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from Pinata Killer #15 which also used a Girandola group. My walkthrough for that puzzle only used the group at the end, with naked singles, to reach the unique solution. For Assassin 252 the group helped throughout the solving path, making it a more enjoyable way for a solver to use a Girandola group.

Also, this puzzle is unique even without the Girandola group. The group makes it an easier puzzle. The SS score is 1.65 using the Girandola group or 2.00 without the group.

Prelims

a) R1C12 = {17/26/35}, no 4,8,9
b) R1C89 = {17/26/35}, no 4,8,9
c) R23C2 = {89}
d) R23C8 = {18/27/36/45}, no 9
e) R9C12 = {29/38/47/56}, no 1
f) R9C34 = {29/38/47/56}, no 1
g) R9C67 = {18/27/36/45}, no 9
h) R9C89 = {49/58/67}, no 1,2,3
i) 10(3) cage at R7C2 = {127/136/145/235}, no 8,9

1. Naked pair {89} in R23C2, locked for C2 and N1, clean-up: no 2,3 in R9C1

2. 45 rule on R5 1 innie R5C5 = 3, placed for Girandola group, clean-up: no 5 in R1C2, no 5 in R1C8

3. 45 rule on N5 2 innies R5C46 = 3 = {12}, locked for R5 and N5

4. 45 rule on C5 2 remaining innies R46C5 = 10 = {46}, locked for C5 and N5

5. 45 rule on R9 1 innie R9C5 = 1, clean-up: no 8 in R9C67
5a. 14(3) cage at R7C5 = {158} (only remaining combination), locked for C5 and N8, clean-up: no 3,6 in R9C3, no 4 in R9C7

6. Naked triple {279} in 18(3) cage at R1C5, locked for N2

7. 1 in Girandola group only in R1C19, locked for R1, clean-up: no 7 in R1C1, no 7 in R1C9
7a. One of the 8(2) cages at R1C1 and R1C8 must be {17} -> 7 in R1C28, locked for R1

8. 2 in Girandola group only in R1C19 + R2C5, CPE no 2 in R1C5 -> R1C5 = 9

[In this position there’s the possibility of a UR step, R23C5 = {27} -> R23C8 cannot be {27} because can’t then determine whether these pairs of cells are [27] or [72]. However I don’t use UR, because it relies on uniqueness and doesn’t solve the complete puzzle.
Ed pointed out that this comment isn’t valid because the Girandola group can determine which of these values is in R2C5. Similar comments can apply to other restricted cages patterns including Centre Dot Killers and Killer-Xs.]

9. 9 in Girandola group only in R5C8 + R9C19, CPE no 9 in R9C8, clean-up: no 4 in R9C9

10. 45 rule on R1234 3 innies R4C456 = 20 = {479/569} (cannot be {578} because R4C5 only contains 4,6), no 8, 9 locked for R4 and N5
10a. 8 in N5 only in R6C46, locked for R6

11. 45 rule on C6789 2 innies R46C6 = 15 = {78} (only remaining combination) -> R6C6 = 8, R4C6 = 7, R6C4 = 5, R4C4 = 9, R4C5 = 4 (step 10), R6C5 = 6, clean-up: no 2 in R9C3, no 2 in R9C7
11a. 9 in N8 only in R78C6, locked for 23(5) cage at R6C7, no 9 in R6C78 + R7C7

12. 45 rule on R1 2 outies R2C37 = 11 = [29/38]/{47/56}, no 1, no 2,3 in R2C7

13. 16(3) cage at R1C6 = {259/268/349/358/457} (cannot be {367} which clashes with 8(2) cage at R1C8)
13a. 6 of {268} must be in R1C6 -> no 6 in R12C7, clean-up: no 5 in R2C3 (step 12)
13b. 7 of {457} must be in R2C7 -> no 4 in R2C7, clean-up: no 7 in R2C3 (step 12)

14. 15(3) cage at R1C3 = {258/348/456}
14a. 5 of {258/456} must be in R1C3 -> no 2,6 in R1C3
14b. 8 of {348} must be in R1C4 -> no 3 in R1C4
14c. 6 of {456} must be in R2C3 (cannot be [564] which clashes with the pair of 8(2) cages in R1) -> no 6 in R1C4

15. 8(2) cage at R1C1 = [17/26/62] (cannot be [53] which clashes with 15(3) cage at R1C3), no 3,5

16. 45 rule on C1 3 innies R159C1 = 18 = {189/279/468/567} (cannot be {459} because R1C1 only contains 1,2,6)
16a. 6 of {468/567} must be in R1C1 -> no 6 in R59C1, clean-up: no 5 in R9C2

17. 45 rule on C9 3 innies R159C9 = 17 = {179/269/278/458/467}
17a. 5 of {458} must be in R1C9 -> no 5 in R59C9, clean-up: no 8 in R9C8

18. 45 rule on N7 2 innies R79C3 = 1 outie R6C1 + 10
18a. Max R79C3 = 17 -> max R6C1 = 7
18b. Min R79C3 = 11, no 1 in R7C3

19. 15(3) cage at R6C9 = {159/258/267/348/357/456} (cannot be {168/249} which clash with R159C9)
19a. 45 rule on N9 2 innies R79C7 = 1 outie R6C9 + 3
19b. 15(3) cage cannot be 9{15} which clashes with R79C7 = 12 = {57}, no 9 in R6C9

20. R6C3 = 9 (hidden single in R6), clean-up: no 2 in R9C4

21. 9 in R9 only in R9C19, locked for Girandola group, no 9 in R5C8

22. 9 in N6 only in R5C79, locked for R5
22a. 21(4) cage at R5C6 = {1479/1569/2469}, no 8
22b. 8 in R5 only in R5C13, locked for N4

23. R79C7 = R6C9 + 3 (step 19a)
23a. R6C9 = {12347} -> R79C7 = 4,5,6,7,10 = [13/23/15/16/25/43/37/46/73], no 5,6,8 in R7C7

24. R79C3 = R6C1 + 10 (step 18)
24a. Max R79C3 = 15 -> no 7 in R6C1
24b. Min R79C3 = 11, no 2 in R7C3

25. 13(3) cage at R2C1 = {157/247/256/346}
25a. R159C1 (step 16) = {189/279/468} (cannot be {567} which clashes with 13(3) cage), no 5, clean-up: no 6 in R9C2
25b. 9 of {279} must be in R9C1 -> no 7 in R9C1, clean-up: no 4 in R9C2

26. 4 in Girandola group only in R5C28 + R9C1, CPE no 4 in R5C1
26a. R159C1 (step 25a) = {189/279/468}
26b. R5C1 = {78} -> no 8 in R9C1, clean-up: no 3 in R9C2
26c. 8 in Girandola group only in R8C5 + R9C9, CPE no 8 in R8C789

27. R9C67 = [36/45/63] (cannot be [27] which clashes with R9C2), no 2,7

28. R9C2 = 2 (hidden single in R9), R9C1 = 9, clean-up: no 6 in R1C1, no 4 in R9C8
28a. 6 in Girandola group only in R1C9 + R5C28 + R9C9, CPE no 6 in R5C9

29. R9C34 = [47/74/83] (cannot be [56] which clashes with R9C67), no 5,6

30. 10(3) cage at R7C2 = {136/145}, no 7, 1 locked for N7

31. R159C1 (step 26a) = {189/279}
31a. 13(3) cage at R2C1 = {247/256/346} (cannot be {157} which clashes with R159C1), no 1
31b. 14(3) cage at R6C1 = {158/257/347} (cannot be {167/248} which clashes with R159C1, cannot be {356} which clashes with 10(3) cage at R7C2), no 6
31c. 6 in C1 only in 13(3) cage at R2C1 = {256/346}, no 7

32. 45 rule on N1 2(1+1) outies R1C4 + R4C1 = 1 innie R3C3 + 8
32a. Max R1C4 + R4C1 = 14 -> no 7 in R3C3

33. R1C2 = 7 (hidden single in N1), R1C1 = 1, R5C1 = 8 (step 31)

34. 2 in R1 only in R1C789, locked for N3, clean-up: no 7 in R23C8
[This makes the UR unnecessary! ]

35. R5C3 = 7 (hidden single in N4), clean-up: no 4 in R9C4
35a. R5C13 = [87] = 15 -> R5C24 = 6 = [42/51], no 6

36. 6 in R5 only in R5C78, locked for N6

37. 4 in Girandola group only in R5C28, locked for R5 -> R5C9 = 9
37a. R159C9 (step 17) = {269} (only remaining combination) -> R1C9 = 2, placed for Girandola group, R1C8 = 6, R9C9 = 6, R9C8 = 7, R9C4 = 3, R9C67 = [45], R9C3 = 8, R23C5 = [72], R5C7 = 6, clean-up: no 4,6 in R2C3 (step 12), no 3 in R23C8

38. Naked pair {45} in R5C28, locked for Girandola group -> R8C5 = 8, R7C5 = 5
[The Girandola group is now complete apart from placements for R5C28.]

39. 15(3) cage at R1C3 (step 14) = {258/348} -> R1C4 = 8
39a. R2C3 = {23} -> no 3 in R1C3

40. 5 in C9 only in 13(3) cage at R2C9 = {157} (only remaining combination) -> R3C9 = 7, R24C9 = {15}, locked for C9

41. R7C9 = 8 (hidden single in C9)

42. 14(3) cage at R7C8 = {149/239}
42a. Killer pair 3,4 in 14(3) cage and R8C9, locked for N9

43. R6C7 = 7 (hidden single in R6)
43a. 23(5) cage at R6C7 contains 7,9 = {12479} (only remaining combination) -> R6C8 = 4, R7C7 = 1, R78C6 = {29}, locked for C6 and N8 -> R5C68 = [15], R5C24 = [42], R68C9 = [34]

44. R6C23 = [19] = 10, R78C4 = {67} = 13 -> R7C3 = 4 (cage sum), R1C3 = 5, R2C3 = 2 (cage sum), R1C67 = [34], R2C7 = 9 (cage sum)

and the rest is naked singles.

I'll rate my walkthrough for A252 at 1.5. A fairly long solving path, but no particularly difficult steps; step 19 was the hardest one.

Have to be very careful about using UR for puzzles with extra constaints such as Girandola. The Girandola group is involved at r2c5 in r23c58 so can't use UR. Have to be careful with X killers for the same reason. Got JSudoku to knock out this puzzle which it says has a unique solution.

"Paste Into" A252 in SudokuSolver but not v3.6.1 since it has a bug.

.-------------------------------.-------------------------------.-------------------------------.
| 126       267       345       | 48        9         3456      | 23458     2367      1256      |
| 1234567   89        2346      | 13468     27        13456     | 5789      12345678  123456789 |
| 1234567   89        1234567   | 13468     27        13456     | 123456789 12345678  123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 123568    12356     123568    | 9         4         7         | 123568    123568    123568    |
| 45789     4567      456789    | 12        3         12        | 456789    456789    46789     |
| 12347     12347     123479    | 5         6         8         | 12347     12347     123479    |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 1234567   23456789  | 23467     58        23469     | 12345678  123456789 123456789 |
| 123456789 1234567   1234567   | 23467     58        23469     | 123456789 123456789 123456789 |
| 45789     23467     45789     | 23467     1         2346      | 3567      4567      6789      |
'-------------------------------.-------------------------------.-------------------------------'

20. r19c9 in Girandola Group (GG) cannot be [58] because of r8c5 in GG = (58) -> [548] blocked from h17(3)r159c9
20a. -> h17(3) = {179/269/278/467}(no 5) = [2/7..]
20b. no 3 in r1c8

21. 15(3)r6c9: {267} blocked by h17(3)r159c9 (step 20a)
21a. 15(3) = {159/258/348/357/456} = [5/8 in n9..]

22. 13(2)n9: [58] blocked by 15(3)r6c9 (step 21a)
22a. 13(2) = [49]/{67}(no 5,8) = [4/7..]

23. {47} blocked from both 11(2) cages in r9 by 13(2)n9 (step 22a)
23a. both 11(2)r9: no 4,7

24. 4 in GG only in r5c28: 4 locked for r5

25. Difference between the 8(2)n3 and 13(2)n9 = +5 -> [27] blocked from r19c9 -> {278} blocked from h17(3)r159c9 (Combo crossover clash CCC)
25a. h17(3) = {179/269}(no 8)
25b. must have 9: 9 locked for c9

26. r5c8 sees both r9c9 through GG and r5c9: 9 in c9 only in r59c9 -> no 9 in r5c8 (Common Peer Elimination CPE)

27. 9 in c8 only in r78c8: 9 locked for n9
27a. 14(3)n9 must have 9 = {149/239}(no 5,6,7,8)
27b. 13(2)n9 = {67} only: both locked for r9 and n9
27c. 9(2)r9c6 = [45] only

It's cracked now but just a few more of the most beneficial steps and missing some easier ones.....eg a hidden single 9 in the GG
28. h17(3)r159c9 = {179/269}; r1c1 = (12), r5c9 = 9, r9c9 = (67)
28a. no 2 in r1c8

29. Naked pair {67} in r19c8: both locked for c8
29a. no 2,3 in 9(2)n3

30. "45" on n9: 1 remaining outie r6c9 - 2 = 1 remaining innie r7c7 = [31/42]

31. 23(5)r6c7: must have 9 = {12479/13469}
31a. must have 4: 4 locked for r6 and n6
31b. r6c9 = 3 -> r7c7 = 1 (step 30)

32. 7 in n8 only in r78c4: 7 locked for 27(5)r6c2: no 7 in r6c23 nor r7c3

33. Hidden single 9 in r6: r6c3 = 9
33a. r9c34 = [83]
33b. r9c12 = [92]
33c. r6c2 = 1
33d. no 6 in r1c1

34. "45" on n7: 1 remaining outie r6c1 + 2 = 1 remaining innie r7c3 = [24]

On from there.

3x3::k:768:768:3585:3585:1794:5379:5379:3332:3332:4103:2821:3585:6921:1794:7946:5379:774:4104:4103:2821:6921:6921:1794:7946:7946:774:4104:4103:6921:6921:10251:10251:10251:7946:7946:4104:5132:5132:5132:5132:10251:4877:4877:4877:4877:3598:7698:7698:10251:10251:10251:4883:4883:3087:3598:4368:7698:7698:4116:4883:4883:4113:3087:3598:4368:4368:7698:4116:4883:4113:4113:3087:1814:1814:2327:2327:4116:2072:2072:4117:4117:

The nine coloured cells form a Girandola group, in which numbers cannot be repeated.

Prelims

a) R1C12 = {12}
b) R1C89 = {49/58/67}, no 1,2,3
c) R23C2 = {29/38/47/56}, no 1
d) R23C8 = {12}
e) R9C12 = {16/25/34}, no 7,8,9
f) R9C34 = {18/27/36/45}, no 9
g) R9C67 = {17/26/35}, no 4,8,9
h) R9C89 = {79}
i) 7(3) cage at R1C5 = {124}
j) 21(3) cage at R1C6 = {489/579/678}, no 1,2,3

Steps resulting from Prelims
1a. Naked pair {12} in R1C12, locked for R1 and N1, clean-up: no 9 in R23C2
1b. R1C5 = 4, R23C5 = {12}, locked for C5 and N2, clean-up: no 9 in R1C89
1c. Naked pair {12} in R23C8, locked for C8 and N3
1d. Naked pair {79} in R9C89, locked for R9, clean-up: no 2 in R9C34, no 1 in R9C67
1e. Naked pair {12} in R1C1 + R2C5, locked for Girandola group, no 1,2 in R5C2 + R9C1, clean-up: no 5,6 in R9C2

2. 45 rule on R5 1 innie R5C5 = 6, placed for Girandola group, clean-up: no 7 in R1C8, no 1 in R9C2

3. 45 rule on C5 2 remaining innies R46C5 = 16 = {79}, locked for C5 and N5
3a. Naked triple {358} in 16(3) cage at R7C5, locked for N8, clean-up: no 1,4,6 in R9C3, no 3,5 in R9C7
3b. Naked pair {26} in R9C67, locked for R9, clean-up: no 5 in R9C1, no 3 in R9C3
3c. Naked pair {34} in R9C12, locked for R9 and N7 -> R9C4 = 1, R9C3 = 8, R9C5 = 5

4. 45 rule on C1234 2 innies R46C4 = 12 = {48}, locked for C4 and N5

5. 45 rule on N5 2 innies R5C46 = 5 = {23}, locked for R5 and N5
5a. Naked pair {15} in R46C6, locked for C6

6. 45 rule on C1 3 innies R159C1 = 15 = {249} (only remaining combination) -> R5C1 = 9, R1C1 = 2, placed for Girandola group, R1C2 = 1, R23C5 = [12], R23C8 = [21], R9C1 = 4, placed for Girandola group, R9C2 = 3, clean-up: no 8 in R23C2

7. R8C5 = 3 (hidden single in Girandola group), R7C5 = 8

8. R9C9 = 9 (hidden single in Girandola group), R9C8 = 7
8a. 45 rule on C9 2 remaining innies R15C9 = 8 = {17} (only remaining combination) -> R1C9 = 7, placed for Girandola group, R1C8 = 6, R5C9 = 1

9. 21(3) cage at R1C6 = {489} (only remaining combination) -> R2C7 = 4, R1C67 = {89}, locked for R1, clean-up: no 7 in R3C2

10. R1C34 = {35} -> R2C3 = 6 (cage sum), clean-up: no 5 in R23C2
10a. R23C2 = [74]

11. 45 rule on R1234 3 innies R4C456 = 18 = {189/459} -> R4C5 = 9, R6C5 = 7

12. 9 in R6 only in R6C78, locked for 19(5) cage at R6C7, no 9 in R78C6
12a. 19(5) cage contains 9 = {12349} (only remaining combination) -> R7C7 = 1
12b. Naked pair {24} in R78C6, locked for C6, N8 and 19(5) cage -> R9C67 = [62]
12c. Naked pair {39} in R6C78, locked for R6 and N6

13. R5C46 = [23]
13a. Naked pair {58} in R5C28, locked for R5 -> R5C7 = 7, R5C8 = 8 (cage sum), R5C23 = [54]

14. R6C8 = 9 (hidden single in C8), R6C7 = 3
14a. R7C8 = 3 (hidden single in C8), R8C78 = 13 = [85], R1C67 = [89]

15. R23C6 = [97], R3C7 = 5, R4C78 = [64]
15a. R4C4 = 8, R4C6 = 1 (step 11)

16. R4C2 = 2, R78C2 = {69}, locked for C2 and N7, R8C3 = 2 (cage sum)

and the rest is naked singles.