Ruudiculous tag Killer - UTA

[Nasenbaer]

Here are two more minor steps:

59. According to Step 16 R8C679 = 14 = {167}/{257}/{356}
Concentrating on the 7:
If R8C679 = {167} -> R8C9 = 1
If R8C679 = {257} -> R8C7 = 7 -> 7 can be eliminated from R8C9, not possible
60. Possible combinations for 17(4) in N89: {1367}/{1457}/{2357}/{2456}
Concentrating on the 6:
If 17(4) = {1367} -> R7C5 = 1
If 17(4) = {2456} -> R8C7 = 6 -> 6 can be eliminated from R7C5, not possible

Do you think that it is now solved? I don't see it yet.
From your smilie I figur that R9C4 is a keyposition for you, so I have these two assumptions:
a. If R9C4 = 9 -> R9C3 = 3, 10(2) in R9 = {28}, 23(4) in N89 = {4568} with the 8 in R8C5 and the 4 in R9C7, 17(3) in N9 = {179} with the 9 in R8C8
b. If R9C4 = 7 -> R9C3 = 5 -> R456C4 = {149} -> R6C3 = {27}

Then there would be some minor eliminations, but nothing that "jumps in the eye" and would invalidate one of the two choices.

Or did I miss something obvious?

Peter

[sudokuEd]

Or did I miss something..?

Yeah.

61. 8 is locked in the 23(4) cage in N89.
-Cannot be {1589} as r9c7 has none of these.
-Cannot be {2678} as the {267} must be in r9 which means {39} in 12(2) cage in r9 and {19} in 10(2) cage in r9 - but both need 9's
-Cannot be {3578} as the {357} must be in r9. But that clashes with 12(2) cage in r9.

62. Only combinations left are 8{249/456} -> r9c7 can only be 4 -> no 1, 3 or 7 in r9c56.
[edit: eliminations added].

[ps A very big thankyou to Andrew for making many suggestions to improve the accuracy and clarity of my steps]

The rest of the puzzle unravels from there!

[sudokuEd]

Here is the condensed walk-through V2 for UTA2

Preliminary eliminations for 2 cell cages
R2C67 = 7 -> no 7, 8 or 9
R2C89 = 9 -> no 9
R3C89 = {14/23}
R7C12 = {69/87}
R7C34 = 9 -> no 9
R8C12 = {14/23}
R8C34 = 9 -> no 9
R9C12 = 10 -> no 5
R9C34 = 12 -> no 1,2 or 6

1. "45" on R12 -> R2C1 = 7 -> no 2 in R2C89, no 3 in R9C2, R7C12 = {69/[87]}

2. 22(3) in R3 = {589/679} -> 9 locked in R3, nowhere else

3. R34C1 = 13 = [49]/{58}

4. "45" on R123 -> 2 outies = 12 -> R4C12 = [57/84/93]

5. "45" on R9 -> 2 outies = 17 -> R8C58 = {89} -> 8 and 9 locked in R8 -> no 1 in R8C34

6. since R8C58 = {89}-> 8 and 9 eliminated from R9C7 (same cage as R8C5) and R5C5 (linked through D\)

7. 17(3) cage in N9 must have 8 or 9 but cannot have both since 8 + 9 = 17 ->no 8 or 9 in R9C89

8. this step moved to 10a

9. this step moved to 10b

10. "45" on R89 -> 3 innies = 14 -> R8C679 = {167}/{257}/{356} (cannot be {347} because that would clash with the 5(2) cage in R8C12) -> no 4

10a. "45" on N78 -> R89C7 = 10 ->{37/[64]}

10b. R9C7 = {347} -> 10(2) cage in R9C12 cannot be [37] because{347} in R9C127 would clash with the 12(2) cage in R9 -> no 3 or 7 in R9C12

11. In N9, the only other place (apart from R8C8) for [8/9] must be in R7C789. 15(2) cage in R7C12 also must have [8/9] -> Killer pair on 8/9 in r7 -> no 8/9 elsewhere R7 -> no 1 in R7C34

12. 5 in N7 locked in C3 -> no 5 elsewhere in C3

13. "45" on N7 -> 3 innies = 15 [hidden (h)15(3) cage] and must have 5 -> other 2 cells = 10
-Cannot be {19} since no 1 in R789C3
-Cannot be {28} as that requires 15(2) cage = {69} but this leaves no 2, 6 or 9 for 10(2) cage in N7
-> h15(3) cage in N7 = 5{37/46} -> no 2, 8 or 9 -> no 7 in R78C4, no 3 or 4 in R9C4

14. h15(3) in N7 = [6/7...], 15(2) cage in N7 = {69/[87]} = [6/7...] -> Killer pair on 6 and 7 -> not elsewhere in N7 -> 10(2) cage now {19/28}

15."45" on N3 -> 1 outie + 11 = 2 innies -> min R23C7 = 1 + 11 = 12
-Max. R3C7 = 9 -> min. R2C7 = 3 -> no 1 or 2 in R2C7, no 5 or 6 in R2C6
-Max R23C7 = {69} = 15 -> Max R1C6 = 4

16. 7(2) cage in N23 cannot have [43] since that would require 9(2) cage in N3 = {18} but [3{18}] in R2C789 would leave no 3 or 1 for 5(2) cage in N3 -> no 3 in R2C7 -> no 4 in R2C6

17. "45" on N3 -> 2 outies + 4 = 1 innie. R12C6min = {12} = 3 -> min R3C7 = 7

18. "45" on N7 -> R789C4 = 15

19. "45" on N1234 -> R456C4 = 14

20. "45" on C4 -> R123C4 = 16 = h16(3) cage

21. "45" on C1234 -> 2 innies = 9 -> no 9 in R1C34 and no 2 or 4 in R1C4

22. 9 in N1 now locked in 27(5) cage -> no 9 in R2C4

23. "45" on C1234 -> 2 outies = 11 -> no 1 in R12C5 and no 4 in R1C5

24. 22(3) cage in R3 = {589/679} = [5/6...] with the 5 or 6 locked in N2 -> no {56} combination in R12C5 since = 11 (step 23) -> no 5 or 6

25. The only other place for [5/6] in N2 is in R123C4 -> h16(3) cage = {268/358/367/457} -> no 1 in R123C4, no 8 in R1C3

26. 1 locked in R12C6 for N2 -> 1 locked for C6 -> 1 in N8 locked in C5 and 1 locked in C4 for N5

27. we know that 5 is locked in R789C3 -> [4/7] must be in R789C4 (since R789C34 are linked through 2 9(2) cages or the 12(2) cage -> h16(3) cage in N2 cannot be {457} (since 4/7 must be in R789C4)-> h16(3) cage in N2 = {268/358/367} = [3/8,5/6...] -> no 4 in R123C4

28. R789C4 = 15 and must contain a 4 or 7 = {249/267/357} ({348/456} are blocked because a 3/8 or 5/6 are needed for R123C4- step 27) -> no 8 in R789C4. Each combination needs a 7 or 9 which are only available in R9C4 -> R9C4 = {79} -> R9C34 = [39/57]

29. 8 in N8 now locked in 23(4) cage in N89
-Cannot be {1589} as R9C7 has none of these
-Cannot be {2678} as the {267} must be in R9 which means both the 12(2) and 10(2) cages in R9 need 9's!
-Cannot be {3578} as the {357} must be in R9. But that clashes with 12(2) cage in R9

30. Only combinations left are 8{249/456} -> only candidate available in R9C7 is 4 -> R9C7 = 4, R89C7 = 10 -> R8C7 = 6, R2C67 = [25], R1C6 = 1(hidden single N2), R3C7 = 7 (step 15), no other 7s on D/ , no 1, 3 or 7 in R9C56

31. R3C56 = 15 = {69} -> 5 in N2 locked in C4 in hidden 16(3) cage = {358} -> r12c5 = [74] -> R1C34 = 9 = [63], R23C4 = [85], no 1 in R2C89, h15(3) cage in N8 = {249/267} = 2{49/67}, 2 cannot be in R7C4 since no 7 available in R7C3 -> R8C4 = 2 (hidden single N8), R8C3 = 7, R7C12 = {69}, R9C12 = {28}, R8C12 = {14}, R7C4 = 4, R7C3 = 5, R9C34 = [39], 17(4) cage in N89 now {1367} only ->R78C6 = [73], R7C5 = 1, R8C58 = [89], no other 9 on D\, R8C9 = 5

32. 2 in N5 locked in 14(3) cage = {239}, R456C6 = {458}, R3C56 = [69], R9C56 = [56]

33."45" on N9 -> 3 outies = 20 -> no 1 or 2 in R56C8 or R6C9, max. R56C8 = {78} = 15 -> min. R7C78 = 8 so can only be {28/38} = 12/13 -> 8 locked in R7C78 -> no 8 in R7C9 or in R56C8

34. R67C9 = 10 = [73/82]

35. 9(2) cage in N3 = {36}, R3C89 = {14}, R1C789 = {289}
the rest are singles, (remembering to use the diagonals for elimination)

[edited 24Oct: condensed walkthrough V2. Since there have been 606 views for this thread, probably only you and me will read this Andrew - so great job with this final walkthrough. Your suggestions were all spot on. We're slowly getting better at this! I also like the double spacing - works great in notepad, don't get lost nearly as much. So UTA is finally finished. Now - time to work on that nasty X-treme ]

[rcbroughton]

After a few late nights staring at the original UTA I have tweaked my solver to take this one through to a logical conclusion.

Interestingly, I could get it to a point where I could see the next step I wanted to take. I tweaked my solver in another unrelated area and hey presto the blocker went away.

Anyway, I hope this provides some consolation that at least the UTA1 is solvable through logic.

Pastes below is more or less raw output from the solver. I've deleted a couple of redundant hidden cage disoveries and moved a couple of hidden cage discoveries to the step where they are used.

Just for completeness, I've left in all the single value exliminations to the bitter end.

Also - before I get any comment - I don't differentiate {xy} from [xy] in this listing. That's for another day.

Rgds
Richard


************************
*** Finished Initial Population

1. Must use 9 in cage 22(3) at r3c5
-> Removed candidate 9 from r3c1 r3c2 r3c3 r3c4

2. 45 rule on row 3. Included cells r3c1 minus excluded cells r4c2 equals 1
-> Min of excluded cells is 2. Set min candidate in r4c2
-> Max of excluded cells is 7. Set max candidate in r4c2

3. 45 rule on row 3. Included cells r3c1 r3c2 r3c3 r3c4 equal 18
-> Cage 22(3) at r3c5 doesn't allow permutations with {68}, {56}, {57}, {78}
-> Only combinations {1458} {2358} {1467} {2367} allowed
-> Removed candidates 37 from r3c1

4. Only combinations {389} {569} {578} {479} allowed in cage 20(3) at r2c1
-> Removed candidate 4 from r2c1
-> Removed candidate 4 from r4c1

5. 45 rule on row 3. Included cells r3c1 minus excluded cells r4c2 equals 1
-> Min of excluded cells is 3. Set min candidate in r4c2

6. 45 rule on row 3. Included cells r3c1 minus excluded cells r4c2 equals 1
-> Only combinations {34} {45} {56} {78} allowed
-> Removed candidate 6 from r4c2

7. 45 rule on row 9. Excluded cells r8c5 r8c8 equal 17
-> Only combination {89} allowed
-> Removed candidates 1234567 from r8c5
-> Removed candidates 1234567 from r8c8

8. Only combinations {278} {368} {458} {179} {269} {359} allowed in cage 17(3) at r8c8
-> Removed candidates 89 from r9c8
-> Removed candidates 89 from r9c9

9. Naked pair 89 found in row 8 at r8c5 r8c8
-> Removed value 8 from r5c5 r8c3 r8c4 r8c6 r8c7 r8c9 r9c7
-> Removed value 9 from r5c5 r8c6 r8c7 r8c9 r9c7
-> Removed combination {18} from cage 9(2) at r8c3
-> Removed candidate 1 from r8c3
-> Removed candidate 1 from r8c4

10. Value 4 locked in row 8 of combined cages 9(2) at r8c3 & 5(2) at r8c1
-> Removed 4 from r8c6 r8c7 r8c9

13. 45 rule on N3. Included cells r2c7 r3c7 minus excluded cells r1c6 equals 11
-> Min of included cells is 12. Set min candidate in r2c7 r3c7
-> Max of excluded cells is 4. Set max candidate in r1c6

14. Only combinations {16} {25} {34} allowed in cage 7(2) at r2c6
-> Removed candidates 56 from r2c6

15. 45 rule on N3. Included cells r2c7 r3c7 minus excluded cells r1c6 equals 11
-> Combined cages 5(2) at r3c8 & 9(2) at r2c8 doesn't allow permutations in r2c7 r3c7 with {48}
-> Only combinations {139} {469} {157} {249} {258} {267} {359} {368} allowed
-> Removed candidate 6 from r3c7

16. 45 rule on N3
-> Found a hidden cage 31(5) at r1c7 r1c8 r1c9 r2c7 r3c7

17. 45 rule on N3
-> Found a hidden cage 18(4) at r1c6 r2c6 r3c5 r3c6

18. 45 rule on N7
-> Found a hidden cage 15(3) at r7c4 r8c4 r9c4

19. 45 rule on rows 1 to 2 found single cell at r2c1 value 7
-> Removed combinations {389} {569} from cage 20(3) at r2c1
-> Removed candidate 6 from r3c1
-> Removed candidates 36 from r4c1

20. From value 7 found at r2c1
-> Removed 7 from r2c234589 r145679c1 r1c2 r1c3 r3c2 r3c3

21. Only combinations {18} {36} {45} allowed in cage 9(2) at r2c8
-> Removed candidate 2 from r2c8
-> Removed candidate 2 from r2c9

22. Only combinations {69} {78} allowed in cage 15(2) at r7c1
-> Removed candidate 8 from r7c2

23. 45 rule on row 1
-> Found a hidden cage 22(4) at r2c2 r2c3 r2c4 r2c5

24. 45 rule on row 2
-> Found a hidden cage 29(5) at r2c2 r2c3 r2c4 r2c5 r2c1

25. 45 rule on row 3. Included cells r3c1 minus excluded cells r4c2 equals 1
-> Only combinations {34} {45} {78} allowed
-> Removed candidate 5 from r4c2

26. 45 rule on row 3. Included cells r3c1 r3c2 r3c3 r3c4 equal 18
-> Cage 22(3) at r3c5 doesn't allow permutations with {57}, {68}
-> Only combinations {1458} {1467} {2358} allowed
-> Removed candidate 6 from r3c4

27. 45 rule on N3. Included cells r2c7 r3c7 minus excluded cells r1c6 equals 11
-> Combined cages 5(2) at r3c8 & 9(2) at r2c8 doesn't allow permutations in r2c7 r3c7 with {3}, {48}
-> Only combinations {469} {368} {157} {249} {258} {267} {359} allowed
-> Removed candidate 3 from r2c7

28. Only combinations {16} {25} {34} allowed in cage 7(2) at r2c6
-> Removed candidate 4 from r2c6

29. 45 rule on N3. Included cells r1c7 r1c8 r1c9 r2c7 r3c7 equal 31
-> Cage 9(2) at r2c8 doesn't allow permutations with {8365}, {834}
-> Only combinations {16789} {25789} {45679} allowed
-> Removed candidate 3 from r1c7
-> Removed candidate 3 from r1c8
-> Removed candidate 3 from r1c9

30. 45 rule on rows 7 to 8. Included cells r7c7 r7c8 r8c5 r8c8 minus excluded cells r6c9 equals 20
-> Min of excluded cells is 3. Set min candidate in r6c9

34. 45 rule on N7, N8. Excluded cells r8c7 r9c7 equal 10
-> Only combinations {37} {46} allowed
-> Removed candidates 125 from r8c7
-> Removed candidates 1256 from r9c7
-> Found a hidden cage 10(2) at r8c7 r9c7

35. 45 rule on row 9. Included cells r9c5 r9c6 r9c7 r9c8 r9c9 equal 23
-> Cage h10(2) at r8c7 doesn't allow permutations in r9c8 r9c9 with {36}
-> Only combinations {14567} {12479} {23459} {23567} allowed
-> Removed candidates 48 from r9c5
-> Removed candidates 48 from r9c6

37. 45 rule on N7, N8, N9. Excluded cells r5c8 r6c8 r6c9 equal 20
-> Only combinations {389} {479} {569} {578} allowed
-> Removed candidates 12 from r5c8
-> Removed candidates 12 from r6c8
-> Found a hidden cage 20(3) at r5c8 r6c8 r6c9

38. 45 rule on rows 7 to 8. Included cells r8c5 r8c8 minus excluded cells r5c8 r6c8 r6c9 equals -3
-> Only combinations {38899} {47899} {56899} {57889} with r8c5 {89}, r8c8 {98} allowed
-> Removed candidate 3 from r6c9

39. Found an exclusive pair {8/9} at r8c8 only other place in that nonet is in row 7
-> Pair is restricted in cells of cage 15(2) at r7c1
-> Removed candidate 8 from r7c3 r7c4 r7c5 r7c6
-> Removed candidate 9 from r7c5 r7c6

40. Only combinations {27} {36} {45} allowed in cage 9(2) at r7c3
-> Removed candidate 1 from r7c3
-> Removed candidate 1 from r7c4

41. Only combinations {249} {258} {267} {348} {357} {456} allowed in cage h15(3) at r7c4
-> Removed candidate 1 from r9c4

42. 45 rule on N7, N8. Included cells r7c5 r7c6 r8c6 r8c5 r9c5 r9c6 equal 30
-> Cage 15(2) at r7c1 doesn't allow permutations in r7c5 r7c6 with {67}
-> Combined cages 9(2) at r7c3 & 15(2) at r7c1 doesn't allow permutations in r7c5 r7c6 with {46}, {47}, {56}, {57}
-> Cage h15(3) at r7c4 doesn't allow permutations with {249573}, {248673}
-> Only combinations {135678} {123789} {134679} {125679} with r8c5 {89} allowed
-> Removed candidate 2 from r8c6
-> Found a hidden cage 30(6) at r7c5 r7c6 r8c6 r8c5 r9c5 r9c6

43. 45 rule on N7. Excluded cells r7c4 r8c4 r9c4 equal 15
-> Cage h30(6) at r7c5 doesn't allow permutations with {7}
-> Only combinations {249} {258} {456} {348} allowed
-> Removed candidate 7 from r7c4
-> Removed candidate 7 from r8c4
-> Removed candidates 237 from r9c4

44. Only combinations {36} {45} {27} allowed in cage 9(2) at r7c3
-> Removed candidate 2 from r7c3

45. Only combinations {36} {45} {72} allowed in cage 9(2) at r8c3
-> Removed candidate 2 from r8c3

46. 45 rule on N7. Included cells r7c3 r8c3 minus excluded cells r9c4 equals 3
-> Cage 5(2) at r8c1 doesn't allow permutations in r7c3 r8c3 with {34}
-> Only combinations {579} {355} {366} {478} {456} {568} allowed
-> Removed candidate 4 from r9c4

47. 45 rule on N1, N2, N3, N4. Excluded cells r4c4 r6c4 equal 7
-> Only combinations {16} {25} {34} allowed
-> Removed candidates 789 from r4c4
-> Removed candidates 789 from r6c4
-> Found a hidden cage 7(2) at r4c4 r6c4

48. 45 rule on N7. Excluded cells r7c4 r8c4 r9c4 equal 15
-> Cage h7(2) at r4c4 doesn't allow permutations with {654}
-> Only combinations {249} {258} {348} allowed
-> Removed candidate 6 from r7c4
-> Removed candidate 6 from r8c4
-> Removed candidates 56 from r9c4

49. Only combinations {45} {63} {27} allowed in cage 9(2) at r7c3
-> Removed candidate 3 from r7c3

50. Only combinations {45} {63} {72} allowed in cage 9(2) at r8c3
-> Removed candidate 3 from r8c3

51. Naked pair 89 found in N8 at r8c5 r9c4
-> Removed value 9 from r9c5 r9c6
-> Removed combination {2489} from cage 23(4) at r8c5

52. 45 rule on N7. Included cells r7c3 r8c3 r9c1 r9c2 r9c3 equal 25
-> Cage 15(2) at r7c1 doesn't allow permutations with {79}
-> Only combinations {14578} {23578} {14569} {23569} allowed
-> Removed candidate 4 from r7c3
-> Removed candidate 4 from r8c3
-> Removed candidates 56 from r9c1
-> Removed candidates 567 from r9c2
-> Removed candidates 567 from r9c3
-> Found a hidden cage 25(5) at r7c3 r8c3 r9c1 r9c2 r9c3

53. Only combinations {45} {36} {27} allowed in cage 9(2) at r7c3
-> Removed candidate 5 from r7c4

54. Only combinations {45} {36} {27} allowed in cage 9(2) at r8c3
-> Removed candidate 5 from r8c4

55. Value 5 locked in column 3 of N7
-> Removed 5 from r1c3 r2c3 r3c3 r4c3 r5c3 r6c3

56. Value 4 locked in column 4 of cage h15(3) at r7c4
-> Removed 4 from r1c4 r2c4 r3c4 r4c4 r5c4 r6c4

57. Only combinations {16} {25} allowed in cage h7(2) at r4c4
-> Removed candidate 3 from r4c4
-> Removed candidate 3 from r6c4

58. Value 4 locked for column 4 in N8
-> Removed 4 from r7c5 r7c6

59. Must use 37 in cage 17(4) at r7c5
-> Removed candidate 3 from r8c4

60. Only combinations {45} {27} allowed in cage 9(2) at r8c3
-> Removed candidate 6 from r8c3

61. Value 6 locked in row 7 of N7
-> Removed 6 from r7c5 r7c6 r7c7 r7c8 r7c9

62. Value 2 locked in row 8 of combined cages 9(2) at r8c3 & 5(2) at r8c1
-> Removed 2 from r8c9

63. 45 rule on row 1. Excluded cells r2c2 r2c3 r2c4 r2c5 equal 22
-> Cage 7(2) at r2c6 doesn't allow permutations with {653}
-> Only combinations {1489} {2389} {2569} {3469} allowed
-> Removed candidate 5 from r2c5

64. 45 rule on row 7. Included cells r7c7 r7c8 r7c9 r7c5 r7c6 equal 21
-> Cage 9(2) at r7c3 doesn't allow permutations with {45327}
-> Cage h15(3) at r7c4 doesn't allow permutations in r7c5 r7c6 with {23}
-> Only combinations {12459} {12378} {13458} allowed
-> Removed candidate 9 from r7c9
-> Found a hidden cage 21(5) at r7c7 r7c8 r7c9 r7c5 r7c6

65. 45 rule on row 8. Included cells r8c9 r8c6 r8c7 r8c5 r8c8 equal 31
-> Cage h15(3) at r7c4 doesn't allow permutations in r8c6 r8c5 with {39}
-> Only combinations {16789} {35689} with r8c5 {89}, r8c8 {98} allowed
-> Removed candidate 3 from r8c9

66. Only combinations {456} {357} {267} {168} {258} {159} allowed in cage 15(3) at r6c9
-> Removed candidate 7 from r7c9

68. 45 rule on N8. Included cells r7c4 r8c4 r9c4 minus excluded cells r8c7 r9c7 equals 5
-> Cage 5(2) at r8c1 doesn't allow permutations in r8c7 r8c4 with {34}
-> Cage h30(6) at r7c5 doesn't allow permutations in r7c4 r8c4 r9c4 with {28}, {23}, {39}
-> Cage h21(5) at r7c7 doesn't allow permutations in r7c4 r8c7 with {34}, {47}
-> Only combinations {24469} {33478} {23479} {34468} with r8c7 {67}, r8c4 {24}, r9c7 {43}, r9c4 {98} allowed
-> Removed candidate 3 from r8c7
-> Removed candidate 7 from r9c7

69. Only combinations {4568} {3578} {3479} {3569} with r8c5 {89}, r9c7 {43} allowed in cage 23(4) at r8c5
-> Removed candidates 12 from r9c5
-> Removed candidates 12 from r9c6

11. 45 rule on row 8
-> Found a hidden cage 31(5) at r8c9 r8c6 r8c7 r8c5 r8c8

70. Only combinations {16789} {35689} with r8c7 {76}, r8c5 {89}, r8c8 {98} allowed in cage h31(5) at r8c9
-> Removed candidate 5 from r8c6

12. 45 rule on row 9
-> Found a hidden cage 23(5) at r9c5 r9c6 r9c7 r9c8 r9c9

71. Only combinations {23567} {14567} with r9c7 {34} allowed in cage h23(5) at r9c5
-> Removed candidate 3 from r9c5
-> Removed candidate 3 from r9c6
-> Removed candidates 34 from r9c8
-> Removed candidates 34 from r9c9

72. Only combinations {278} {179} {269} allowed in cage 17(3) at r8c8
-> Removed candidate 5 from r9c8
-> Removed candidate 5 from r9c9

73. Must use 37 in cage 17(4) at r7c5
-> Removed candidate 3 from r7c4

74. Only combinations {45} {27} allowed in cage 9(2) at r7c3
-> Removed candidate 6 from r7c3

75. Only combinations {249} with 9 locked in r9c4 allowed in cage h15(3) at r7c4
-> Set candidate 9 in r9c4

76. From value 9 found at r9c4
-> Removed 9 from r9c123 r125c4 r8c5->8

77. From value 8 found at r8c5
-> Removed 8 from r8c8 r8c8->9 r12346c5

78. From value 9 found at r8c8
-> Removed 9 from r14567c8 r7c7 r1c1 r2c2 r6c6

79. Only combinations {3578} {4568} {2678} allowed in cage 23(4) at r5c8
-> Removed candidate 1 from r7c7
-> Removed candidate 1 from r7c8

80. Only combinations {389} {479} {569} {578} allowed in cage h20(3) at r5c8
-> Removed candidates 46 from r6c9

81. Only combinations {357} {456} {267} {168} {258} {159} allowed in cage 15(3) at r6c9
-> Removed candidate 8 from r7c9

82. Only combinations {135678} with 8 locked in r8c5 allowed in cage h30(6) at r7c5
-> Removed candidate 2 from r7c5
-> Removed candidate 2 from r7c6

83. Only combinations {1367} with r8c7 {76} allowed in cage 17(4) at r7c5
-> Removed candidate 5 from r7c5
-> Removed candidate 5 from r7c6

67. 45 rule on N5
-> Found a hidden cage 20(4) at r4c4 r4c6 r6c4 r6c6

84. Only combinations {1568} {1289} {1469} {2468} {2567} {2459} {2369} allowed in cage h20(4) at r4c4
-> Removed candidate 3 from r4c6

85. Naked pair 24 found in cage h15(3) at r7c4 at r7c4 r8c4
-> Removed value 2 from r1c4 r2c4 r3c4 r4c4 r5c4 r6c4
-> Removed combination {2348} from cage 17(4) at r4c3

86. Only combination {16} allowed in cage h7(2) at r4c4
-> Removed candidate 5 from r4c4
-> Removed candidate 5 from r6c4

87. Only combinations {1568} {1469} with r4c4 {16}, r6c4 {61} allowed in cage h20(4) at r4c4
-> Removed candidates 12467 from r4c6
-> Removed candidates 12367 from r6c6

88. Naked pair 57 found in cage h25(5) at r7c3 at r7c3 r8c3
-> Removed value 7 from r4c3 r5c3 r6c3 r7c2
-> Removed combination {1457} from cage 17(4) at r4c3
-> Removed combination {23459} from cage 23(5) at r5c1
-> Removed combination {78} from cage 15(2) at r7c1
-> Removed candidate 8 from r7c1

89. Naked pair 16 found in cage h20(4) at r4c4 at r4c4 r6c4
-> Removed value 1 from r1c4 r2c4 r3c4 r5c4 r4c5 r5c5 r5c6 r6c5
-> Removed value 6 from r1c4 r2c4 r5c4 r4c5 r5c5 r5c6 r6c5
-> Removed combination {1469} from cage 20(4) at r1c3
-> Removed combinations {12589} {12679} {13489} {13579} {13678} {14569} {14578} {23569} {24568} {34567} from cage 25(5) at r4c5

90. Must use 9 in cage 27(5) at r1c1
-> Removed candidate 9 from r1c3

91. Must use 1367 in cage 17(4) at r7c5
-> Removed candidate 6 from r8c9

92. Only combinations {357} {258} {159} allowed in cage 15(3) at r6c9
-> Removed candidate 4 from r7c9

93. Must use 5 in cage 15(3) at r6c9
-> Removed candidate 5 from r1c9 r2c9 r4c9 r5c9

94. Only combinations {18} {36} {45} allowed in cage 9(2) at r2c8
-> Removed candidate 4 from r2c8

95. Value 8 locked for row 7 in cage 23(4) at r5c8
-> Removed 8 from r5c8 r6c8

96. Only combinations {479} {569} {578} allowed in cage h20(3) at r5c8
-> Removed candidate 3 from r5c8
-> Removed candidate 3 from r6c8
-> Removed candidates 57 from r6c9

97. Only combinations {4568} {3578} {2678} allowed in cage 23(4) at r5c8
-> Removed candidate 7 from r7c7
-> Removed candidate 7 from r7c8

98. Only combinations {258} {159} allowed in cage 15(3) at r6c9
-> Removed candidate 3 from r7c9
-> Removed candidate 7 from r8c9

99. Only combinations {16789} {35689} with r8c9 {15}, r8c7 {76}, 8 locked in r8c5, 9 locked in r8c8 allowed in cage h31(5) at r8c9
-> Removed candidate 1 from r8c6

36. 45 rule on N7, N8, N9
-> Found a hidden cage 18(4) at r7c7 r7c8 r7c9 r8c9

100. Only combinations {2358} {1458} with r8c9 {51} allowed in cage h18(4) at r7c7
-> Removed candidates 25 from r7c7
-> Removed candidates 25 from r7c8

101. Only combinations {4568} {3578} allowed in cage 23(4) at r5c8
-> Removed candidate 4 from r5c8
-> Removed candidate 4 from r6c8

102. Only combinations {12378} {13458} with r7c9 {25} allowed in cage h21(5) at r7c7
-> Removed candidate 1 from r7c9

103. Must use 58 in cage 23(4) at r5c8
-> Removed candidate 5 from r1c8 r2c8 r4c8 r4c7 r5c7 r6c7

104. Only combinations {18} {36} allowed in cage 9(2) at r2c8
-> Removed candidate 4 from r2c9

105. 45 rule on row 1. Excluded cells r2c2 r2c3 r2c4 r2c5 equal 22
-> Cage 7(2) at r2c6 doesn't allow permutations with {653}
-> Cage 9(2) at r2c8 doesn't allow permutations with {38}
-> Only combinations {1489} {2569} {3469} allowed
-> Removed candidates 358 from r2c2
-> Removed candidates 238 from r2c3
-> Removed candidate 3 from r2c5

106. Only combinations {13689} {14589} {34569} {23589} allowed in cage 27(5) at r1c1
-> Removed candidate 2 from r1c1
-> Removed candidate 2 from r1c2

107. 45 rule on row 7. Excluded cells r5c8 r6c8 r6c9 r8c9 r8c6 r8c7 equal 34
-> Cage 9(2) at r8c3 doesn't allow permutations in r8c9 r8c6 r8c7 with {57}
-> Cage 17(3) at r8c8 doesn't allow permutations in r8c9 r8c7 with {16}
-> Only combinations {355678} {156679} {355669} with r6c9 {89}, r8c9 {51}, r8c6 {36}, r8c7 {67} allowed
-> Removed candidate 7 from r8c6

108. 45 rule on column 1
-> Found a hidden cage 25(6) at r1c1 r5c1 r6c1 r7c1 r8c1 r9c1

109. 45 rule on N3. Included cells r1c7 r1c8 r1c9 r2c7 r3c7 equal 31
-> Cage 9(2) at r2c8 doesn't allow permutations with {16}
-> Cage h10(2) at r8c7 doesn't allow permutations in r1c7 r2c7 r3c7 with {47}, {67}
-> Only combinations {25789} {45679} with r2c7 {54}, r3c7 {79} allowed
-> Removed candidate 1 from r1c7
-> Removed candidate 1 from r1c8
-> Removed candidate 1 from r1c9
-> Removed candidate 6 from r2c7
-> Removed candidate 8 from r3c7

110. Only combinations {25} {34} allowed in cage 7(2) at r2c6
-> Removed candidate 1 from r2c6

111. Only combinations {589} {679} allowed in cage 22(3) at r3c5
-> Removed candidate 5 from r3c6

112. Value 1 locked for column 7 in N6
-> Removed 1 from r4c8 r4c9 r5c9

113. Only combinations {12569} {12578} {13568} {14567} {23459} {23567} {12389} {13478} {23468} {12479} {13469} allowed in cage 23(5) at r4c6
-> Removed candidate 8 from r4c7

114. 45 rule on N3. Included cells r2c7 r3c7 minus excluded cells r1c6 equals 11
-> Max of excluded cells is 3. Set max candidate in r1c6

115. Value 4 locked in column 5 of N2
-> Removed 4 from r4c5 r5c5 r6c5

116. Only combinations {23578} {23479} allowed in cage 25(5) at r4c5
-> Removed candidate 9 from r5c6

117. Value 4 locked for column 5 in cage 20(4) at r1c3
-> Removed 4 from r1c3

118. 45 rule on row 1. Included cells r1c1 r1c2 r1c3 r1c4 r1c5 equal 25
-> Cage 20(4) at r1c6 doesn't allow permutations with {28465}
-> Only combinations {14578} {12589} {13678} {13489} {34567} {23569} allowed
-> Removed candidates 25 from r1c5
-> Found a hidden cage 25(5) at r1c1 r1c2 r1c3 r1c4 r1c5

119. 45 rule on N2. Included cells r2c4 r1c6 r2c6 r3c4 minus excluded cells r1c3 r3c7 equals 3
-> Cage 9(2) at r2c8 doesn't allow permutations in r2c4 r2c6 r3c7 with {38}
-> Only combinations {122389} {123579} {125678} {235689} {235788} {126789} {237889} with r2c6 {23}, r3c7 {97} allowed
-> Removed candidate 1 from r1c3

120. 45 rule on N1. Included cells r1c3 r3c1 minus excluded cells r2c4 r3c4 r4c2 equals -6
-> Cage 22(3) at r3c5 doesn't allow permutations in r3c4 r3c1 with {57}, {78}
-> Cage 5(2) at r3c8 doesn't allow permutations in r3c4 r3c1 with {34}
-> Only combinations {23445} {34788} {33347} {56788} {33358} {34568} {34588} {44567} {45568} {23588} allowed
-> Removed candidate 3 from r3c4

124. 45 rule on N1, N4. Included cells r1c3 minus excluded cells r2c4 r3c4 r4c4 r6c4 equals -14
-> Only combinations {13367} {15668} {16788} with r4c4 {16}, r6c4 {61} allowed
-> Removed candidate 2 from r1c3

125. 45 rule on row 1. Excluded cells r2c2 r2c3 r2c4 r2c5 equal 22
-> Only combinations {1489} {2569} {3469} with 9 locked in r2c3 allowed
-> Set candidate 9 in r2c3
-> Removed candidate 9 from r2c5

126. From value 9 found at r2c3
-> Removed 9 from r456c3 r1c2

127. Only combinations {1268} {1367} {2456} {1358} {1349} with r4c4 {61} allowed in cage 17(4) at r4c3
-> Removed candidates 34 from r5c2

128. 45 rule on row 1. Included cells r1c1 r1c2 r1c3 r1c4 r1c5 equal 25
-> Only combinations {14578} {13678} {34567} with r1c4 {73} allowed
-> Removed candidates 58 from r1c4
-> Removed candidate 9 from r1c5

129. Value 9 locked in row 3 of N2
-> Removed 9 from r3c7->7

130. From value 7 found at r3c7
-> Removed 7 from r3c456 r14568c7 r8c7->6 r1c8 r1c9 r5c5 r7c3->5

131. From value 5 found at r7c3
-> Removed 5 from r7c9 r7c9->2 r8c3 r8c3->7 r4c6 r5c5

132. From value 2 found at r7c9
-> Removed 2 from r7c4 r7c4->4 r13459c9 r9c8

133. From value 4 found at r7c4
-> Removed 4 from r7c78 r8c4 r8c4->2

134. From value 2 found at r8c4
-> Removed 2 from r8c12

135. From value 6 found at r8c7
-> Removed 6 from r8c6 r8c6->3 r1456c7 r9c8 r9c9

136. From value 3 found at r8c6
-> Removed 3 from r8c12 r1257c6 r2c6->2 r7c5

137. From value 2 found at r2c6
-> Removed 2 from r2c25 r15c6 r1c6->1

138. From value 1 found at r1c6
-> Removed 1 from r1c125 r7c6 r7c6->7 r2c5

139. From value 7 found at r7c6
-> Removed 7 from r7c5 r7c5->1 r59c6 r9c5

140. Only combinations {3467} with r1c3 {36}, r1c4 {73}, r2c5 {64} allowed in cage 20(4) at r1c3
-> Removed candidate 8 from r1c3

141. Only combination {25} allowed in cage 7(2) at r2c6
-> Set candidate 5 in r2c7

142. From value 5 found at r2c7
-> Removed 5 from r2c4 r1c7

143. Only combinations {14} {23} allowed in cage 5(2) at r3c8
-> Removed candidate 3 from r3c8

144. Only combinations {12389} {13478} {23468} {12479} {13469} with r4c6 {89} allowed in cage 23(5) at r4c6
-> Removed candidate 9 from r4c7
-> Removed candidate 8 from r4c8

145. Only combinations {3578} with r5c8 {57}, r6c8 {75}, r7c7 {38}, r7c8 {83} allowed in cage 23(4) at r5c8
-> Removed candidate 6 from r5c8
-> Removed candidate 6 from r6c8

146. Only combinations {258} with 8 locked in r6c9, 2 locked in r7c9, 5 locked in r8c9 allowed in cage 15(3) at r6c9
-> Set candidate 8 in r6c9
-> Set candidate 5 in r8c9

147. From value 8 found at r6c9
-> Removed 8 from r6c12367 r1245c9 r5c7

148. Only combinations {36} {18} allowed in cage 9(2) at r2c8
-> Removed candidate 1 from r2c8

149. Only combinations {159} {249} allowed in cage 15(3) at r5c7
-> Removed candidates 34 from r5c7
-> Removed candidates 34 from r6c7

150. Only combinations {4568} with 8 locked in r8c5, r9c5 {56}, r9c6 {65}, 4 locked in r9c7 allowed in cage 23(4) at r8c5
-> Set candidate 4 in r9c7

151. From value 4 found at r9c7
-> Removed 4 from r9c123 r14c7

152. Only combinations {2389} with 9 locked in r9c4 allowed in cage 22(4) at r9c1
-> Removed candidate 1 from r9c1
-> Removed candidate 1 from r9c2
-> Removed candidate 1 from r9c3

153. Only combinations {34567} with r1c3 {63}, r1c4 {73} allowed in cage h25(5) at r1c1
-> Removed candidate 8 from r1c1
-> Removed candidate 8 from r1c2

154. Naked pair 69 found in cage 22(3) at r3c5 at r3c5 r3c6
-> Removed value 6 from r1c5 r2c5->4 r3c2 r3c3
-> Removed combination {2456} from cage 17(4) at r3c2

155. From value 4 found at r2c5
-> Removed 4 from r2c2 r1c5

156. Only combinations {3467} with 6 locked in r1c3, r1c4 {37}, r1c5 {73}, 4 locked in r2c5 allowed in cage 20(4) at r1c3
-> Set candidate 6 in r1c3

157. From value 6 found at r1c3
-> Removed 6 from r1c1289 r456c3 r2c2->1

158. From value 1 found at r2c2
-> Removed 1 from r2c9 r3568c2 r8c2->4 r3c3 r4c4->6 r9c9->7

159. From value 6 found at r4c4
-> Removed 6 from r4c89 r6c4 r6c4->1 r5c2

160. From value 1 found at r6c4
-> Removed 1 from r6c137 r5c1

161. From value 4 found at r8c2
-> Removed 4 from r8c1 r8c1->1 r1346c2 r1c9->9

162. From value 9 found at r1c9
-> Removed 9 from r1c7 r45c9 r4c6->8

163. From value 8 found at r4c6
-> Removed 8 from r4c13 r5c6 r5c4 r2c8 r9c1

164. From value 7 found at r9c9
-> Removed 7 from r9c8 r9c8->1 r45c9

165. From value 1 found at r9c8
-> Removed 1 from r3c8

166. Only combinations {14589} with 4 locked in r1c1, 5 locked in r1c2, 1 locked in r2c2, 9 locked in r2c3, 8 locked in r2c4 allowed in cage 27(5) at r1c1
-> Set candidate 4 in r1c1
-> Set candidate 5 in r1c2
-> Set candidate 8 in r2c4

167. From value 4 found at r1c1
-> Removed 4 from r1c8 r356c1 r3c3 r6c6->5

168. From value 5 found at r1c2
-> Removed 5 from r356c2 r3c1->8

169. From value 8 found at r2c4
-> Removed 8 from r3c4 r3c4->5

170. From value 8 found at r3c1
-> Removed 8 from r3c23 r5c1

171. From value 5 found at r3c4
-> Removed 5 from r5c4

172. From value 5 found at r6c6
-> Removed 5 from r6c158 r6c8->7 r59c6 r5c6->4 r9c6->6 r4c5

173. From value 4 found at r5c6
-> Removed 4 from r5c39

174. From value 7 found at r6c8
-> Removed 7 from r6c25 r45c8 r5c8->5

175. From value 5 found at r5c8
-> Removed 5 from r5c1

176. From value 6 found at r9c6
-> Removed 6 from r9c5 r9c5->5 r3c6 r3c6->9

177. From value 9 found at r3c6
-> Removed 9 from r3c5 r3c5->6

178. Only combinations {578} with 7 locked in r2c1, 8 locked in r3c1, 5 locked in r4c1 allowed in cage 20(3) at r2c1
-> Set candidate 5 in r4c1

179. Only combinations {2357} with r3c2 {23}, r3c3 {32}, 5 locked in r3c4, 7 locked in r4c2 allowed in cage 17(4) at r3c2
-> Set candidate 7 in r4c2

180. From value 7 found at r4c2
-> Removed 7 from r4c5 r5c2

181. Only combinations {23} {14} allowed in cage 5(2) at r3c8
-> Removed candidate 4 from r3c9

182. Only combinations {1268} with r4c3 {12}, 6 locked in r4c4, r5c2 {28} allowed in cage 17(4) at r4c3
-> Removed candidates 34 from r4c3
-> Removed candidate 9 from r5c2
-> Removed candidate 3 from r5c3

183. Only combinations {23479} with 7 locked in r5c4, r5c5 {32}, 4 locked in r5c6 allowed in cage 25(5) at r4c5
-> Set candidate 7 in r5c4

184. From value 7 found at r5c4
-> Removed 7 from r1c4 r1c4->3

185. From value 3 found at r1c4
-> Removed 3 from r1c5 r1c5->7

186. Only combinations {23468} with 8 locked in r4c6, r4c7 {23}, r4c9 {43}, 6 locked in r5c9 allowed in cage 23(5) at r4c6
-> Removed candidate 1 from r4c7
-> Set candidate 6 in r5c9

187. From value 6 found at r5c9
-> Removed 6 from r5c1 r2c9 r2c9->3

188. From value 3 found at r2c9
-> Removed 3 from r2c8 r2c8->6 r34c9 r3c9->1 r4c9->4

189. From value 4 found at r4c9
-> Removed 4 from r4c8

190. Only combination {14} allowed in cage 5(2) at r3c8
-> Set candidate 4 in r3c8

191. Only combinations {13469} with r5c1 {39}, 4 locked in r6c3, 1 locked in r6c4 allowed in cage 23(5) at r5c1
-> Removed candidate 2 from r5c1
-> Removed candidate 2 from r6c1
-> Removed candidate 2 from r6c2
-> Set candidate 4 in r6c3

192. Only combinations {159} with 1 locked in r5c7, 5 locked in r6c6, 9 locked in r6c7 allowed in cage 15(3) at r5c7
-> Set candidate 1 in r5c7
-> Set candidate 9 in r6c7

193. From value 1 found at r5c7
-> Removed 1 from r5c3

194. From value 9 found at r6c7
-> Removed 9 from r6c125

195. Only combinations {1268} with 1 locked in r4c3, 6 locked in r4c4, r5c2 {28}, r5c3 {82} allowed in cage 17(4) at r4c3
-> Set candidate 1 in r4c3

196. Only combinations {23479} with 9 locked in r4c5, 7 locked in r5c4, r5c5 {23}, 4 locked in r5c6, r6c5 {32} allowed in cage 25(5) at r4c5
-> Set candidate 9 in r4c5

197. Only combinations {13469} with 9 locked in r5c1, r6c1 {36}, r6c2 {63}, 4 locked in r6c3, 1 locked in r6c4 allowed in cage 23(5) at r5c1
-> Set candidate 9 in r5c1

198. From value 9 found at r5c1
-> Removed 9 from r7c1 r7c1->6

199. From value 6 found at r7c1
-> Removed 6 from r7c2 r7c2->9 r6c1 r6c1->3

200. From value 3 found at r6c1
-> Removed 3 from r6c25 r6c2->6 r6c5->2 r9c1 r9c1->2

201. From value 2 found at r6c5
-> Removed 2 from r5c5 r5c5->3

202. From value 3 found at r5c5
-> Removed 3 from r3c3->2 r7c7->8

203. From value 2 found at r3c3
-> Removed 2 from r3c2 r3c2->3 r59c3 r5c3->8

204. From value 3 found at r3c2
-> Removed 3 from r9c2

205. From value 8 found at r5c3
-> Removed 8 from r5c2 r5c2->2 r9c3 r9c3->3

206. From value 2 found at r5c2
-> Removed 2 from r9c2 r9c2->8

207. From value 8 found at r7c7
-> Removed 8 from r7c8 r7c8->3 r1c7 r1c7->2

208. From value 2 found at r1c7
-> Removed 2 from r1c8 r1c8->8 r4c7 r4c7->3

209. From value 3 found at r4c7
-> Removed 3 from r4c8 r4c8->2
****** FINISHED ******
Solved by logical deduction

[sudokuEd]

Finally worked out how rcbrougton's solver solved UTA original! Very interesting path taken too. Lots of innies and hidden cages that we never thought of - r7, r9, n9. Oh yeah - and did I mention combinations? Lots of combination conflicts from many different directions at once.

This walk-through is the sweetened-condensed version of rcbroughton's - lots of steps left out, changed the order of many - and lots of my own explanations included. The step numbers should correspond.

Oh yeah - and did I mention combination charts? Make sure you've got one that works Good luck - a very rough road ahead

Just a quick reminder, UTA is a diagonals puzzle: 1-9 cannot repeat on diagonals. [edit: colours changed to get better match with burgundy]

1. Must use 9 in cage 22(3) at r3c5
-> Removed 9 from r3c1234

19. 45 rule on r12 -> r2c1 = 7

19a. r34c1 = 13 = [49]/{58}
-> Removed candidate 369 from r3c1
-> Removed candidates 346 from r4c1

21. Only combinations {18/36/45} allowed in cage 9(2) at r2c8
-> Removed candidate 2 from r2c89

22. Only combinations {69/78} allowed in cage 15(2) at r7c1
-> Removed candidate 8 from r7c2

13. 45 rule on N3. Included cells r23c7 minus excluded cell r1c6 equals 11
-> Min of included cells is 12. Set min candidate in r2c7 (3)
-> min r3c7 = 7 - (can't have r23c7 = {66})

-> Max of excluded cells is 4. Set max candidate in r1c6

14. Only combinations {16/25/34} allowed in cage 7(2) at r2c6
-> Removed candidates 56 from r2c6

27. 3 locked in n3 in 9(2) or 5(2)

27a.if 9(2) = [1/4]->5(2) = {23};

27b.if 5(2) = {14} ->9(2) = {36})
-> Removed candidate 3 from r2c7, r1c789

28. Only combinations {16/25/34} allowed in cage 7(2) at r2c6
-> Removed candidate 4 from r2c6

7. 45 rule on row 9. Excluded cells r8c5 r8c8 equal 17
-> Only combination {89} allowed

8. Only combinations with 8 or 9 (not both) allowed in cage 17(3) at r8c8.
-> Removed candidates 89 from r9c89

9. Naked pair 89 found in row 8 at r8c58

9a.-> Removed value 8 from r5c5 (because both cells connected through D\)

9b.-> Removed value 8 from r5c5 r9c7 (because r9c7 is in the same cage as r8c5 and same n as r8c8)

9c.-> Removed value 8 from r5c5 r8c34 r8c679

9d.-> Removed value 9 from r5c5(as above) r9c7(as above) r8c6 r8c7 r8c9

9e.-> Removed combination {18} from cage 9(2) at r8c3

9f.-> Removed candidate 1 from r8c34

10. Value 4 locked in row 8 of combined cages 9(2) at r8c3 & 5(2) at r8c1

10a.ie 5(2) = {23} -> 9(2) = {45};
9(2) = [2/3] -> 5(2) = {14}
-> Removed 4 from r8c679

34. 45 rule on N7, N8. Excluded cells r89c7 equal 10
-> Only combinations {37/46} allowed
-> Removed candidates 125 from r8c7
-> Removed candidates 1256 from r9c7
-> Found a hidden cage 10(2) at r89c7

This is a tricky step - but absolutely critical. Get your combination tables ready!
35. 45 rule on row 9. Included cells r9c56789 equal 23 = h23(5) cage

35a.-> Cage h10(2) at r8c7 doesn't allow permutations in r9c89 with {36}
->17(3)n9 {368} combo eliminated

35b. h23(5)r9 must include {347} (r9c7)
-> {12569} excluded

35c. Possible combinations for h23(5)r9 must have a triple overlap of combination from r9c56:23(4) and then double overlap from r9c89:17(3), AND must agree with the {89} pair in r8 AND must agree with the h10(2)n9

ie. combinations h23(5)r9 = {r9c56}[r9c7]{r9c89}

-{12389} Blocked (must have 3 in r9c7 but no triple overlap of combination with r9c567:23(4))

-{12479} = {29}[4]{17} (7 in r9c7 blocked - no triple overlap of combination with r9c567:23(4))

-{12578} Blocked (only be {25}[7]{18} but no 8 in r9c89)

-{13469} Blocked (r9c7 = [3/4] but no triple overlap with r9c567:23(4))

-{13478} Blocked (only be {347} in r9c567: but no 8 left in r9c89)

-{13568} Blocked (only be {56}[3] in r9c567: but no 8 left in r9c89)

-{14567} = {56}[4]{17}/{16}[7]{45}

-{23459} = {29}[4]{35} (3 in r9c6 blocked: no triple overlap with r9c567:23(4))

-{23468} Blocked ({28}[4]{36} blocked - see step 35a; 3 in r9c6: no triple overlap with r9c567:23(4))

-{23567} = {57}[3]{26}/{35}[7]{26}
-({56}[3]{27} blocked since 7 must be in r8c7 in h10(2) -> 2 7's n9)
-({25}[7]{36} blocked since no {36} possible r9c89 - step 35a)
-({26}[7]{35} blocked since 3 must be in r8c7 in h10(2) -> 2 3's n9)

35d.In summary h23(5)r9 =
{12479} = [{29}4{17}]
{14567} = [{56}4{17}/{16}7{45}]
{23459} = [{29}4{35}]
{23567} = [{57}3{26}/{35}7{26}]

-> Removed candidates 48 from r9c56

35e. from step 35d. r8c5 + r9c56 (part of 23(4) that's in n8) = {289/568/169/578/358}

35f. from step 35d. the only combinations in 23(4)n89 = {2489/4568/1679/3578} = {1679/2489/3578/4568}

35g. from step 35d. 17(3)n9 = {179/458/359/269} = {179/269/359/458} = [8/9..]

39. r8c8 = [8/9]. Only other place for [8/9] in nonet 9 is in row 7

39a. 15(2) at r7c1 = {69/78} = [8/9..]

39b.->Killer pair {89}: locked for r7
-> Removed candidate 8 from r7c3456
-> Removed candidate 9 from r7c56

39c. ->17(4)n89 = {1367/1457/2357/2456}

40. Only combinations {27/36/45} allowed in cage 9(2) at r7c3
-> Removed candidate 1 from r7c34

18. 45 rule on N7
-> Found a hidden cage 15(3) at r789c4

41. Only combinations {249/258/267/348/357/456} allowed in cage h15(3) at r7c4
-> Removed candidate 1 from r9c4

43. from step 41. h15(3)n8 = {249/258/267/348/357/456}

43a. {267} blocked
-from step 39c.the only combination in 17(4)n89 possible is {1457} with {145} in n8. All other combinations are blocked since they have 2 candidates in common with {267}.

-But{267-145} in h15(3) + 3 cells from 17(4) in n8 is blocked by r8c5 + r9c56 (see step 35e.)

43b.{357} blocked
-the only available combination in 17(4)n89 (step 39c.) without a 5 is {1367},
-but they have both {37} in common -> blocked

43c.
-> Only combinations allowed in h15(3) = {249/258/348/456} (no 7)
-> Removed candidate 7 from r78c4
-> Removed candidates 237 from r9c4 (since is the only cell with an 8 or 9)

44. Only combinations {27/36/45} allowed in cage 9(2) at r7c3
-> Removed candidate 2 from r7c3

45. Only combinations {27/36/45} allowed in cage 9(2) at r8c3
-> Removed candidate 2 from r8c3

47. 45 rule on N1, N2, N3, N4. Excluded cells r46c4 equal 7
-> Only combinations {16/25/34} allowed
-> Removed candidates 789 from r46c4
-> Found a hidden cage 7(2) at r46c4

48. h15(3) in n8
-> Cage h7(2) at r4c4 doesn't allow permutations with {456}
-> Only combinations {249/258/348} allowed (no 6)
-> Removed candidate 6 from r78c4
-> Removed candidates 456 from r9c4 (only cell with 8/9)

49. Only combinations {45/63/27} allowed in cage 9(2) at r7c3
-> Removed candidate 3 from r7c3

50. Only combinations {27/45/63} allowed in cage 9(2) at r8c3
-> Removed candidate 3 from r8c3

51. Naked pair 89 found in N8 at r8c5 r9c4
-> Removed value 9 from r9c56
-> Removed combination {2489} from cage 23(4) at r8c5
-> removed 2 from r9c56

51a.from step 35d. h23(5)r9
-> Only combinations =
{14567} = [{56}4{17}/{16}7{45}]
{23567} = [{57}3{26}/{35}7{26}]
=567{14/23}

51b.-> no 3 r9c89

51c.->17(3) = {179/269/458}

51d.->567 locked for r9

51e.->22(4)r9 = 89{14/23}

51f. combining the information from step 51a with the h10(2)n9
->r8c78 + r9c789 = [69417/38745/79326/39726] = 7{1469/2369/3458}

51g.-> 7 locked for n9 in h10(2) and 17(3)

51h. "45"n9 -> 4 innies = 18(4) = {1269/1458/2358} ({1359/1368/2349/3456} blocked by combined h10(2)-17(3) step 51f)

51i. 22(4)n78 = {1489/2389} = 89{14/23}
-since {14/23} must be in n7 -> Killer quad with 5(2)n7
-> no 4 r78c3

53. Only combinations {27/36/45} allowed in cage 9(2) at r7c3
-> Removed candidate 5 from r7c4

54. Only combinations {27/36/45} allowed in cage 9(2) at r8c3
-> Removed candidate 5 from r8c4

55. Value 5 locked in column 3 of N7
-> Removed 5 from r123456c3

56. Since 5 is locked in r78c3 -> Value 4 locked in r78c4 (since connected by 2 9(2)cages)
-> 4 locked for c4
-> Removed 4 from r123456c4

57. Only combinations {16/25} allowed in cage h7(2) at r4c4
-> Removed candidate 3 from r46c4

58. Value 4 locked for column 4 in N8
-> Removed 4 from r7c56

58a. 17(4)n89 = {1367/2357} = 37{16/25}

59. Must use 37 in cage 17(4) at r7c5
-> Removed candidate 3 from r8c4

60. Only combinations {27/45} allowed in cage 9(2) at r8c3
-> Removed candidate 6 from r8c3

61. Value 6 locked in row 7 of N7
-> Removed 6 from r7c56789

62. Value 2 locked in row 8 of combined cages 9(2) at r8c3 & 5(2) at r8c1
-> Removed 2 from r8c69

65. 45 rule on row 89. Included cells r8c679 = h14(3)

65a. = [176/671/761/356/365/536] ([563] not compatable with 17(4) combo's)
-> Cage h15(3) at r7c4 doesn't allow permutations in r8c56 with {39}
-> Only combinations {167/356}
-> Removed candidate 3 from r8c9

68a.From step 51h. we know that innies n9 = 18(4) = {1269/1458/2358}

68b. -> with r8c9 = {156} -> {r7c789} = {269/129/458/148/238}

68c. "45" r7 -> 5 innies = h21(5)

68d. combining steps 68b and c and keeping an eye on the combinations in the 17(4)n89: {1367/2357}
-> h21(5) = {r7c56}{r7c789}
= {13-269}/{36-129}/{13-458}/{35-148}/{17-238}

68e. -> h21(5) = {12369/12378/13458} = 13{269/278/458}

68f. -> no 3 r7c4

68g. and no 3 in r8c7 (since 3 locked in h21(5) r7 is in the same cage or nonet as r8c7)

68h. -> no 7 r9c7

68i.removed 6 from r7c3

69. from step 68h and 51a.
h23(5)r9 = {14567} = [{56}4{17}]
= {23567} = [{57}3{26}]

69a. -> Only combinations {3578/4568} allowed in cage 23(4) at r8c5

69b. = 58{37/46} (no 19)

69c. -> r8c5 = 8

69d. 5 is locked for n8 and r9 in r9c56 = 5[6/7](no 3)

75. Only combinations {249} with 9 locked in r9c4 allowed in cage h15(3)n8 at r7c4
-> Set candidate 9 in r9c4

75a. r78c4 = {24}:locked for n8, c4

75b. r8c8 = 9

75c. r9c89 = {17/26}(no 3,4)

86. Only combination {16} allowed in cage h7(2) at r4c4
-> Removed candidate 5 from r4c4
-> Removed candidate 5 from r6c4

86a. {16}locked for c4,n5

87. "45"n5 -> r46c6 = 13 = [94]/{58}

88. Naked pair {57} found in r78c3
-> Removed value 7 from r456c3 r7c2
-> Removed combination {1457} from cage 17(4) at r4c3
-> Removed combination {23459} from cage 23(5) at r5c1
-> Removed combination {78} from cage 15(2) at r7c1 = {69} only:locked for r7

89. Naked pair {16} found in cage h7(2)c4
-> Removed combination {1469} from cage 20(4) at r1c3
-> cage 25(5) at r4c5 = 237{49/58}

91. Must use {1367} in cage 17(4) at r7c5

91a. 6 is locked for r8
-> Removed candidate 6 from r8c9

99 from step 68d. "45" r7 -> 5 innies = h21(5)

99a. -> {r7c56}{r7c789} = {13-458}/{17-238}

99b. -> 1 locked in r7c56 for r7, n8

99c. -> h21(5) = {12378/13458} = 138{27/45}


Now moving into n6 - and the key moves that finally unlock this puzzle
37. 45 rule on N7, N8, N9. Excluded cells r56c8 r6c9 = 20

37a.-> Only combinations {389/479/569/578} allowed

37b.-> Removed candidates 12 from r5c8

37c.-> Removed candidates 12 from r6c8

37d.-> Found a hidden cage 20(3) at r56c8 r6c9

80. 23(4)n69 = {2678/3578/4568}.

80a.From step 37, r56c8 + r6c9 = 20.
-r6c9 = 3..9 -> r56c8 = 11..17 -> r7c78 = 6..12

80b.from step 99a. ->{r7c789} = {458}/238}
from 80a. r7c78 = 6..12 -> = {45/48/28/38}

80c. from step 80 ->r56c8 = {68/56/67/57}

80d. But since r56c8 are part of a h20(3) (step 37a) -> {67/68} are blocked

80e. ->r56c8 = {56/57} = 5{6/7} = 11/12

80f.->5 locked for c8,n6 and no 5 in r7c78

80g. -> r6c9 = 8/9 only (from h20(3)n6)

80h. from 80e. the rest of 23(4)n69 = {38/48} = 8{3/4} (no 2)

80i. 15(3)n69 = [825/951] with r7c9 = {25}

80j. -> 15(3) = 5{28/19}: 5 locked for c9, n9

80k. -> r6c9 = {89}, r7c9 = {25}, r56c8 = {567} (no 8), r7c78 = {348} = 8{3/4}

80l. 23(4) n69 = {3578/4568} = 58{37/46} with 5 locked for c8 -> no 4 r2c9

80m. 9(2)n3 = {18/36}(no 4) = [1/3...]

80n. 5(2)n3 = {14/23} = [1/3..] -> Killer pair {13} locked for n3


109/114. 45 rule on N3. Included cells r23c7 minus excluded cell r1c6 equals 11

-1 in r1c6 -> r23c7 = 12 = {57}
({48} blocked since requires 9(2)n3 = {36} and 5(2) = {23} = 2 3's)

-2 in r1c6 -> r23c7 = 13 = {49}
({58} blocked since requires 9(2)n3 = {36} and 5(2) = {14} = but this leaves {279} for r1 -> 2 2's in r1; {67} blocked by r8c7)

-3 in r1c6 -> r23c7 = 14 = {59}
({68} blocked by 9(2)n3)

-4 in r1c6 -> r23c7 = 15 = blocked
({69} requires 9(2) = {18}, 5(2) = {23} -> 2 4's in r1)

109a. r23c7 = [57/49/59]
-> Removed candidate 6 from r2c7
-> Removed candidate 8 from r3c7
-> removed 4 from r1c6

110. Only combinations {25/34} allowed in cage 7(2) at r2c6
-> Removed candidate 1 from r2c6

111. Only combinations {589/679} allowed in cage 22(3) at r3c5
-> Removed candidate 5 from r3c6

112. Value 1 locked for column 7 in N6
-> Removed 1 from r4c89 r5c9

115. Value 4 locked in column 5 of N2
-> Removed 4 from r456c5

90. Must use 9 in cage 27(5) at r1c1
-9 for 27(5)n12 only in n1
-> no 9 in r1c3

117. Value 4 locked for column 5 in cage 20(4) at r1c3
-> Removed 4 from r1c3

117a. 20(4) must have 4 = {1478/2459/2468/3458/3467} ({1469} blocked since no candidates in r1c4)

117b. 45 on r123 -> r4c12 = 12 = [57/84/93]: r4c2 = {347}

117c. 45 on n1 -> r23c4 - 7 = r1c3.

-r1c3 = 1 -> r23c4 = 8 = {35} -> rest of 20(4) = {478}

-r1c3 = 2 -> r23c4 = 9 = no options -> no 2 in r1c3

-r1c3 = 3 -> r23c4 = 10 = [37] -> rest of 20(4) = {458} ({467} blocked by r23c4)

-r1c3 = 6 -> r23c4 = 13 = {58} -> rest of 20(3) = {347} ({248} blocked by r23c4)

-r1c3 = 8 -> r23c4 = 15 = [87] -> rest of 20(3) = {345} ({147} blocked by r23c4;{246} blocked since no candidates in r1c4)

117d. In summary, r23c4 = {35/58}[37/87]

117e. In summary, rest of 20(3) = 4{78/58/37/35} (no 1269)

117f. -> r2c3 = 9 (hsingle r2)

117g. -> 9 for n2 locked in 22(3) -> no 9 in r3c7

117h. r3c7 = 7

126a. naked quint on {34578} in n2 -> r12c6 = [12], r3c56 = {69} -> r23c7 = [57], r89c7 = [64], r7c34 = [54], r7c78 = {38}, r78c6 = [73], r56c8 = {57}, 15(3)n56 = 9{28/46} with 9 locked for n6, c7 -> r1c9 = 9, r1c78 = {28}, 9(2)n3 = {36}, r3c89 = [41] etc

[Para]

Hi all

Also worked to through this killer in the last few days. Now done both killers from before i came here. Really nice puzzle. Really tough work to finish it.

Walk-through Assassin UTA-1

1. R234C1 = {389/479/569/578}: no 1,2

2. R2C67 = {16/25/34}: no 7,8,9

3. R2C89, R7C34 and R8C34 = {18/27/36/45}: no 9

4. R3C567 = {589/679}: no 1,2,3,4; 9 locked for R3

5. R3C89 = {14/23}: no 5,6,7,8

6. R7C12 = {69/78}: no 1,2,3,4,5

7. R8C12 = {14/23}: no 5,6,7,8,9

8. 45 on R12: 1 innie: R2C1 = 7
8a. In 20(3) at R2C1: R34C1 = 13 = [49/58/85]: no 3,6; R4C1: no 4
8b. Clean up: R7C2: no 8; R2C89: no 2

Let’s first attack the bottom
9. 45 on R9: 2 outies: R8C58 = 17 = {89} -->> locked for R8; pointing: R5C5 + R9C7: no 8,9
9a. Clean up: R8C34: no 1

10. 45 on R89: 3 innies: R8C679 = 14 = {167/257/356}: {347 blocked by R8C12): no 4

11. 45 on N78: 2 outies: R89C7 = 10 = [37/64/73]: no 1,2,5 ; R9C7: no 6

12. 17(3) at R8C8 = [9]{17/26/35}/[8]{27/36/45} -->> R9C89 = {17/26/35/27/36/45}: no 8,9

13. Hidden Killer Pair {89} in N9: R8C8 = {89} and R7C789 needs one of {89}
13a. Killer Pair {89} in R7C12 + R7C789 -->> locked for R9
13b. Clean up: R7C34: no 1

14. Hidden Killer Pair {89} in N8: R8C5 = {89} and R9C456 needs one of {89}

15. Hidden Killer Pair {89} in R9: R9C456 needs one of {89} and R9C123 needs one of {89}

16. Either 22(4) at R9C1(when R9C4 ={89}) or 23(4) at R8C5(when one of R9C56 = {89}) needs 2 of {89}(from step 14)
16a. 22(4) = {1489/2389} or 23(4) = {2489}({1589} blocked by R9C7)
16b. Hidden Killer Quad {1234} in R9: R9C89 = {1|2|3|4..}, 22(4) or 23(4) with {89} had 2 of {1234}, so 22(4) or 23(4) with one of {89} needs one of {1234} -->> 22(4) at R9C1: {2479/3469/3478} blocked; 23(4): {3479 blocked}
16c. 23(4) at R8C5 = {1679/2489/2579/2678/3569/3578/4568}: When 4, it has to go in R9C7 -->> R9C56: no 4

17. 45 on N1234: R46C4 = 7 = {16/25/34}: no 7,8,9

18. 45 on N7: 3 outies: R789C4 = {249/258/267/348/357}: ({159} blocked because 1,9 only in R9C4; {456} blocked by R46C4) -->> R9C4: no 1,4

19. 1 in N8 locked within 17(4) cage at R7C5 or 23(4) cage at R8C5
19a. Either 17(4) = {1367/1457} or 23(4) = {1679} -->> R9C7 = 7 -->> R8C7 = 3
19b. So either 17(4) = {1367/1457} or R8C7 = 3 -->> 17(4) at R7C5 = {1367/1457/2357}: 7 locked within cage -->> R8C4: no 7
19c. Clean up: R8C3: no 2

20. 17(4) at R7C5: {1457} blocked: When {1457}; R7C56 + R8C6 = {145} and R8C7 = 7 -->> R9C7 = 3 -->> R8C5 + R9C56 (within 23(4) cage at R8C5) = {569/578}: 2 5’s in N8
20a. 17(4) = {1367/2357}: no 4; 3 locked within cage -->> R8C4: no 3
20b. 4 locked in N8 locked within R78C4 -->> locked for N4; h15(3) at R789C4 = {24}[9]/[348] -->> R7C4 = {234}; R8C4 = {24}; R9C4 = {89}
20c. Naked Pair {89} within R8C5 + R9C4 -->> locked for N8
20d. Clean up: R46C4: no 3; R78C3 = {57}/[65]; 5 locked for C3 and N7; R7C3 = {567}; R8C3 = {57}

21. 21(4) at R9C1 needs 2 of {89}(R9C123 and R9C4) -->> 21(4) = {1489/2389}: no 6,7
21a. 6 in N7 locked for R7

22. Killer Pair {24} in R8C12 + R8C4 -->> locked for R8

23. R8C12 and R8C4679 need either both {23} or neither.
23a. 17(4) in R7C5 = {1367/2357}: 3 locked
23b. When 3 in R7C56 + R8C6 -->> R78C4 = {24}
23c. When 3 in R8C7 -->> R8C4 = 2(step 23)
23d. Conclusion: 2 locked in R78C4 -->> locked for C4 and N8
23e. Hidden Pair: R78C4 = {24} -->> R9C4 = 9(step 20b)
23f. R8C58 = [89]
23g. Clean up: R46C4 = {16} -->> locked for C4 and N5
23h. Clean up: R78C3 = {57} -->> locked for C3 and N7
23i. Clean up: R7C1: no 8

24. 17(4) at R7C5 = {1367}: no 5

25. 23(4) at R8C5 = 8{357/456}: no 1; 5 locked for R9

26. 17(3) at R8C8 = 9{17/26}: no 3,4
26a. Killer Pair {67} in R89C7 + R9C89 -->> locked for N9

27. 45 on R789: R56C8 + R6C9 = 20 = {389/479/569/578}: no 1,2
27a. 9 only in R6C9 -->> R6C9: no 3,4,6

28. 15(3) at R6C9 = [9]{15}/[825]/[7]{35}: ([843] blocked by R89C7): R6C9 = {789}; R7C9 = {1235}; 5 in R78C9 for C9 and N9

Slowly moving up.
29. 23(4) at R5C8 = {2678/3578/4568}: no 1; R56C8 = {567}(only place in cage for these numbers and needs at least 2 of these)

30. h20(3) at R56C8 + R6C9 = {56}[9]/{57}[8] -->> R6C9 = {89}; R56C8 = {56/57} -->> 5 locked for C8 and N6
30a. 23(4) at R5C8 = {3578/4568}(needs 5 in R56C8): no 2
30b. 15(3) at R6C9 = [9]{15}/[825]: no 3
30c. Clean up: R2C89: no 4

31. Killer Pair {13} in R2C89 + R3C89 -->> locked for N3
31a. R2C67 = {25}/[34]: {16} blocked by R2C89; R2C6: no 1,4,6; R2C7: no 1,6

Now for some work on top.
32. 45 on N3: 2 outies and 1 innie: R3C7 = R12C6 + 4: Min R12C6 = 3 -->> Min R3C7 = 7; R3C7 = {789} -->> R12C6 = [12/13/23/32]: no 4,5,6,7,8,9
32a. Clean up: R2C7: no 2
32b. 4 in N2 locked for C5 and 20(4) cage at R1C3

33. 45 on N23: R1C3 + 7 = R23C4 : R1C3 = {123689} -->> R23C4 can be 8/9/10/13/15/16: R23C4 = {35/58}/[37/87] = 8/10/13/15 -->> R1C3 = {1368}
33a. R23C4 = {3|8..},{5|7..}

34. 20(4) at R1C3 = {1478/2459/2468/3458/3467}(needs 4 in R12C5): {1469} blocked by R1C4
34a. 20(4) = {2468} blocked -->> R12C6 = {2|3..}; R23C4 = {3|8..}; When {2468}, R12C5 = {24} and R1C4 = 8 -->> clash with R12C6 + R23C4
34b. 20(4) = {1478/2459/3458/3467} = {5|7..}: only {57} in R1C45 + R2C5

And now the easier work.
35. Killer Pair {57} in R1C45 + R2C5 and R23C4 -->> locked for N2
35a. 22(3) at R3C5 = {679} -->> R3C7 = 7; R3C56 = {69} -->> locked for R3 and N2
35b. R2C3 = 9(hidden); R12C6 = [12](step 32); R2C7 = 5; R78C3 = [57]; R78C4 = [42]
35c. R89C7 = [64](step 11); R8C6 = 3; R7C56 = [17]; R7C9 = 2; R8C9 = 5(hidden); R6C9 = 8

36. Clean up: R8C12 = {14} locked for N7; R56C8 = {57}(step 30) -->> locked for N6 and C8
36a. R9C89 = [17]

37. 45 on N23: R1C3 + 7 = R23C4 -->> R1C3 = 6; R23C4 = [85]
37a. Clean up: R2C9: no 1
37b. R2C2 = 1(hidden); R2C5 = 4(hidden); R46C4 = [61]; R8C12 = [14]; R1C9 = 9; R4C6 = 8

38. 45 on N5: 1 innie: R6C6 = 5
38a. R9C56 = [56]; R56C8 = [57]; R3C56 = [69]; R5C6 = 4
38b. R3C9 = (hidden); R3C8 = 4; R3C1 = 8; R4C1 = 5; R1C12 = [45](hidden)
38c. R4C9 = 4(hidden) R6C3 = 4(hidden); R7C7 = 8(hidden); R7C8 = 3
38d. R1C78 = [28]; R2C89 = [63]; R4C8 = 2; R5C9 = 6; R456C7 = [319]; R4C3 = 1
38e. R4C5 = 9(hidden) ; R4C2 = 7; R5C4 = 7(hidden); R1C45 = [37]

39. 17(4) at R4C3 = 16{28} (last possible combo): R5C23 = {28} -->> locked for R5 and N4
39a. R56C5 = [32]; R3C23 = [32]; R9C123 = [283]; R5C123 = [928]
39b. R6C12 = [36]; R7C12 = [69]

greetings

Para