrough for v0.9 which is one step shorter. The trickiest moves are similar in terms of difficulty though so same rating.


(Edited: typo fixed thanks to Andrew)

_________________
ADYFNC HJPLI BVSM GgK Oa m

I just finished 118 - it seemed like it took me hours before I finally found the key. Thanks for the fun puzzle, J-C! (At first, it looked like it should be easy, but, wow!) As I felt I should have found it sooner, I'll rate it a hard 1.0.