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Here is my entry to the beauty of the asymmetrical.

If you don't find the cracking move which is available right from the start, then you'll have a harder time than SS suggests. JSudoku didn't find that move and needed 2 Turbot Fishes and 1 XY-X-Chain to solve it.

Hint: Look at Innies/Outies of R1234.



3x3::k:6144:6144:6146:6146:6146:2565:4614:4614:4614:6144:6144:2315:2315:7693:2565:2565:4614:4625:3858:6144:3604:3604:7693:5143:5143:4625:4625:3858:1820:3604:7693:7693:7693:5143:5143:4625:3858:1820:6182:6182:6182:3881:3881:5143:6700:4653:4653:2095:2864:6182:6182:6700:6700:6700:4653:4663:2095:2864:3130:3130:3130:1085:7486:4663:4663:3905:3905:4931:2116:2116:1085:7486:4663:2377:2377:3905:4931:4931:4931:7486:7486:

Solution:

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

SS Score: 1.04
Estimated rating: (Hard) 1.0, depends on how long it takes you to find that move.

Nice puzzle, Afmob!

Don't think I saw the cracking move you intended though, because I didn't see anything like that that was available "right from the start". Haven't read your TT hint.

Nevertheless very enjoyable and still only about a 1.25 rating the way I did it. Certainly didn't need any chains. My moves 8 - 10 were what did it for me.

Edit: Added steps 9a/9b and simplified step 10, as proposed by Afmob. Thanks once again!
Edit2: Typo fixed in step 5. Thanks, Andrew!

Messy One #2 Walkthrough

Prelims

a) 24(3) at R1C3 = {789}, locked for R1
b) 10(3) at R1C6 = {127/136/145/235} (no 8,9)
c) 9(2) at R2C3 and R9C2 = {18/27/36/45} (no 9)
d) 7(2) at R4C2 = {16/25/34} (no 7..9)
e) 15(2) at R5C6 = {69/78} (no 1..5)
f) 26(4) at R5C9 = {2789/3689/4589/4679/5678} (no 1)
g) 8(2) at R6C3 and R8C6 = {17/26/35} (no 4,8,9)
h) 11(2) at R6C4 = {29/38/47/56} (no 1)
i) 4(2) at R7C8 = {13}, locked for C8 and N9; cleanup: no 5,7 in R8C6
j) 29(4) at R7C9 = {5789}, locked for N9; cleanup: no 1,3 in R8C6


1. Naked pair (NP) at R8C67 = {26}, locked for R8

2. Naked triple (NT) at R789C7 = {246}, locked for C7; cleanup: no 9 in R5C6

3. Innie C12: R9C2 = 8
3a. -> R9C3 = 1
3b. cleanup: no 7 in R67C3, no 8 in R2C4

4. 8 in N9 locked in R78C9 for C9

5. Innies N789: R7C134 = 21(3) = {579/678} (no 2..4)
(Note: {489} unplaceable)
5a. only 1 of {56}, which must go in R7C3
5b. -> no 5,6 in R7C14
5c. 7 locked in R7C14 for R7
5d. cleanup: no 5,6 in R6C3; no 5..9 in R6C4

6. Innie/Outie (I/O) diff. N89: R7C4 = R8C3 + 3
6a. -> R7C4 = {78} (no 9); R8C3 = {45} (no 3,7,9)
6b. cleanup: no 2 in R6C4

7. Innies N7: R7C13+R8C3 = 18(3) = {459/567}
7a. -> 5 locked in R78C3 for C3 and N7
7b. cleanup: no 4 in R2C4

8. Hidden killer mutual on {26} within N7:
8a. {26} in N7 locked in R7C23+R9C1
8b. -> R7C23 must contain at least one of {26} (no eliminations yet)

9. 12(3) at R7C5 = {129/345} (no 6,8)
(Note: {138} unplaceable, {156} blocked by R7C3, {246} blocked by R7C23 (step 8b))
9a. can only have 1 of {24}, which must go in R7C7
9b. -> no 2,4 in R7C56

10. Hidden pair (HP) in R7 at R7C27 = {24} (no 3,6,9)

11. Hidden single (HS) in R7 at R7C3 = 6
11a. -> R6C3 = 2
11b. cleanup: no 3,7 in R2C4; no 5 in R45C2

12. Innies N7 (step 7): R7C1+R8C3 = 12(2) = [75]
12a. -> R67C4 = [38]

13. HS in R8/C9/N9 at R8C9 = 8

14. Split 11(2) at R6C12 = {56} (no 1,4,8,9) (last combo), locked for R6 and N4
14a. cleanup: no 1 in R45C2

15. NP at R45C2 = {34}, locked for C2 and N4

16. R78C2 = [29]
16a. -> split 7(2) at R89C1 = {34}, locked for C1

17. R7C7 = 4
17a. -> split 8(2) at R7C56 (step 9) = {35} (no 1,9), locked for C7 and N8

18. R78C8 = [13]
18a. -> R89C1 = [43]

19. Naked single at R7C9 = 9
19a. -> split 12(2) at R9C89 = {57}, 7 locked for R9

20. Split 10(2) at R89C4 = [19] (last permutation)
20a. cleanup: no 8 in R2C3

21. NS at R8C5 = 7

22. NS at R1C4 = 7

23. HP in N1 at R23C3 = {34} (no 7..9)
23a. cleanup: no 2 in R2C4

24. 1 in R6 locked in R6C56 for N5

25. HS in R5 at R5C1 = 1
25a. -> spilt 14(2) at R34C1 = [59/68]
25b. -> no 2,8,9 in R3C1

26. NP at R36C1 = {56}, locked for C1
26a. -> R1C1 = 2 (NS)

27. Naked quad at R5C7+R6C789 = {4789}, locked for N6
27a. 4 locked in R6C89 for R6

28. I/O diff. R1234: R5C8 = R4C2 + 1
28a. -> R4C2 = 4, R5C8 = 5
28b. -> R5C2 = 3

29. R9C89 = [75]

30. Split 15(4) at R3C67+R4C78 = {1239/1248} (no 6,7)
(Note: {2346} unplaceable)
30a. -> R4C8 = 2
30b. 4 of {1248} only available in R3C6
30c. -> no 8 in R3C6

31. NS at R5C9 = 6
31a. cleanup: no 9 in R5C7

32. NP at R5C67 = {78}, locked for R5
32a. -> R5C3 = 9

33. R4C13 = [87]
33a. -> R3C1 = 6 (cage sum)

34. R1C35 = [89]

This next move intended to get to all singles more quickly:

35. R4C456 = {569} = 20
35a. -> R23C5 = 10(2) (30(5) cage split)
35b. 8 in N2 locked in R23C5
35c. -> split 10(2) at R23C5 = {28}, locked for C5 and N2

Only naked singles and a couple of simple cage sums left now.

_________________
Cheers,
Mike

I thought this one was excellent.


1.O r789-> r7c134=21 and only combos are 957 and 768.So r6c3=2/3.
2.r5c128=9.So r5c8=5/6.
3.r789c7={246} only perm.
4.Thus 15/2 cage n5/6 cannot be {69} because the 26/4 cage in n6 must have a 5 or a 9.
So r5c67={78}.Thus 26/4 cage n6 <> 1 OR 2 in it.
5.I-O r6789-> r6c56=r5c9+3 so<> {12}
6Now,if r5c12={12} this forces {12} into r6c56 ..impossible.So r5c12={13}.-> r6c3=2 etc and it's a mop-up from here.[size=50]

Very nice

Many thanks Afmob

Regards

Gary

Thanks Afmob for a challenging puzzle.


Yes, it's available from the diagram at the start. That move isn't a difficult one but it's hard to spot (my step 30). Maybe that's because the 15(3) and 7(2) cages sticking out into R5C12 draw the eye away from the move.

Mike's step 8 was unusual and very powerful because it leads to a key combination elimination from the 12(3) cage in R7. I'm not sure if I've seen a hidden killer pair used that way before; it's something I'll try to look out for in future. I'm guessing that most/all software solvers wouldn't currently find that step. It looks to be the sort of thing that only an expert human solver would consider to be useful.

I'll rate the way I solved it as Hard 1.25. It's clearly easier with Mike's step 8 which I think was more powerful than the move that Afmob hinted at. If it's 1.25 with Mike's step then it's also 1.25 with Afmob's breakthrough step.

Here is my walkthrough. I used 16 different 45 tests, still slightly short of my record!

Prelims

a) R2C34 = {18/27/36/45}, no 9
b) R45C2 = {16/25/34}, no 7,8,9
c) R5C67 = {69/78}
d) R67C3 = {17/26/35}, no 4,8,9
e) R67C4 = {29/38/47/56}, no 1
f) R78C8 = {13}, locked for C8 and N9
g) R8C67 = [17/26/35/62], no 4,8,9, no 5,7 in R8C6
h) R9C23 = {18/27/36/45}, no 9
i) R1C345 = {789}, locked for R1
j) 10(3) cage at R1C6 = {127/136/145/235}, no 8,9
k) 26(4) cage in N6 = {2789/3689/4589/4679/5678}, no 1
l) 29(4) cage in N9 = {5789}, locked for N9, clean-up: no 1,3 in R8C6

1. 45 rule on C12 1 innie R9C2 = 8, R9C3 = 1, clean-up: no 8 in R2C4, no 7 in R67C3
1a. 8 in N9 locked in R78C9, locked for C9

2. Naked pair {26} in R8C67, locked for R8

3. Naked triple {246} in R789C7, locked for C7, clean-up: no 9 in R5C6

4. 1 in N6 locked in R4C79, locked for R4, clean-up: no 6 in R5C2

5. R7C567 = {129/147/156/237/246/345} (cannot be {138} which clashes with R7C8), no 8

6. 45 rule on N36 2 innies R25C7 = 1 outie R3C6 + 8
6a. Max R25C7 = 16 -> max R3C6 = 8

7. 45 rule on N7 3 innies R7C13 + R8C3 = 18 = {279/369/459/567}
7a. 2 of {279} must be in R7C3 -> no 2 in R7C1

8. 45 rule on N3 2 innies R23C7 = 1 outie R4C9 + 9
8a. Max R23C7 = 16 -> max R4C9 = 7
8b. Min R4C9 = 1 -> min R23C7 = 10 -> no 1 in R3C7

9. 45 rule on N89 1 innie R7C4 = 1 outie R8C3 + 3, R8C3 = {345}, R7C4 = {678}, R6C4 = {345}

10. R7C13 + R8C3 (step 6) = {369/459/567} (cannot be {279} because 7,9 only in R7C1), no 2, clean-up: no 6 in R6C3
10a. 7,9 can only be in R7C1 -> R7C1 = {79}
10b. 6 of {369} must be in R7C3 -> no 3 in R7C3, clean-up: no 5 in R6C3
[Could also eliminate {369} with complex block using step 9 but it goes soon with simple steps.]

11. 18(3) cage at R6C1 = {189/279/369/378/459/567} (cannot be {468} because R7C1 only contains 7,9)
11a. 8 of {189} must be in R6C1 -> no 1 in R6C1

12. 45 rule on R1234 3 outies R5C128 = 9 = {126/135/234}, no 7,8,9
12a. 2 of {234} must be in R5C8 (R5C12 cannot be {23} which clashes with R6C3) -> no 4 in R5C8
12b. 5 of {135} must be in R5C8 -> no 5 in R5C12, clean-up: no 2 in R4C2

13. 45 rule on R789 3 innies R7C134 = 21 = {579/678}, 7 locked for R7
13a. 6 of {678} must be in R7C3 -> no 6 in R7C4, clean-up: no 5 in R6C4, no 3 in R8C3 (step 9)

14. R7C13 + R8C3 (step 7) = {459/567}, 5 locked in R78C3, locked for C3 and N7, clean-up: no 4 in R2C4

15. 15(3) cage at R8C3 = {159/249/258/348/357/456} (cannot be {168/267} because R8C3 only contains 4,5)
15a. 6 of {456} must be in R9C4, for all other combinations 4,5 must be in R8C3 -> no 4,5 in R9C4

16. Max R1C789 = 15 -> no 2 in R2C8

17. 14(3) cage at R3C3 = {149/158/167/239/248/257/347/356}
17a. 1 of {149} must be in R3C4
17b. 9 of {239} must be in R34C3 (R34C3 cannot be {23} which clashes with R6C3)
17c. -> no 9 in R3C4

18. 45 rule on R89 3 outies R7C289 = 12 = {129/138/156/246/345}
18a. 2 of {129} must be in R7C2 -> no 9 in R7C2

19. 45 rule on R789 1 innie R7C1 = 2 outies R6C34 + 2
19a. R7C1 = {79} -> R6C34 = 5,7 = [23/34], 3 locked for R7

20. 45 rule on N47 3 innies R458C3 = 1 outie R3C1 + 15
20a. Max R458C3 = 22 -> max R3C1 = 7

21. 15(3) cage at R8C3 (step 15) = {159/249/258/348/456} (cannot be {357} because R89C4 = {37} clashes with R67C4), no 7
21a. 8 of {348} must be in R8C4 -> no 3 in R8C4

22. 45 rule on R789 4 outies R6C1234 = 16 and must contain [23/34] in R6C34 (step 19a) = {1348/2347/2356} -> R6C12 = {18/27/56} (cannot be {47} because 18(3) cage cannot be {47}7), no 4,9

23. 26(4) cage in N6 = {3689/4589/4679/5678} (cannot be {2789} which clashes with R5C7), no 2
23a. Killer triple 7,8,9 in R5C7 and 26(4) cage, locked for N6

24. 45 rule on C89 2 outies R16C7 = 2 innies R45C8 + 5
24a. Min R45C8 = 6 -> min R16C7 = 11, no 1 in R1C7, no 5 in R6C7
24b. Max R16C7 = 14 -> max R45C8 = 9
24c. R45C8 = {24/25/26/45}

25. Hidden killer triple 7,8,9 in R23C7, R5C7 and R6C7 -> R23C7 must contain one of 7,8,9
25a. R23C7 = R4C9 + 9 (step 8)
25b. Max R23C7 = 14 (cannot be {78} which contains two of 7,8,9) -> max R4C9 = 5
25c. R4C9 = {12345} -> R23C7 = 10,11,12,13,14 = [19/38/39/57/58/59/75] (cannot be [37/73] because R2C7 must be 1 when R4C1 = 1), no 3 in R3C7

26. 45 rule on C9 4 (3+1) outies R369C8 + R6C7 = R1C9 + 28
26a. Max R369C8 + R6C7 = 24 + 9 = 33 -> max R1C9 = 5
26b. Min R369C8 + R6C7 = 29 -> min R369C8 = 20, no 2 in R3C8

27. 45 rule on N36 2 outies R35C6 = 1 innie R2C7 + 7
27a. R2C7 = {1357} -> R35C6 must be even and cannot be [77] -> no 7 in R3C6

28. 45 rule on R6789 2 innies R6C56 = 1 outie R5C9
28a. Min R5C9 = 3 -> min R6C56 = 6, cannot be {12} -> at least one of 1,2 must be in R6C123

29. R5C128 (step 12) = {126/135/234}
29a. R5C12 cannot be {12} which clashes with R6C123 (step 28a) -> no 6 in R5C8

30. 45 rule on R1234 2 outies R5C18 = 1 innie R4C2 + 2, IOU no 2 in R5C8 -> R5C8 = 5, R5C12 = {13} (step 29), locked for R5 and N4 -> R6C3 = 2, R7C3 = 6, R4C8 = {24} (step 24c), clean-up: no 3,7 in R2C4, no 5 in R4C2
30a. R8C3 = 5 (hidden single in C3)
30b. 5 in N9 locked in R79C9, locked for C9

31. R6C4 = 3 (hidden single in R6), R7C4 = 8, R7C1 = 7 (step 13)
31a. R7C1 = 7 -> R6C12 = {56} (step 11), locked for R6 and N4 -> R4C2 = 4, R5C2 = 3, R5C1 = 1, R7C2 = 2, R8C2 = 9, R7C7 = 4, R4C8 = 2
31b. R7C7 = 4 -> R7C56 = {35} (step 5), locked for R7 and N8 -> R7C89 = [19], R8C8 = 3, R9C8 = 7, R89C9 = [85], R89C1 = [43], R8C45 = [17], R9C4 = 9 (step 15), R1C4 = 7, clean-up: no 8 in R2C3

32. 26(4) cage in N6 (step 23) = {4679} (only remaining combination) -> R5C9 = 6, clean-up: no 9 in R5C7
32a. Naked triple {479} in R6C789, locked for R6 and N6 -> R5C7 = 8, R5C6 = 7, R5C3 = 9, R4C13 = [87], R1C35 = [89], R3C1 = 6 (cage sum), R6C12 = [56], R12C1 = [29], clean-up: no 2 in R2C4

33. R4C3 = 7 -> R3C34 = [34] (step 17) (cannot be {25} because 2,5 only in R3C4), R5C45 = [24], R2C3 = 4, R2C4 = 5, R4C456 = [659], R7C56 = [35]

34. 30(5) cage at R2C5 = {25689} (only remaining combination) -> R23C5 = {28}, locked for C5 and N2

35. 20(5) cage at R3C6 = {12359} (only remaining combination) -> R34C7 = [93] , R3C6 = 1

and the rest is naked singles

Agree. It was my key move and was very hard to find.Very clever Mike! I spent a lot of time in n7 & r7 and completely missed it. SS can't do it. It has a routine "hidden killer mutuals", but this can't handle the implied block in r7c23.

Here's an alternative way to get past Mike's step 8. It is the same as Andrew used, just gets to it a lot quicker. I'd still give this way a 1.25 rating. I haven't got time to do a full WT.


Messy One #2 (ALT ending)
Mike's steps 1-7: should be to here

ALT steps

8. "45" r1234: 3 outies r5c128 = h9(3)r5 = {126/135/234}(no 7..9)

9. "45" r1234: r5c18 - 2 = r5c8
9a. since 1 innie & 1 outie are in the same house (n4) -> r5c8 cannot = 2 (IOU)
9b. h9(3)r5 = 1 of 4/5/6 (step 8) -> no (456) in r5c12
9c. no (123) in r4c2

10. Naked triple (123) in n4: all locked for n4
10a. 1 locked for r5
10b. 1 locked in h9(3)r5 = 1{26/35}(no 4)

11. 18(3)n4 must have 7/9 = {459/567}(no 8)
11a. must have only 1 of 7/9 -> no 7 or 9 in r6c12
11b. r6c12 = 5{4/6}
11c. 5 locked for n4 & r6
11d. no 2 r5c2

12. "45" n789: 4 outies r6c1234 = h16(4) & must have 5 (step 11c) & no 1
12a. ={2356} only = {56}[23]
12c. r7c1 = 7 (cage sum)

Cracked now.

Cheers
Ed