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Hi folks,

The cage pattern for this Assassin reminded me of a mounted photo, so I decided to stick with this analogy whilst coloring it.

A picture may be proverbally worth a thousand words, but this one sure ain't givin' anything away!


Assassin 103 (A103) (Est. rating: 1.25)



3x3::k:5632:5632:3074:3843:3843:3843:5126:3591:3591:5632:3074:1547:1547:3085:1038:1038:5126:3591:3074:2835:2835:3605:3085:5143:2840:2840:5126:5147:2835:3605:3605:5663:5143:5143:2840:4131:5147:1061:1061:5663:5663:5663:3114:3114:4131:5147:3374:3887:3887:5663:2610:2610:6196:4131:4918:3374:3374:3887:3386:2610:6196:6196:2622:3135:4918:3137:3137:3386:3908:3908:2622:2887:3135:3135:4918:4171:4171:4171:2622:2887:2887:

Solution:

9 7 4 6 8 1 5 2 3
6 5 2 4 7 3 1 8 9
3 1 8 2 5 9 6 4 7
5 2 9 3 6 7 4 1 8
8 3 1 9 2 4 7 5 6
7 4 6 8 1 5 3 9 2
4 6 3 1 9 2 8 7 5
2 8 5 7 4 6 9 3 1
1 9 7 5 3 8 2 6 4

SudokuSolver v3.1 scores this at 1.24, which seems pretty accurate again.

Good luck!

I get an SS(v3.1) score of 1.74. Might need that good luck and 2 weeks!

Cheers
Ed

Interesting puzzle - I managed to do it with a bit of T&E and I think I can now see how to do it without. Main point:


I've posted a Killer Modulo in the other variants section - you may wish to try it as it uses the same techniques but with less information on the cage sums.

This was an interesting Killer where the hardest move (step 4b) was available right from the start. Thanks Mike!

I'm not sure about the rating. My walkthrough could also justify a 1.25 depending on how you rate step 4b. My first gut feeling went for 1.5, so I'll stay with that. But it's definitely overrated by SudokuSolver and JSudoku (which used XY-Chains).

A103 Walkthrough:

1. R123
a) 4(2) = {13} locked for R2
b) 6(2) = {24} locked for R2
c) Outies N1 = 6(1+1) = {24}
d) Outies N3 = 4(1+1) = {13}
e) 12(2): R3C5 <> 8,9
f) 11(3) @ N1 <> 7 because R4C2 = (24)
g) 12(3) <> 6 because R2C3 = (24) blocks {246} and {156} blocked by Killer pair (56) of 22(3)
h) 22(3) = 9{58/67} -> 9 locked for N1
i) 12(3) can only have one of (578) and R2C2 = (578) -> R1C3+R3C1 <> 5,7,8

2. R6789
a) Innies N9 = 24(3) = {789} locked for N9
b) 15(2): R8C6 <> 9
c) Innies N8 = 16(4): R78C4 <> 8,9 because R8C6 >= 6
d) 12(2): R8C3 <> 3,4
e) Outies N7 = 11(1+1) -> R6C2 = (4678)
f) Outies R89 = 18(3) <> 1,2 because R7C78 = (789) blocks 9{18/27}
g) Killer triple (789) locked in Outies R89 + R7C78 for R7

3. R456 !
a) 4(2) = {13} locked for R5+N4
b) 12(2) <> 9
c) ! Killer triple (789) locked in 16(3) + 12(2) + R6C8 for N6
d) 20(3) @ N5: R34C6 <> 3,4 because R4C7 <> 7,8,9

4. C123 !
a) 22(3) = 9{58/67} must have exactly two of (569)
b) ! 20(3) = 7{49/58} because 20(3) <> {569} since 22(3) could have only one of (569)
-> 7 locked for C1+N4
c) 7 locked in R89C3 for N7
d) 22(3): R1C2 <> 6 because 7 only possible there
e) 22(3): R1C2 <> 5,8 because {589} blocked by Killer pairs (59,89) of 20(3)
f) Innies+Outies C1: 9 = R19C2 - R37C1 -> R7C1 <> 8,9

5. R789
a) Outies R89 = 18(3): R7C5 <> 4,5,6 because R7C19 <= 11
b) 13(2): R8C5 <> 7,8,9
c) Outies N7 = 11(1+1): R8C4 <> 4
d) 12(2) <> 8
e) Killer pair (79) locked in 12(2) + 15(2) for R8
f) 19(3) <> 3 because 7,9 only possible @ R9C3

6. C123 !
a) ! Hidden triple (123) locked in R389C1 for C1
b) 12(3) @ N7: R9C2 = (89) because R89C1 <= 5
c) 12(2) = 1{29/38} -> 1 locked for C1+N7
d) Killer pair (89) locked in R9C2 + 19(3) for N7
e) 12(2) = {57} locked for R8
f) Hidden Single: R8C7 = 9 @ R8 -> R8C6 = 6
g) R8C5 = 4 -> R7C5 = 9,
h) Hidden Single: R8C2 = 8 @ R8, R9C2 = 9, R1C2 = 7, R2C2 = 5
i) 22(3) = {679} -> {69} locked for C1+N1
j) 11(3) = {128} -> R4C2 = 2, R3C2 = 1, R3C3 = 8
k) 20(3) = {578} locked for C1+N4
l) R5C2 = 3

7. R789
a) R7C1 = 4 -> R9C3 = 7
b) 24(3) = {789} -> R6C8 = 9
c) R7C2 = 6, R6C2 = 4, R6C3 = 6, R8C3 = 5, R8C4 = 7
d) 15(3) = {168} -> R7C4 = 1, R6C4 = 8

8. R456
a) R4C3 = 9
b) 14(3) = {239} -> R4C4 = 3, R3C4 = 2
c) R3C1 = 3
d) 11(3) = {146} -> R4C8 = 1, {46} locked for N3
e) 22(5) = {12469} -> R4C5 = 6, R5C5 = 2, R6C5 = 1; {49} locked for R5
f) 12(2) = {57} locked for R5+N6
g) R4C7 = 4
h) 20(3) @ N5 = {479} -> R4C6 = 7, R3C6 = 9
i) R4C9 = 8, R5C9 = 6 -> R6C9 = 2

9. Rest is singles.

Rating: (Easy) 1.5. I used Killer triples and combo conflicts to solve it.

Hmm. You're right. On my Windows Vista installation, I get 1.75. However, I've just repeated the same test on my Windows XP installation, and got the published score of 1.24 again. Looked at the solver list and found that the default scoring options were not set. For some reason, SS did not alert me to this fact like it normally does.

Despite this, I do quite a bit of analysis before posting a puzzle, and would not have published it as a V1 if I had felt that it was a genuine 1.75. The moral of this story is that we shouldn't always take what the automated solvers say for granted, even though they have an invaluable role to play in the puzzle evaluation process these days.

Thanks for pointing out the discrepency, Ed!

_________________
Cheers,
Mike

Thanks Mike for a challenging puzzle.

Very strange that the SS score depends so much on which version of Windows is being used. Even if that changes the order that SS applies tests, I wouldn't have expected that much difference.

Yes, it was there right after the Prelims, which is where Afmob starts. It took me a very long time to find this key move. Then I just came across it after I found that the other moves I was working with didn't seem to be making any more progress. With hindsight I feel that I ought at least to have got it after step 19 but I didn't find it until step 54!

Yes, your hidden text was the key breakthrough.


I'll rate this puzzle as a solid 1.5 the way I did it. However if one got that key move right after the Prelims I'm guessing that it might be a normal or hard 1.25.

Here is my walkthrough. I got into some interesting stuff because I didn't find the key move early enough.

Thanks Afmob for pointing out that step 17a was invalid. I must have seen 3 in R7C9 but not noticed that it also contained 6. Later steps that depended on step 17a are coloured red; consider them to be deleted but I've left them in so that the effect of one incorrect elimination can be seen, some of them have been used later. Other editing, plus the re-use of earlier steps when they became valid, is in blue.

Prelims

a) R2C67 = {13}, locked for R2
b) R2C34 = {24}, locked for R2
c) R23C5 = {57}/[84/93], no 1,2,6, no 8,9 in R3C5
d) R5C78 = {39/48/57}, no 1,2,6
e) R5C23 = {13}, locked for R5 and N4, clean-up: no 9 in R5C78
f) R78C5 = {49/58/67}, no 1,2,3
g) R8C34 = {39/48/57}, no 1,2,6
h) R8C67 = {69/78}
i) 22(3) cage in N1 = {589/679}, 9 locked for N1
j) 20(3) diagonal cage in N3 = {389/479/569/578}, no 1,2
k) 11(3) cage at R3C2 = {128/137/146/236/245}, no 9
l) 11(3) cage at R3C7 = {128/137/146/236/245}, no 9
m) 20(3) cage at R3C6 = {389/479/569/578}, no 1,2
n) R456C1 = {479/569/578}, no 2
o) 10(3) cage at R6C6 = {127/136/145/235}, no 8,9
p) 24(3) cage at R6C8 = {789}, CPE no 7,8,9 in R89C8
q) 19(3) diagonal cage in N7 = {289/379/469/478/568}, no 1
r) 10(3) diagonal cage in N9 = {127/136/145/235}, no 8,9
s) 11(3) cage in N9 = {128/137/146/236/245}, no 9

1. 45 rule on N1 1 outie R4C2 = 1 innie R2C3 -> R4C2 = {24}

2. 45 rule on N3 1 outie R4C8 = 1 innies R2C7 -> R4C8 = {13}

3. 45 rule on N7 1 innie R8C3 = 1 outie R6C2 + 1, no 5,9 in R6C2, no 4 in R8C3, clean-up: no 8 in R8C4

4. 45 rule on N9 1 outie R6C8 = 1 innie R8C7, no 6 in R8C7, clean-up: no 9 in R8C6

5. Naked triple {789} in R7C78 + R8C7, locked for N9

6. 45 rule on R1234 3 innies R4C159 = 19 = {289/379/469/478/568}, no 1

7. 45 rule on R6789 3 innies R6C159 = 10 = {127/136/145/235}, no 8,9
7a. 6,7 of {127/136} must be in R6C1 -> no 6,7 in R6C59

8. 45 rule on C1234 3 innies R159C4 = 20 = {389/479/569/578}, no 1,2

9. 45 rule on C6789 3 innies R159C6 = 13 = {148/157/238/247/256/346} (cannot be {139} which clashes with R2C6), no 9

10. 9 in C6 locked in R34C6 for 20(3) cage -> no 9 in R4C7
10a. 20(3) cage at R3C6 = {389/479/569}

11. 11(3) cage at R3C2 = {128/146/236/245} (cannot be {137} because R4C2 only contains 2,4), no 7

12. 12(3) diagonal cage in N1 = {138/147/237/345} (cannot be {156} which clashes with 22(3) cage, cannot be {246} which clashes with R2C3), no 6
12a. R2C2 = {578} -> no 5,7,8 in R1C3 + R3C1

13. 11(3) cage at R3C7 = {128/137/146/236} (cannot be {245} because R4C7 only contains 1,3), no 5
13a. R2C7 = R4C8 (step 2) -> R2C7 + R3C78 = {128/137/146/236}

14. 45 rule on N2 4 innies R23C46 = 18 = {1269/1278/1458/1467/2349/2367} (cannot be {1359/1368} because R2C4 only contains 2,4, cannot be {2457} because R2C6 only contains 1,3, cannot be {2358/3456} which clash with R23C5)
14a. 1,3 must be in R2C6 -> no 1,3 in R3C46

15. Combined cage R8C3467 = 27 = {3789/4689/5679}, 9 locked for R8, clean-up: no 4 in R7C5

16. 45 rule on R12 3 outies R3C159 = 15 = {159/249/258/267/348/357/456} (cannot be {168} because R3C5 only contains 3,4,5,7}
16a. 6,8,9 of {249/348/456} must be in R3C9 and 3 of {357} must be in R3C1 -> no 3,4 in R3C9

17. 45 rule on R89 3 outies R7C159 = 18 = {369/459/468/567} (cannot be {189/279/378} which clash with R7C78), no 1,2
17a. 3 of {369} must be in R7C9 -> no 3 in R7C1

18. Killer triple 7,8,9 in R7C159 and R7C78, locked for R7

19. R389C1 = {123} (hidden triple in C1)

20. 12(3) cage in N7 = {129/138/237} (cannot be {147/156/246/345} because R89C1 only contain 1,2,3)
20a. 7,8,9 can only be in R9C2 -> R9C2 = {789}

21. 45 rule on N8 4 innies R78C46 = 16 = {1258/1267/1348/1357/2347/2356} (cannot be {1249} because R8C6 only contains 6,7,8, cannot be {1456} which clashes with R78C5), no 9, clean-up: no 3 in R8C3, no 2 in R6C2 (step 3)
21a. 1,2 of {1267} must be in R7C46, 6 of {2356} must be in R8C6 -> no 6 in R7C46

22. 45 rule on C789 4 innies R2468C7 = 17 = {1259/1268/1349/1358/1367/2348/2357} (cannot be {1457} which clashes with R5C78, cannot be {2456} because R8C7 only contains 7,8,9)
22a. R8C7 = {789} -> no 7,8 in R46C7

23. 45 rule on C1 2 outies R19C2 = 2 innies R37C1 + 9
23a. Max R19C2 = 17 -> max R37C1 = 8, no 8,9 in R7C1

24. 20(3) cage at R3C6 (step 10a) = {389/479/569}
24a. 3,4 of {389/479} must be in R4C7 -> no 3,4 in R34C6

25. 10(3) cage at R6C6 = {127/136/145/235}
25a. 6 of {136} must be in R6C6 (R67C6 cannot be {13} which clashes with R2C6) -> no 6 in R6C7

26. 14(3) cage in N3 = {149/158/239/248/257/347/356} (cannot be {167} which clashes with R2C7 + R3C78)
26a. 9 of {149/239} must be in R2C9 -> no 9 in R1C89

27. 14(3) cage at R3C4 = {149/158/167/239/248/257/347/356}
27a. 1,3 of {149/167/239/356} must be in R4C4 -> no 6,9 in R4C4

28. R8C3 = R6C2 + 1 (step 3)
28a. 45 rule on C123 4 innies R2468C3 = 22 = {2479/2569/2578/4567}
28b. 8 of {2578} must be in R46C3 (R8C3 cannot be 8 when R46C3 = {57} clashes with R6C2 = 7), no 8 in R8C3, clean-up: no 7 in R6C2 (step 3), no 4 in R8C4

29. Combined cage R8C3467 (step 15) = {3789/5679}, 7 locked for R8, clean-up: no 6 in R7C5

30. 13(3) cage at R6C2 = {148/256/346} (cannot be {238} which clashes with R89C1)
30a. Killer triple 1,2,3 in R7C23 and R89C1, locked for N7

31. R3C159 (step 16) = {159/249/258/267/348/357} (cannot be {456} because R3C1 only contains 1,2,3)
31a. 3 of {348/357} must be in R3C1 -> no 3 in R3C5, clean-up: no 9 in R2C5

32. R78C5 = [76/94] (cannot be {58} which clashes with R23C5), no 5,8
32a. Combined cage R2378C5 = {4579/4678}, 4,7 locked for C5

33. Naked triple {789} in R7C578, locked for R7
33a. 8 in R7 locked in R7C89, locked for N9 and 24(3) cage -> no 8 in R6C8, clean-up: no 7 in R8C6

34. Hidden killer pair 1,3 in R1C456 and R2C6 for N2 -> R1C456 must contain 1 or 3
34a. R1C456 = {159/168/348/357} (cannot be {249/258/267/456} which don’t contain 1 or 3), no 2

35. 2 in N2 locked in R23C4, locked for C4 and locked in R23C46
35a. R23C46 (step 14) = {1269/2349/2367} (cannot be {1278} which clashes with R23C5, cannot be {1458/1467} which don’t contain 2), no 5,8

36. 19(3) diagonal cage in N7 = {379/469/478/568} (cannot be {289} because 2,8,9 only in R8C2 + R9C3), no 2
36a. 7,9 of {469/478} can only be in R9C3 -> no 4 in R9C3
[Afmob pointed out that I could have eliminated 3 from R7C1 + R9C3, because no 7,9 in R8C2, and then inserted the deleted important step 19 instead of putting it as step 56. I missed that because while editing for the effects of deleting step 17a, I was only looking for which other steps before step 54 were still valid and avoiding any re-work until after that step.]

37. R456C9 = {169/259/268/349/367} (cannot be {178/358/457} which clash with R5C78)

38. Hidden killer triple 7,8,9 in R12C9, R3C9 and R45C9 for C9 -> R12C9 must contain one of 7,8,9 (cannot have two of them in 14(3) cage) -> R3C9 = {789}
38a. 14(3) cage in N3 (step 26) = {149/158/239/248/257/347} (cannot be {356} which doesn’t contain 7,8,9), no 6
38b. 7,8,9 in R12C9 -> no 7,8 in R1C8

39. 20(3) diagonal cage in N3 = {389/479/569/578}
39a. 3,4 can only be in R1C7 -> no 9 in R1C7
39b. 9 in C7 locked in R78C7, locked for N9

40. R3C159 (step 16) = {159/249/258/348/357}
40a. R3C9 = {789} -> no 7 in R3C5, clean-up: no 5 in R2C5

41. 11(3) cage at R3C2 (step 11) = {128/146/236/245}
41a. 4 of {146/245} must be in R4C2 (R3C23 cannot be {45} which clashes with R3C5) -> no 4 in R3C23

42. 4 in N1 locked in R12C3, locked for C3

43. 13(3) cage at R6C2 (step 30) = {148/256/346}
43a. 1 of {148} must be in R7C3 -> no 1 in R7C2

44. R78C46 (step 21) = {1267/1348/2356} (cannot be {1258} which clashes with combined cage R8C3467, cannot be {1357/2347} because R8C6 only contains 6,8)
44a. 5 of {2356} must be in R8C4 (R8C46 cannot be {36} which clashes with combined cage R8C3467) -> no 5 in R7C46
44b. 3 of {1348} must be in R8C4, 2 of {2356} must be in R7C6 -> no 3 in R7C6

45. Combined cage R78C456 = {124679/134678/234569}, 4,6 locked for N8

46. 4 in R9 locked in R9C789, locked for N9

47. R2468C7 (step 22) = {1259/1349/1367/2357} (cannot be {1268/1358/2348} because R8C7 only contains 7,9)
[These combinations also apply for R46C78 because R2C7 = R4C8 and R6C8 = R8C7]
47a. 2 of {1259/2357} must be in R6C7 -> no 5 in R6C7

48. R46C78 (step 47) = {1259/1349/1367/2357}
48a. Combined cage R456C78 = {124589/134579/134678/234578}, 4 locked for N6

49. 10(3) cage at R6C6 = {127/136/145/235}
49a. 5,6,7 can only be in R6C6 -> R6C6 = {567}

50. R456C9 (step 37) = {169/259/268/367}
50a. 3 of {367} must be in R6C9 -> no 3 in R4C9

51. Hidden killer quint 5,6,7,8,9 in R159C6 and R3468C6 for C6 -> R159C6 must contain one of 5,6,7,8
51a. R159C6 (step 9) = {148/238/247/256/346} (cannot be {157} which contains both 5 and 7)

52. 15(3) cage at R6C3 = {159/168/249/348/357/456} (cannot be {258/267} because R7C4 only contains 1,3,4)
52a. 1 of {159/168} must be in R7C4 -> no 1 in R6C4

53. 2 in N5 locked in 22(5) cage = {12379/12469/12568/23458} (cannot be {12478/23467} which clash with R5C78)
53a. 2 of {23458} must be in R5C456 (R5C456 cannot be {458} which clashes with R5C78) -> no 2 in R6C5

54. 22(3) cage in N1 = {589/679}
54a. R12C1 = {58/69} (cannot be {59/67/79/89} which clash with R456C1), no 7, R1C2 = {79}
54b. R456C1 = {479/578} (cannot be {569} which clashes with R12C1), no 6, 7 locked for C1 and N4
54c. 7 in N1 locked in R12C2, locked for C2

55. 19(3) diagonal cage in N7 (step 36) = {469/478/568} (cannot be {379} because 7,9 only in R9C3), no 3
55a. 7,9 of {469/478} can only be in R9C3 -> no 4 in R9C3
[That has at last made the elimination that I tried to do in step 17a! I can now use some of the steps that I had to delete earlier.]

56. R389C1 = {123} (hidden triple in C1)

57. 12(3) cage in N7 = {129/138} (cannot be {156/246/345} because R89C1 only contain 1,2,3)
57a. 8,9 can only be in R9C2 -> R9C2 = {89}
57b. 1 locked in R89C1, locked for C1 and N7

58. R3C159 (step 40) = {249/258/348/357}
58a. 3 of {348/357} must be in R3C1 -> no 3 in R3C5, clean-up: no 9 in R2C5

59. R78C5 = [76/94] (cannot be {58} which clashes with R23C5), no 5,8
59a. Combined cage R2378C5 = {4579/4678}, 4,7 locked for C5

60. 11(3) cage at R3C2 (step 11) = {128/146/236/245}
60a. 4 of {146/245} must be in R4C2 (R3C23 cannot be {45} which clashes with R3C5) -> no 4 in R3C23

61. 4 in N1 locked in R12C3, locked for C3

62. 13(3) cage at R6C2 = {256/346} (cannot be {238} which clashes with R89C1), no 8, clean-up: no 9 in R8C3 (step 3), no 3 in R8C4

[At this stage I was going to use 45 rule on R789 4 innies R7C2346 = 1 outie R6C8 + 3 which I’d seen a long time ago but was only useful now that 1 was locked in R7C46. However the naked pairs and naked triple in the next steps are more direct.]

63. Naked pair {57} in R8C34, locked for R8, clean-up: no 8 in R8C67
63a. R8C67 = [69], R8C5 = 4, R7C5 = 9, R8C2 = 8, R9C2 = 9, R12C2 = [75], R3C5 = 5, R2C5 = 7, R6C8 = 9 (step 4), R3C6 = 9, clean-up: no 8 in R12C1 (step 54a)

64. Naked pair {69} in R12C1, locked for C1 and N1, clean-up: no 4 in R456C1 (step 54b)
64a. Naked triple {578} in R456C1, locked for C1 and N1 -> R7C1 = 4, R9C3 = 7 (step 36), R8C34 = [57]

65. 45 rule on R789 2 outies R6C28 = 2 outies R7C46 + 10
65a. 1 in R7 locked in R7C46, locked for N8
65b. R6C28 must be odd -> R7C46 must be odd = {12}, locked for R7 and N8, R7C23 = {36}, locked for R7, N7 and 13(3) cage -> R7C9 = 5, R6C2 = 4, R4C2 = 2
[I missed R6C2 = 4 (step 3) after step 62a but if I’d done it then I might not have used this interesting step.]

66. R46C3 = [96] (naked pair), R7C23 = [63], R5C23 = [31], R3C23 = [18], R3C6 = 9, R3C9 = 7

67. Naked pair {12} in R89C1, locked for C1 -> R3C1 = 3, R1C3 = 4 (step 12), R2C34 = [24]

68. R4C3 = 9 -> R34C4 = 5 = [23], R4C8 = 1

69. Naked pair {46} in R3C78, locked for N3 -> R2C89 = [89], R12C1 = [96], R7C78 = [87], R1C7 = 5 (step 39)

70. Naked pair {46} in R34C7, locked for C7 -> R5C78 = [75], R5C1 = 8

71. Naked pair {23} in R6C79, locked for R6 and N6 -> R6C5 = 1

72. R4C9 = 8 (hidden single in C9), R56C9 = 8 = [62]

and the rest is naked singles and a hidden single (or cage sum)