SudokuSolver Forum

Got a bit messed up with the symmetry. And seem to have inadvertently gone fishing with this cage pattern. Unfortunately, this is the one that got away. SS(v3.3.0)score: 1.58 but estimated rating: Hard 1.0! "Easy" Assassin.

Think I know why the score is so wrong....but won't talk about that now. It might just have to be one of those that SS will always get wrong. Unfortunately, I won't be able to make a harder version for you. Going OS for a few weeks.

Assassin 138


Cheers
Ed

Thanks Ed for the new Assassin!

I liked those J shaped cages and they offered some interesting moves like step 1e which cracks this Killer. But I have to say that I'm struggling to rate it 1.25 because I saw the important move immediately though I've might have been lucky.

A138 Walkthrough:

1. C456 !
a) Innies N2 = 29(4) = {5789} locked for N2
b) 6(2) = {24} locked for R2+N2
c) Innies C456 = 10(2) = [73/82/91]
d) 5 locked in 26(4) @ N2 for R3 -> 26(4) = 58{49/67} -> R4C6 = (46); 8 locked for R3+N2
e) ! R7C5 = R4C6 since R7C5 sees all of N5 but R4C6 -> R7C5 = (46)
f) ! R7C5 = R4C6 = 4 since they see all 6 of 10(3)
g) R2C5 = 2, R2C4 = 4
h) 26(4) = {4589} -> 9 locked for R3+N2
i) Innies C456 = 10(2) = [73] -> R1C4 = 7, R9C4 = 3
j) 36(8) must have 3 -> 3 locked for C6+N5
k) 17(3) = {179} locked for C5+N5

2. R789
a) 15(2) = {69} -> R8C5 = 6, R8C4 = 9
b) 36(8) must have 1,7 -> R7C6 = 7, R7C4 = 1
c) 17(3) = [59/86]3
d) 14(2) = [59/86]
e) Naked pair (69) locked in R9C37 for R9
f) 7 locked in 8(2) @ N7 = {17} locked for C1+N7
g) Hidden Single: R3C3 = 1 @ N1, R1C3 = 4 @ C3
h) Cage sum: R2C3 = 9
i) R9C3 = 6 -> R8C3 = 8

3. C123
a) 20(3) = {578} -> R3C2 = 7, {58} locked for C2+N1
b) 7(2) = {34} -> R9C2 = 4, R8C2 = 3
c) 33(7) = {1235679} -> R4C3 = 7, R4C1 = 5, R4C2 = 9; {236} locked for C1
d) 8(2) @ N4 = {26} -> R5C3 = 2, R5C2 = 6

4. C789
a) 9(2) = {36} locked for C7
b) R8C7 = 5, R9C7 = 9
c) 17(3) = 6{38/47} because {278} blocked by R7C7 = (28) -> R7C8 = 6
d) 12(2) = [57/93]

5. Rest is singles.

Rating: 1.25. I used unusual CPE analysis.

Edit: After Andrew's comments I looked for a way to avoid step 1f, so here it is:

Thanks Ed for a challenging Assassin. I also enjoyed those J-shaped cages. I'll agree with you that the SS rating is too high but not by as much as you are suggesting.

Afmob's steps 1e and 1f, which break open this puzzle, were really neat but I have to disagree on the rating. While step 1e isn't a difficult move, apart from spotting it, step 1f is IMHO a high rated one, at least 1.5. It's the same type of move as udosuk's "cell cloning" trick in his A122 v1.5 walkthrough.

Thanks Afmob for your alternative start avoiding step 1f. I had no problem with step 1f as a move, it was really neat, just with the rating of it.

I'll rate A138 at 1.25 taking into account difficulty in finding the breakthrough moves 16 and 20.

Here is my walkthrough. Thanks Afmob and Ed for your comments and suggestions.

Prelims

a) R12C9 = {39/48/57}, no 1,2,6
b) R2C45 = {15/24}
c) R34C7 = {18/27/36/45}, no 9
d) R5C23 = {17/26/35}, no 4,8,9
e) R5C78 = {14/23}
f) R67C3 = {17/26/35}, no 4,8,9
g) R89C1 = {17/26/35}, no 4,8,9
h) R89C2 = {16/25/34}, no 7,8,9
i) R8C45 = {69/78}
j) R89C7 = {59/68}
k) R123C2 = {389/479/569/578}, no 1,2
l) 20(3) cage at R1C3 = {389/479/569/578}, no 1,2
m) 26(4) cage at R3C4 = {2789/3689/4589/4679/5678}, no 1
n) 10(3) cage in N2 = {136/235} (cannot be {127/145} which clash with R2C45), no 4,7,8,9, 3 locked for N2
[Oops! That should have been 10(3) cage in N2 = {136} (only remaining combinations, all others clash with R2C45), locked for N2. Fortunately step 2 reaches the same result.]
o) 36(8) cage at R4C4 = {12345678}, no 9

1. 1,2 in N1 locked in 33(7) cage, no 1,2 in R4C123

2. 45 rule on N2 4 innies R1C4 + R3C456 = 29 = {5789}, locked for N2, clean-up: no 1 in R2C45
2a. Naked pair {24} in R2C45, locked for R2 and N2, clean-up: no 8 in R1C9

3. 45 rule on C123 2 outies R19C4 = 10 = [73/82/91]
3a. 45 rule on C123 4 innies R1289C3 = 27 = {3789/4689} (cannot be {5679} which clashes with R67C3), no 1,2,5, 8,9 locked for C3

4. 20(3) cage at R1C3 = {389/479}, no 6, CPE no 9 in R1C12

5. 45 rule on N2 1 innie R1C4 = 1 outie R4C6 + 3 -> R4C6 = {456}

6. 26(4) cage at R3C4 = {4589/5678} (cannot be {4679} because 4,6 only in R3C4)
6a. 4,6 only in R3C4 -> R3C4 = {46}, clean-up: no 8 in R1C4 (step 5), no 2 in R9C4 (step 3)
6b. 5,8 in N2 locked in R3C456, locked for R3, clean-up: no 1,4 in R4C7

7. 9 in N5 locked in R456C5, locked for C5, clean-up: no 6 in R8C4
7a. R456C5 = {179/269/359}, no 4,8
7b. 8 in N5 locked in 36(9) cage, no 8 in R7C456
7c. 6 in C4 locked in R4567C4, locked for 36(9) cage, no 6 in R56C6 + R7C56

8. 20(3) cage at R1C3 (step 4) = {389/479}
8a. 7 of {479} must be in R1C4 (R12C3 cannot be [47] which clashes with R1289C3), no 7 in R12C3
8b. 9 of {389} must be in R1C4, 4 of {479} must be in R1C3 -> no 9 in R1C3
8c. R12C3 = {38}/[49]

9. R123C2 = {479/569/578} (cannot be {389} which clashes with R12C3), no 3
9a. Killer pair 8,9 in R123C2 and R12C3, locked for N1

10. 17(3) cage at R8C3 = {179/368} (only combinations which contain 1 or 3), no 4
10a. R9C4 = {13} -> no 3 in R89C3

11. 45 rule on R1234 1 outie R5C9 = 2 innies R4C45 + 2
11a. Min R4C45 = 3 -> min R5C9 = 5
11b. Max R4C45 = 7, no 7,8,9
11c. R456C5 (step 7a) = {179/269/359}
11d. 1 of {179} must be in R4C5 -> no 1 in R56C5

12. 45 rule on C12 3 outies R345C3 = 10 = {127/145/235} (cannot be {136} which clashes with R67C3), no 6, clean-up: no 2 in R5C2
12a. 7 of {127} must be in R4C3 -> no 7 in R35C3, clean-up: no 1 in R5C2

13. 45 rule on R89 1 outie R7C8 = 2 innies R89C9 + 3
13a. Min R89C9 = 3 -> min R7C8 = 6
13b. Max R89C9 = 6, no 6,7,8,9

14. R789C8 = {179/278/359/368/467} (cannot be {269/458} which clash with R78C7)
14a. 45 rule on N9 4 innies R7C7 + R789C9 = 14 = {1238/1247/1346/2345} (cannot be {1256} which clashes with R78C7), no 9

15. Hidden killer pair 8,9 in R7C12 and R89C3 for N7 -> R7C12 must contain one of 8,9
15a. Hidden killer pair 8,9 in R7C12 and R7C789 for R7 -> R7C789 must contain one of 8,9
15b. Killer pair 8,9 in R7C789 and R89C7, locked for N9

16. Hidden killer pair 4,6 in 36(8) cage and R4C6 for N5 -> 36(6) cage cannot contain more than one of 4,6 within N5 (but might not contain either of them) -> R7C456 must contain at least one of 4,6
16a. 45 rule on N8 4 innies R7C456 + R9C4 = 15 = {1347/1356/2346} (cannot be {1257} which doesn’t contain 4 or 6), 3 locked for N8, CPE no 3 in R456C4
16b. 6 of {1356/2346} must be in R7C4 -> no 2,5 in R7C4
16c. 3 in C4 locked in R79C4, locked for N8

17. 15(3) cage in N8 = {159/249/258} (cannot be {168/267} which clash with R8C45, cannot be {456} which clashes with R7C456 + R9C4), no 6,7

18. 45 rule on R5 5 innies R5C14569 = 32 = {26789/35789/45689}, no 1

19. 45 rule on N7 5 innies R7C123 + R89C3 = 30 = {15789/24789/25689/34689} (cannot be {35679/45678} which clash with R89C1)
19a. 6,7 must be in R89C3 -> no 6,7 in R7C123, clean-up: no 1,2 in R6C3
19b. 3 of {34689} must be in R7C3 -> no 3 in R7C12

20. R9C4 = {13} -> R456C4 + R7C456 cannot contain both of 1,3 -> R56C6 must contain at least one of 1,3
20a. R12C6 contain two of 1,3,6 -> R56C6 can only contain one of 1,3
20b. Killer triple 1,3,6 in R12C6 and R56C6, locked for C6 -> R4C6 = 4, R1C4 = 7 (step 5), R9C4 = 3 (step 3), clean-up: no 5 in R2C9, no 5 in R8C1, no 4 in R8C2, no 8 in R8C5
20c. 6 in C6 locked in R12C6, locked for N2

21. 3 in 36(8) cage at R4C3 locked in R56C6, locked for C6 [Also locked for N5; I missed that but it comes from the next sub-step anyway.]
21a. Naked pair {16} in R12C6, locked for C6 and N2 -> R1C5 = 3, clean-up: no 9 in R2C9, no 5 in R456C5 (step 11c)

22. 4 in 36(8) cage at R4C4 locked in R7C45, locked for R7 and N8
22a. 15(3) cage in N8 (step 17) = {159/258}, 5 locked for N8

23. R1C4 = 7 -> R12C3 = [49] (step 8c), clean-up: no 6 in R123C2 (step 9), no 8 in R2C9, no 7 in R89C3 (step 10)
23a. R3C2 = 7, clean-up: no 2 in R4C7, no 1 in R5C3
23b. Naked pair {58} in R12C2, locked for C2 and N1, clean-up: no 3 in R5C3, no 2 in R89C2

24. Killer pair 3,6 in R5C2 and R89C2, locked for C2 -> R4C2 = 9

25. 45 rule on N1 2 remaining outies R4C13 = 12 = {57}, locked for R4 and N4 -> R5C3 = 2, R5C2 = 6, R6C3 = 3, R7C3 = 5, R3C3 = 1, R4C13 = [57], clean-up: no 2,4 in R3C7, no 8 in R4C7, no 3 in R5C78, no 3 in R8C1, no 1 in R89C2

26. R89C2 = [34], R67C2 = [12], R7C6 = 7, R8C5 = 6, R89C3 = [86], R7C1 = 9, R8C4 = 9, R8C7 = 5, R9C7 = 9, R8C6 = 2, clean-up: no 2 in R46C5 (step 11c)

27. R4C5 = 1, R7C45 = [14], R2C45 = [42]

28. R3C6 = 9, R5C6 = 3 (hidden singles in C6)

29. Naked pair {36} in R34C7, locked for C7 -> R7C7 = 8, R7C8 = 6, R89C8 = 11 = [47]

and the rest is naked singles[/size]

I missed it so think it's difficult and would rate those 2 moves higher! I definitely thought about the relationship between r4c6 and r7c45 like Andrew did (his step 16) [edit: though couldn't make it productive like Andrew did] but didn't think about the relationship between r7c5 and the whole of n5. 1e is more than just a CPE type move. Really, really elegant! Thanks Afmob!

OK - here's the more standard easy Assassin solution that I thought was the Hard 1.0 way: just need to find the outies of n12.

Assassin 138 ALT quick cracker.

Afmob's step 1d to here.


1e. Innies C456: r19c4 = 10(2) = [73/91]
1f. r9c4 = (13)

2. 1 & 2 in n1 only in 33(7) -> no 1 or 2 in r4c123

3. "45" n12: 4 outies r4c1236 = 25.
3a. must have 4 or 6 for r4c6 = {3679/4579/4678} = 7{..}
3b. 7 locked for n4 and r4 and 33(7)n1
3c. no 2 r3c7
3d. no 1 r5c23
3e. no 1 r7c3

4. 8(2)n4 = {26/35} = [2/3..]
4a. 5(2)n6 = {14} ({23} blocked by 8(2)n4)
4b. 1 and 4 both locked for r5 & n6

5. 1 in r4 only in n5: locked for n5

6. r9c4 see's all of the 1s which is required in 36(8)n5 -> no 1 in r9c4 (CPE)
6a. r9c4 = 3, r1c4 = 7 (h10(2)r19c4)

7. 1 outie n2: r4c7 = 4

Puzzle is cracked.

So, one 4-cell hidden cage is the key with it's locked candidate (step 3) and one CPE from a locked cage (step 6). I think any 4-cell hidden cage counts as hard 1.0 rating (at least) but don't think this one needs to go any higher than that. We used to think of big CPE moves as 1.25 rating (see A86), but this one in step 6 is from a locked original cage so don't think it deserves a 1.25 rating.

BTW - SS misses this locked cage which seems like a bug. I've told Richard about it. But, it won't bring the scoring down since manually giving SS that move when it's first available doesn't make a difference to the number of steps. To get the score down to around 1.25 you have to change the routine order a fair bit which mucks up the scoring for some other puzzles. We'll see which turns out to give the best correlation over-all before changing it.

Turned out to be a really good puzzle.

Cheers
Ed