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groston
 Post subject: Bad puzzle?
PostPosted: Fri Jul 07, 2023 4:27 pm 
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Joined: Fri Jun 23, 2023 4:24 am
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I am, by no one’s imagination, a Killer Sudoku expert, but the PuzzleMadness Daily Hard Killer Sudoku Puzzle for 7 Jul 2023 does not seem to be solvable. Here are the actions I took:
  1. Do the obvious in the individual cages
  2. Deal with the 1/2 pair in the MRN and the 7/9 pair in the MMN. Once the numbers have been deleted, do cleanup.
  3. During cleanup, the 13 cage in BMN becomes a 5/8 pair - deal with this and clean up. This also means that the horizontal 13 cage in the BRN cannot be solved with a 5/8 pair.
  4. The BRN sums to 37, thus the two remaining square sum to 8
  5. The MRN sums to 29, thus the three remaining square sum to 16
  6. The bottom three nonets sum 127, thus the two remaining square sum to 8
  7. Do cleanup and now the only digit available for r4c8 is now a 3, making r3c8 a 2.
  8. r8c9 is the only cell in the BRM with a 3, thus it becomes 3. This forces r7c9 to become a 2 and r6c9 to become a 5.
  9. The 11 nonet in the BRN has a 3, thus the other two cells must add to 8, which forces them to a 1/7
  10. Clean up, which make the horizontal 13 cage in the BRN into 4/9

However, the central 13 cage in the MRN is also a 4/9, see image, so the puzzle cannot be solved. I do not believe that I did anything wrong, but if I did, please tell me where I goofed.

Out of laziness, I have abbreviated the nonets, for example: MRN is middle-right nonet


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Ed
 Post subject: Re: Bad puzzle?
PostPosted: Fri Jul 07, 2023 9:00 pm 
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Joined: Wed Apr 16, 2008 1:16 am
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Hi groston. Check your step 6. Mistake there. Very easy to do.

groston wrote:
I have abbreviated the nonets, for example: MRN is middle-right nonet
Or even more abbreviated, just say "n6" (numbered Left to right, top to bottom).

This puzzle gets a SudokuSolver score of 1.00 so quite a bit harder than the one last time.
triple click code:
3x3::k:6400:6400:6400:5121:5121:5121:6146:6146:6146:3587:3587:6400:6400:5121:6146:6146:4356:4356:3587:3333:3334:3334:2311:1800:1800:1289:4356:3850:3333:2827:2316:2311:4109:782:1289:3343:3850:1296:2827:2316:7185:4109:782:3346:3343:2580:1296:7185:7185:7185:7185:7185:3346:1811:2580:4118:8469:8469:8469:8469:8469:2839:1811:4118:4118:5144:5144:8469:3353:3354:2839:2839:2332:2332:5144:5144:8469:3353:3354:3355:3355:
full SudokuSolver log: 
Preliminaries
Cage 3(2) n6 - cells ={12}
Cage 16(2) n5 - cells ={79}
Cage 5(2) n36 - cells only uses 1234
Cage 5(2) n4 - cells only uses 1234
Cage 15(2) n4 - cells only uses 6789
Cage 7(2) n69 - cells do not use 789
Cage 7(2) n23 - cells do not use 789
Cage 13(2) n8 - cells do not use 123
Cage 13(2) n9 - cells do not use 123
Cage 13(2) n9 - cells do not use 123
Cage 13(2) n6 - cells do not use 123
Cage 13(2) n14 - cells do not use 123
Cage 13(2) n12 - cells do not use 123
Cage 13(2) n6 - cells do not use 123
Cage 9(2) n7 - cells do not use 9
Cage 9(2) n5 - cells do not use 9
Cage 9(2) n25 - cells do not use 9
Cage 10(2) n47 - cells do not use 5
Cage 11(2) n4 - cells do not use 1
Cage 11(3) n9 - cells do not use 9

1. Naked pair {12} found at r45c7
1a. Cage sum in cage 7(2) n23 - removed 56 from r3c6
1b. Cage sum in cage 5(2) n36 - removed 34 from r3c8
1c. Cage sum in cage 7(2) n69 - removed 56 from r7c9

2. Naked pair {79} found at r45c6
2a. Cage sum in cage 9(2) n25 - removed 2 from r3c5
2b. Cage sum in cage 9(2) n5 - removed 2 from r4c4 - removed 2 from r5c4
2c. Cage sum in cage 13(2) n8 - removed 46 from r8c6 - removed 46 from r9c6
2d. Combinations {27} no longer valid in cage 9(2) n5
2e. Only combination {58} valid in cage 13(2) n8

3. Naked pair {58} found at r89c6

4. 45 Rule on c12 split cage 25(5) n12
4a. Included cells set as split cage 8(2) n1
4b. Excluded cells set as split cage 17(3) n12
4c. Original combinations {12589} {13489} {14569} {23479} cannot be split and are removed

5. 45 Rule on c89 split cage 24(5) n23
5a. Included cells set as split cage 11(2) n3
5b. Excluded cells set as split cage 13(3) n23
5c. Original combinations {12678} cannot be split and are removed

6. 45 Rule on r89 - outies total 38 -> remaining cells r7c19 total 7
6a. Set candidates at r7c1 to 346
6b. Removed candidate 2 from r7c9
6c. Cage sum in cage 7(2) n69 - removed 5 from r6c9
6d. Cage sum in cage 10(2) n47 - removed 12389 from r6c1
6e. Combinations {25} no longer valid in cage 7(2) n69
6f. Combinations {19} {28} no longer valid in cage 10(2) n47
6g. Combinations {2689} {1789} no longer valid in combined cages 15(2) n4 & 10(2) n47
6h. Combinations {2459} {2567} no longer valid in combined cages 13(2) n6 & 7(2) n69

7. 45 Rule on n9 - innies r7c79 total 8
7a. Set candidates at r7c7 to 57
7b. Removed candidate 4 from r7c9
7c. Cage sum in cage 7(2) n69 - removed 3 from r6c9
7d. Cage sum in cage h7(2) n79 - removed 3 from r7c1

8. Combinations {37} no longer valid in cage 10(2) n47
8a. Removed redundant candidates 7
8b. Combinations {3679} no longer valid in combined cages 15(2) n4 & 10(2) n47

9. Naked pair {46} found at r67c1
9a. Cage sum in cage 15(2) n4 - removed 9 from r4c1 - removed 9 from r5c1
9b. Cage sum in cage 9(2) n7 - removed 35 from r9c2
9c. Cage sum in split cage 8(2) n1 - removed 2 from r1c2
9d. Combinations {69} no longer valid in cage 15(2) n4
9e. Combinations {1469} {2369} no longer valid in combined cages 15(2) n4 & 5(2) n4

10. Naked pair {78} found at r45c1
10a. Cage sum in cage 13(2) n14 - removed 56 from r3c2
10b. Cage sum in cage 11(2) n4 - removed 34 from r4c3 - removed 34 from r5c3
10c. Cage sum in cage 9(2) n7 - removed 12 from r9c2
10d. Cage sum in split cage 8(2) n1 - removed 1 from r1c2
10e. Combinations {38} {47} no longer valid in cage 11(2) n4
10f. Combinations {3689} {4679} no longer valid in combined cages 15(2) n4 & 11(2) n4
10g. Combinations {1348} {2347} no longer valid in combined cages 11(2) n4 & 5(2) n4

11. Naked pair {46} found at r6c19
11a. Cage sum in cage 5(2) n4 - removed 1 from r5c2
11b. Cage sum in cage 13(2) n6 - removed 79 from r5c8

12. Combinations {1234689} no longer valid in cage 33(7) n789

13. Candidate 1 locked in n4 for r6 nowhere else in r6

14. Candidate 7 locked in r6 for n6 nowhere else in n6
14a. Cage sum in cage 13(2) n6 - removed 6 from r4c9 - removed 6 from r5c9
14b. Combinations {67} no longer valid in cage 13(2) n6
14c. Combinations {1267} no longer valid in combined cages 3(2) n6 & 13(2) n6
14d. Combinations {3467} no longer valid in combined cages 13(2) n6 & 7(2) n69

15. 45 Rule on n789 - outies r6c19 total 10
15a. Found a hidden cage h10(2) n46

16. 45 Rule on r12 - outies r3c19 total 10
16a. Removed candidate 5 from r3c1
16b. Set candidates at r3c9 to 1789

17. 45 Rule on n78 - outies r6c1 r7c7 total 11
17a. Found a hidden innie/outie cells (r6c1 r7c7) = 11

18. 45 Rule on n789 - innies r7c1 equal outies r6c9
18a. Found a hidden innie/outie cells  (r7c1)=(r6c9)

19. 45 Rule on n9 - innies r7c7 minus outies r6c9 equals 1
19a. Found a hidden innie/outie cells (r7c7)-(r6c9)=1

20. 45 Rule on n789 - outies r6c1 minus innies r7c9 equals 3
20a. Found a hidden innie/outie cells (r6c1)-(r7c9)=3

21. 45 Rule on n78 - outies r7c7 minus innies r7c1 equals 1
21a. Found a hidden innie/outie cells (r7c7)-(r7c1)=1

22. Must use candidate 5 in cage 33(7) n789
22a. Removed 5 from r7c28

23. Candidate 2 in n9 must be in cage 11(3) n9
23a. Removed combinations {137} {146} - cells do not use 79

24. Limited placement of candidates in cage 14(3) n1
24a. Removed combination {167} -  no valid placement
24b. Removed combination {248} -  no valid placement
24c. Removed combination {347} -  no valid placement
24d. Removed 15 from r2c2

25. Found a hidden cage h11(3) n456

26. Combinations {137} no longer valid in cage h11(3) n456

27. Found a hidden cage h14(3) n4

28. Combinations {158} {167} {248} {257} {347} no longer valid in cage h14(3) n4

29. Combinations {239} no longer valid in cage h14(3) n4
29a. Removed redundant candidates 2

30. Found a hidden cage h15(3) n123

31. Combinations {348} {357} {456} no longer valid in cage h15(3) n123
31a. Removed redundant candidates 3
31b. Cage sum in cage 9(2) n25 - removed 6 from r4c5

32. Found a hidden cage h16(3) n6

33. Combinations {169} {178} {259} {268} no longer valid in cage h16(3) n6

34. Combinations {358} no longer valid in cage h16(3) n6
34a. Removed redundant candidates 8

35. Candidate 3 in n6 must be in cage h16(3) n6
35a. Removed combination {457} - cells do not use 1258

36. Found a hidden cage h12(3) n456

37. Combinations {147} {237} no longer valid in cage h12(3) n456

38. Combinations {129} {138} {156} no longer valid in cage h12(3) n456
38a. Removed redundant candidates 189
38b. Cage sum in cage 13(2) n14 - removed 4 from r3c2
38c. Cage sum in cage 9(2) n25 - removed 18 from r3c5
38d. Combinations {18} no longer valid in cage 9(2) n25

39. Candidate 9 locked in n4 for c3 nowhere else in c3
39a. Cage sum in cage 13(2) n12 - removed 4 from r3c4

40. Candidate 4 locked in cage h12(3) n456 for r4 nowhere else in r4
40a. Cage sum in cage 9(2) n5 - removed 5 from r5c4
40b. Cage sum in cage 13(2) n6 - removed 9 from r5c9

41. Candidate 9 in n7 must be in cage 16(3) n7
41a. Removed combinations {178} {268} {358} {367} {457} - cells do not use 78

42. Candidate 7 locked in r7 for cage 33(7) n789 nowhere else in cage 33(7) n789

43. Limited placement of candidates in split cage 17(3) n12
43a. Removed 1 from r2c4

44. Found a hidden cage h17(4) n3

45. Found a hidden cage h23(4) n1

46. Found a hidden cage h20(4) n7

47. Combinations {1289} {1379} {1469} {2369} {2459} no longer valid in cage h20(4) n7

48. Combinations {2378} no longer valid in cage h20(4) n7

49. Found a hidden cage h21(4) n13

50. Cell at r9c6 restricts combinations in cage 13(2) n9
50a. Removed combination {58} - blocked by {58}
50b. Removed redundant candidates 58
50c. Combinations {1578} no longer valid in combined cages 13(2) n9 & h8(2) n9

51. Cell at r5c7 restricts combinations in cage h11(3) n456
51a. Removed combination {128} - blocked by {12}
51b. Removed redundant candidates 8
51c. Cage sum in cage 13(2) n6 - removed 5 from r6c8

52. Candidate 5 in r6 must be in cage 28(6) n456
52a. Removed combinations {123679} {124678}

53. Candidate 5 locked in r6 for cage 28(6) n456 nowhere else in cage 28(6) n456

54. Hidden Killer Pair {12} in r5 using r5c7 and cage h11(3) n456
54a. Removed {12} from r5c34
54b. Cage sum in cage 11(2) n4 - removed 9 from r4c3
54c. Cage sum in cage 9(2) n5 - removed 8 from r4c4

55. Hidden triple {789} found at r4c169 in r4
55a. Cage sum in cage 13(2) n6 - removed 8 from r5c9

56. Naked triple {456} found at r5c89 r6c9
56a. Cage sum in cage 5(2) n36 - removed 1 from r3c8
56b. Combinations {14} no longer valid in cage 5(2) n36
56c. Combinations {246} no longer valid in cage h12(3) n456
56d. Combinations {1458} {1467} no longer valid in combined cages 5(2) n36 & 13(2) n6

57. Naked Single 2 found at r3c8
57a. Cage sum in cage h15(3) n123 - removed 7 from r3c5
57b. Combinations {159} {168} no longer valid in cage h15(3) n123
57c. Only combinations {2348} {2357} {2456} valid in cage h17(4) n3

58. Naked Single 3 found at r4c8
58a. Cage sum in cage h16(3) n6 - removed 3 from r6c7
58b. Cage sum in cage h12(3) n456 - removed 6 from r4c2 - removed 23 from r4c5

59. Naked Single 2 at r3c8 - removed from peer at r1c8
59a. Cage sum in split cage 11(2) n3 - removed 9 from r1c9

60. Naked Single 2 at r3c8 - removed from peer at r2c8

61. Naked Single 2 at r3c8 - removed from peer at r7c8

62. Naked Single 2 at r3c8 - removed from peer at r8c8

63. Naked Single 2 at r3c8 - removed from peer at r3c1
63a. Cage sum in cage h10(2) n13 - removed 8 from r3c9
63b. Combinations {28} no longer valid in cage h10(2) n13
63c. Combinations {2489} {2678} no longer valid in combined cages 13(2) n12 & h10(2) n13
63d. Combinations {1268} {2348} no longer valid in combined cages 7(2) n23 & h10(2) n13

64. Naked Single 2 at r3c8 - removed from peer at r3c6
64a. Cage sum in cage 7(2) n23 - removed 5 from r3c7
64b. Combinations {25} no longer valid in cage 7(2) n23
64c. Combinations {2459} {2567} no longer valid in combined cages 13(2) n12 & 7(2) n23
64d. Combinations {1259} {2357} no longer valid in combined cages 7(2) n23 & h10(2) n13

65. Naked Single 2 at r3c8 - removed from peer at r1c9
65a. Cage sum in split cage 11(2) n3 - removed 9 from r1c8
65b. Combinations {29} no longer valid in split cage 11(2) n3
65c. Combinations {1279} {2359} no longer valid in combined cages s8(2) n1 & s11(2) n3

66. Naked Single 2 at r3c8 - removed from peer at r2c9
66a. Combinations {269} {278} no longer valid in cage 17(3) n3

67. Naked Single 3 at r4c8 - removed from peer at r1c8
67a. Cage sum in split cage 11(2) n3 - removed 8 from r1c9

68. Naked Single 3 at r4c8 - removed from peer at r2c8

69. Naked Single 3 at r4c8 - removed from peer at r7c8

70. Naked Single 3 at r4c8 - removed from peer at r8c8

71. Naked Single 3 at r4c8 - removed from peer at r4c4
71a. Cage sum in cage 9(2) n5 - removed 6 from r5c4

72. Naked pair {45} found at r4c25
72a. Cage sum in cage 11(2) n4 - removed 6 from r5c3
72b. Cage sum in cage 9(2) n5 - removed 4 from r5c4
72c. Combinations {45} no longer valid in cage 9(2) n5
72d. Combinations {4579} no longer valid in combined cages 9(2) n5 & 16(2) n5

73. Naked quad {2358} found at r6c456 r5c4
73a. Cage sum in cage 9(2) n25 - removed 46 from r3c5
73b. Cage sum in cage h12(3) n456 - removed 4 from r4c2
73c. Only combination {45} valid in cage 9(2) n25

74. Naked Single 5 found at r3c5
74a. Last cell in cage h15(3) n123 at r3c2 set to 8
74b. Only combination {258} valid in cage h15(3) n123

75. Naked Single 5 found at r4c2
75a. Cage sum in cage h14(3) n4 - removed 4 from r6c1 - removed 159 from r6c3
75b. Combinations {149} no longer valid in cage h14(3) n4

76. Naked Single 4 found at r4c5

77. Naked Single 8 at r3c2 - removed from peer at r2c2
77a. Combinations {158} no longer valid in cage 14(3) n1

78. Naked Single 8 at r3c2 - removed from peer at r9c2
78a. Cage sum in cage 9(2) n7 - removed 1 from r9c1
78b. Combinations {18} no longer valid in cage 9(2) n7
78c. Only combinations {2479} {3469} {4567} valid in combined cages 13(2) n9 & 9(2) n7

79. Naked Single 8 at r3c2 - removed from peer at r3c3
79a. Cage sum in cage 13(2) n12 - removed 5 from r3c4
79b. Only combinations {2678} {3578} {4568} valid in cage h23(4) n1

80. Naked Single 8 at r3c2 - removed from peer at r3c4
80a. Cage sum in cage 13(2) n12 - removed 5 from r3c3
80b. Combinations {58} no longer valid in cage 13(2) n12
80c. Combinations {1568} {3458} no longer valid in combined cages 13(2) n12 & 7(2) n23
80d. Combinations {1589} {3578} no longer valid in combined cages 13(2) n12 & h10(2) n13

81. Naked Single 8 at r3c2 - removed from peer at r1c3

82. Naked Single 8 at r3c2 - removed from peer at r2c3

83. Naked Single 5 at r3c5 - removed from peer at r1c5

84. Naked Single 5 at r3c5 - removed from peer at r2c5

85. Naked Single 5 at r3c5 - removed from peer at r6c5
85a. Combinations {124579} no longer valid in cage 28(6) n456

86. Naked Single 5 at r3c5 - removed from peer at r1c4
86a. Combinations {1568} {2459} {2567} {3458} no longer valid in cage 20(4) n2

87. Naked Single 5 at r3c5 - removed from peer at r2c4

88. Naked Single 5 at r4c2 - removed from peer at r1c2
88a. Cage sum in split cage 8(2) n1 - removed 3 from r1c1

89. Naked Single 5 at r4c2 - removed from peer at r8c2

90. Naked Single 5 at r4c2 - removed from peer at r5c3
90a. Cage sum in cage 11(2) n4 - removed 6 from r4c3
90b. Combinations {56} no longer valid in cage 11(2) n4
90c. Combinations {5678} no longer valid in combined cages 15(2) n4 & 11(2) n4
90d. Only combination {1249} valid in combined cages 11(2) n4 & 5(2) n4

91. Naked Single 2 found at r4c3

92. Naked Single 9 found at r5c3

93. Naked Single 6 found at r6c1
93a. Last cell in cage 10(2) n47 at r7c1 set to 4
93b. Last cell in cage h10(2) n46 at r6c9 set to 4
93c. Last cell in innie/outie cells (r6c1 r7c7) = 11 at r7c7 set to 5
93d. Last cell in innie/outie cells (r6c1)-(r7c9)=3 at r7c9 set to 3

94. Naked Single 2 at r4c3 - removed from peer at r1c3

95. Naked Single 2 at r4c3 - removed from peer at r2c3
95a. Combinations {2678} no longer valid in cage h23(4) n1

96. Naked Single 2 at r4c3 - removed from peer at r7c3
96a. Combinations {1568} {2567} no longer valid in cage h20(4) n7

97. Naked Single 2 at r4c3 - removed from peer at r8c3

98. Naked Single 2 at r4c3 - removed from peer at r9c3
98a. Combinations {2468} no longer valid in cage h20(4) n7

99. Naked Single 2 at r4c3 - removed from peer at r4c7
99a. Cage sum in cage 3(2) n6 - removed 1 from r5c7

100. Naked Single 1 found at r4c7

101. Naked Single 2 found at r5c7

102. Naked Single 2 at r4c3 - removed from peer at r5c2
102a. Cage sum in cage 5(2) n4 - removed 3 from r6c2
102b. Only combination {146} valid in cage h11(3) n456

103. Naked Single 2 at r4c3 - removed from peer at r6c2
103a. Cage sum in cage 5(2) n4 - removed 3 from r5c2
103b. Combinations {23} no longer valid in cage 5(2) n4
103c. Combinations {2378} no longer valid in combined cages 15(2) n4 & 5(2) n4

104. Naked Single 4 found at r5c2
104a. Cage sum in cage h11(3) n456 - removed 46 from r5c5 - removed 45 from r5c8

105. Naked Single 1 found at r5c5
105a. Only combination {123589} valid in cage 28(6) n456

106. Naked Single 6 found at r5c8
106a. Last cell in cage 13(2) n6 at r6c8 set to 7
106b. Only combination {67} valid in cage 13(2) n6
106c. Combinations {4589} no longer valid in combined cages 13(2) n6 & 13(2) n6

107. Naked Single 1 found at r6c2

108. Naked Single 3 found at r6c3

109. Naked Single 4 at r4c5 - removed from peer at r1c5

110. Naked Single 4 at r4c5 - removed from peer at r2c5

111. Naked Single 4 at r4c5 - removed from peer at r7c5

112. Naked Single 4 at r4c5 - removed from peer at r8c5

113. Naked Single 4 at r4c5 - removed from peer at r9c5

114. Naked Single 1 at r4c7 - removed from peer at r4c4
114a. Cage sum in cage 9(2) n5 - removed 8 from r5c4
114b. Combinations {18} no longer valid in cage 9(2) n5
114c. Combinations {1789} no longer valid in combined cages 9(2) n5 & 16(2) n5

115. Naked Single 6 found at r4c4

116. Naked Single 3 found at r5c4

117. Naked Single 6 at r4c4 - removed from peer at r1c4

118. Naked Single 6 at r4c4 - removed from peer at r2c4

119. Naked Single 6 at r4c4 - removed from peer at r3c4
119a. Cage sum in cage 13(2) n12 - removed 7 from r3c3

120. Naked Single 6 at r4c4 - removed from peer at r7c4

121. Naked Single 6 at r4c4 - removed from peer at r8c4

122. Naked Single 6 at r4c4 - removed from peer at r9c4

123. Naked Single 4 at r5c2 - removed from peer at r2c2
123a. Combinations {149} no longer valid in cage 14(3) n1

124. Naked Single 4 at r5c2 - removed from peer at r7c2

125. Naked Single 4 at r5c2 - removed from peer at r8c2
125a. Combinations {349} no longer valid in cage 16(3) n7

126. Naked Single 4 at r5c2 - removed from peer at r9c2
126a. Cage sum in cage 9(2) n7 - removed 5 from r9c1
126b. Combinations {45} no longer valid in cage 9(2) n7
126c. Combinations {4567} no longer valid in combined cages 13(2) n9 & 9(2) n7

127. Naked Single 4 at r5c2 - removed from peer at r5c9
127a. Cage sum in cage 13(2) n6 - removed 9 from r4c9
127b. Combinations {49} no longer valid in cage 13(2) n6

128. Naked Single 8 found at r4c9

129. Naked Single 5 found at r5c9

130. Naked Single 8 at r4c9 - removed from peer at r2c9

131. Naked Single 8 at r4c9 - removed from peer at r8c9

132. Naked Single 8 at r4c9 - removed from peer at r4c1
132a. Cage sum in cage 15(2) n4 - removed 7 from r5c1

133. Naked Single 7 found at r4c1

134. Naked Single 8 found at r5c1

135. Naked Single 7 at r4c1 - removed from peer at r4c6
135a. Cage sum in cage 16(2) n5 - removed 9 from r5c6

136. Naked Single 9 found at r4c6

137. Naked Single 7 found at r5c6

138. Naked Single 3 at r5c4 - removed from peer at r1c4

139. Naked Single 3 at r5c4 - removed from peer at r2c4

140. Naked Single 3 at r5c4 - removed from peer at r6c4

141. Naked Single 3 at r5c4 - removed from peer at r7c4

142. Naked Single 3 at r5c4 - removed from peer at r8c4

143. Naked Single 3 at r5c4 - removed from peer at r9c4

144. Naked Single 3 at r5c4 - removed from peer at r6c5

145. Naked Single 3 at r5c4 - removed from peer at r6c6

146. Naked Single 1 at r5c5 - removed from peer at r1c5

147. Naked Single 1 at r5c5 - removed from peer at r2c5

148. Naked Single 1 at r5c5 - removed from peer at r7c5

149. Naked Single 1 at r5c5 - removed from peer at r8c5

150. Naked Single 1 at r5c5 - removed from peer at r9c5

151. Naked Single 6 at r5c8 - removed from peer at r1c8
151a. Cage sum in split cage 11(2) n3 - removed 5 from r1c9

152. Naked Single 6 at r5c8 - removed from peer at r2c8

153. Naked Single 6 at r5c8 - removed from peer at r7c8

154. Naked Single 6 at r5c8 - removed from peer at r8c8

155. Naked Single 6 at r5c8 - removed from peer at r9c8
155a. Cage sum in cage 13(2) n9 - removed 7 from r9c9

156. Naked Single 5 at r5c9 - removed from peer at r2c9

157. Naked Single 5 at r5c9 - removed from peer at r8c9

158. Naked Single 1 at r6c2 - removed from peer at r7c2

159. Naked Single 1 at r6c2 - removed from peer at r8c2

160. Naked Single 3 at r6c3 - removed from peer at r1c3

161. Naked Single 3 at r6c3 - removed from peer at r2c3
161a. Combinations {359} {368} no longer valid in split cage 17(3) n12
161b. Combinations {3578} no longer valid in cage h23(4) n1

162. Naked Single 3 at r6c3 - removed from peer at r7c3

163. Naked Single 3 at r6c3 - removed from peer at r8c3

164. Naked Single 3 at r6c3 - removed from peer at r9c3
164a. Combinations {1379} {2369} {2378} {3458} {3467} no longer valid in cage 20(4) n78
164b. Only combination {1478} valid in cage h20(4) n7

165. Naked Single 2 found at r6c6

166. Naked Single 2 at r6c6 - removed from peer at r1c6

167. Naked Single 2 at r6c6 - removed from peer at r2c6
167a. Only combinations {13479} {13569} {13578} {14568} valid in cage 24(5) n23
167b. Combinations {238} {247} {256} no longer valid in split cage 13(3) n23

168. Naked Single 2 at r6c6 - removed from peer at r7c6

169. Naked Single 2 at r6c6 - removed from peer at r6c4

170. Naked Single 2 at r6c6 - removed from peer at r6c5

171. Naked Single 8 found at r6c5
171a. Cage sum in cage 28(6) n456 - removed 8 from r6c4 - removed 7 from r6c7

172. Naked Single 5 found at r6c4

173. Naked Single 9 found at r6c7

174. Naked Single 8 at r6c5 - removed from peer at r1c5

175. Naked Single 8 at r6c5 - removed from peer at r2c5

176. Naked Single 9 at r6c7 - removed from peer at r1c7

177. Naked Single 9 at r6c7 - removed from peer at r2c7
177a. Combinations {13479} {13569} no longer valid in cage 24(5) n23
177b. Combinations {139} no longer valid in split cage 13(3) n23

178. Naked Single 9 at r6c7 - removed from peer at r8c7
178a. Cage sum in cage 13(2) n9 - removed 4 from r9c7

179. Naked Single 9 at r6c7 - removed from peer at r9c7
179a. Cage sum in cage 13(2) n9 - removed 4 from r8c7
179b. Combinations {49} no longer valid in cage 13(2) n9

180. Naked Single 7 at r6c8 - removed from peer at r1c8
180a. Cage sum in split cage 11(2) n3 - removed 4 from r1c9

181. Naked Single 7 at r6c8 - removed from peer at r2c8

182. Naked Single 7 at r6c8 - removed from peer at r9c8
182a. Cage sum in cage 13(2) n9 - removed 6 from r9c9
182b. Combinations {67} no longer valid in cage 13(2) n9

183. Naked Single 4 at r6c9 - removed from peer at r2c9

184. Naked Single 4 at r6c9 - removed from peer at r8c9

185. Naked Single 4 at r6c9 - removed from peer at r9c9
185a. Cage sum in cage 13(2) n9 - removed 9 from r9c8
185b. Combinations {5678} no longer valid in combined cages 13(2) n9 & 13(2) n9

186. Naked Single 4 found at r9c8

187. Naked Single 9 found at r9c9

188. Naked Single 4 at r7c1 - removed from peer at r7c3

189. Naked Single 4 at r7c1 - removed from peer at r7c4

190. Naked Single 4 at r7c1 - removed from peer at r7c6
190a. Combinations {1245678} no longer valid in cage 33(7) n789

191. Naked Single 4 at r7c1 - removed from peer at r7c8

192. Naked Single 4 at r7c1 - removed from peer at r8c3

193. Naked Single 4 at r7c1 - removed from peer at r9c3

194. Naked Single 5 at r7c7 - removed from peer at r1c7

195. Naked Single 5 at r7c7 - removed from peer at r2c7
195a. Combinations {157} no longer valid in split cage 13(3) n23
195b. Only combination {2348} valid in cage h17(4) n3

196. Naked Single 5 at r7c7 - removed from peer at r8c7
196a. Cage sum in cage 13(2) n9 - removed 8 from r9c7

197. Naked Single 5 at r7c7 - removed from peer at r9c7
197a. Cage sum in cage 13(2) n9 - removed 8 from r8c7
197b. Combinations {58} no longer valid in cage 13(2) n9

198. Naked Single 5 at r7c7 - removed from peer at r7c3

199. Naked Single 5 at r7c7 - removed from peer at r8c8
199a. Combinations {245} no longer valid in cage 11(3) n9

200. Naked Single 3 at r7c9 - removed from peer at r1c9
200a. Cage sum in split cage 11(2) n3 - removed 8 from r1c8
200b. Combinations {38} no longer valid in split cage 11(2) n3
200c. Combinations {1378} {2368} no longer valid in combined cages s8(2) n1 & s11(2) n3

201. Naked Single 3 at r7c9 - removed from peer at r2c9
201a. Combinations {359} {368} no longer valid in cage 17(3) n3

202. Naked Single 3 at r7c9 - removed from peer at r8c9
202a. Combinations {236} no longer valid in cage 11(3) n9

203. Naked Single 3 at r7c9 - removed from peer at r7c2

204. Naked Single 3 at r7c9 - removed from peer at r7c5

205. Naked Single 3 at r7c9 - removed from peer at r7c6

206. Naked Single 4 at r9c8 - removed from peer at r1c8
206a. Cage sum in split cage 11(2) n3 - removed 7 from r1c9
206b. Combinations {13578} no longer valid in cage 24(5) n23
206c. Combinations {47} no longer valid in split cage 11(2) n3
206d. Only combination {1567} valid in combined cages s8(2) n1 & s11(2) n3

207. Naked Single 5 found at r1c8

208. Naked Single 5 at r1c8 - removed from peer at r2c8
208a. Combinations {458} no longer valid in cage 17(3) n3

209. Naked Single 5 at r1c8 - removed from peer at r1c1
209a. Cage sum in split cage 8(2) n1 - removed 3 from r1c2
209b. Only combinations {12679} {14578} {24568} valid in cage 25(5) n12
209c. Combinations {35} no longer valid in split cage 8(2) n1

210. Naked Single 5 at r1c8 - removed from peer at r1c3

211. Naked Single 6 found at r1c9

212. Naked Single 6 at r1c9 - removed from peer at r2c9
212a. Combinations {467} no longer valid in cage 17(3) n3

213. Naked Single 6 at r1c9 - removed from peer at r8c9

214. Naked Single 6 at r1c9 - removed from peer at r1c2
214a. Cage sum in split cage 8(2) n1 - removed 2 from r1c1
214b. Combinations {24568} no longer valid in cage 25(5) n12
214c. Combinations {26} no longer valid in split cage 8(2) n1

215. Naked Single 1 found at r1c1

216. Naked Single 1 at r1c1 - removed from peer at r2c1

217. Naked Single 1 at r1c1 - removed from peer at r3c1
217a. Cage sum in cage h10(2) n13 - removed 9 from r3c9

218. Naked Single 1 at r1c1 - removed from peer at r8c1
218a. Combinations {169} no longer valid in cage 16(3) n7

219. Naked Single 1 at r1c1 - removed from peer at r1c3

220. Naked Single 1 at r1c1 - removed from peer at r1c4

221. Naked Single 1 at r1c1 - removed from peer at r1c6
221a. Combinations {1289} {1379} {1469} {1478} no longer valid in cage 20(4) n2

222. Naked Single 1 at r1c1 - removed from peer at r2c3
222a. Combinations {179} no longer valid in split cage 17(3) n12

223. Naked Single 7 found at r1c2

224. Naked Single 7 at r1c2 - removed from peer at r2c2
224a. Combinations {257} no longer valid in cage 14(3) n1

225. Naked Single 7 at r1c2 - removed from peer at r9c2
225a. Cage sum in cage 9(2) n7 - removed 2 from r9c1
225b. Combinations {27} no longer valid in cage 9(2) n7

226. Naked Single 3 found at r9c1

227. Naked Single 6 found at r9c2

228. Naked Single 7 at r1c2 - removed from peer at r1c3

229. Naked Single 7 at r1c2 - removed from peer at r1c4

230. Naked Single 7 at r1c2 - removed from peer at r1c5

231. Naked Single 7 at r1c2 - removed from peer at r1c7

232. Naked Single 7 at r1c2 - removed from peer at r2c3

233. Naked Single 7 at r1c2 - removed from peer at r2c4
233a. Combinations {278} {467} no longer valid in split cage 17(3) n12

234. Naked Single 6 at r1c9 - removed from peer at r1c3
234a. Combinations {12679} no longer valid in cage 25(5) n12
234b. Combinations {269} no longer valid in split cage 17(3) n12

235. Naked Single 4 found at r1c3
235a. Cage sum in cage 25(5) n12 - removed 46 from r2c3 - removed 249 from r2c4
235b. Cage sum in cage h23(4) n1 - removed 4 from r3c3

236. Naked Single 5 found at r2c3

237. Naked Single 8 found at r2c4

238. Naked Single 6 found at r3c3
238a. Last cell in cage 13(2) n12 at r3c4 set to 7
238b. Combinations {49} no longer valid in cage 13(2) n12
238c. Combinations {1469} no longer valid in combined cages 13(2) n12 & 7(2) n23
238d. Combinations {3479} no longer valid in combined cages 13(2) n12 & h10(2) n13

239. Naked Single 4 at r1c3 - removed from peer at r1c4

240. Naked Single 4 at r1c3 - removed from peer at r1c6
240a. Combinations {2468} {3467} no longer valid in cage 20(4) n2

241. Naked Single 4 at r1c3 - removed from peer at r1c7

242. Naked Single 6 at r1c9 - removed from peer at r1c5

243. Naked Single 6 at r1c9 - removed from peer at r1c6

244. Naked Single 3 found at r1c6

245. Naked Single 3 at r1c6 - removed from peer at r2c6

246. Naked Single 3 at r1c6 - removed from peer at r3c6
246a. Cage sum in cage 7(2) n23 - removed 4 from r3c7

247. Naked Single 3 at r1c6 - removed from peer at r1c5

248. Naked Single 3 at r1c6 - removed from peer at r1c7

249. Naked Single 3 at r1c6 - removed from peer at r2c5

250. Naked Single 6 at r1c9 - removed from peer at r1c7
250a. Combinations {346} no longer valid in split cage 13(3) n23

251. Naked Single 8 found at r1c7
251a. Cage sum in cage 24(5) n23 - removed 46 from r2c6 - removed 3678 from r2c7
251b. Cage sum in cage h17(4) n3 - removed 6 from r3c7

252. Naked Single 1 found at r2c6

253. Naked Single 4 found at r2c7

254. Naked Single 3 found at r3c7
254a. Last cell in cage 7(2) n23 at r3c6 set to 4
254b. Combinations {16} no longer valid in cage 7(2) n23
254c. Combinations {1367} no longer valid in combined cages 7(2) n23 & h10(2) n13

255. Naked Single 8 at r1c7 - removed from peer at r1c4
255a. Combinations {2378} no longer valid in cage 20(4) n2

256. Naked Single 8 at r1c7 - removed from peer at r2c8
256a. Combinations {1389} {1578} {2478} {2568} {3468} no longer valid in cage h21(4) n13

257. Naked Single 5 at r2c3 - removed from peer at r8c3

258. Naked Single 5 at r2c3 - removed from peer at r9c3
258a. Combinations {1568} {2459} {2567} no longer valid in cage 20(4) n78

259. Naked Single 5 at r2c3 - removed from peer at r2c1
259a. Combinations {356} no longer valid in cage 14(3) n1
259b. Combinations {1569} {3459} {3567} no longer valid in cage h21(4) n13

260. Naked Single 1 at r2c6 - removed from peer at r7c6

261. Naked Single 6 found at r7c6

262. Naked Single 1 at r2c6 - removed from peer at r2c8

263. Naked Single 1 at r2c6 - removed from peer at r2c9
263a. Combinations {1479} no longer valid in cage h21(4) n13

264. Naked Single 4 at r2c7 - removed from peer at r2c8
264a. Combinations {2469} no longer valid in cage h21(4) n13

265. Naked Single 9 found at r2c8
265a. Cage sum in cage 17(3) n3 - removed 9 from r2c9 - removed 7 from r3c9

266. Naked Single 7 found at r2c9
266a. Cage sum in cage h21(4) n13 - removed 9 from r2c1 - removed 69 from r2c2

267. Naked Single 1 found at r3c9
267a. Last cell in cage h10(2) n13 at r3c1 set to 9
267b. Combinations {37} no longer valid in cage h10(2) n13

268. Naked Single 9 at r2c8 - removed from peer at r2c5

269. Naked Single 7 at r2c9 - removed from peer at r2c5

270. Naked Single 9 at r3c1 - removed from peer at r8c1

271. Naked Single 6 at r3c3 - removed from peer at r7c3

272. Naked Single 6 at r3c3 - removed from peer at r8c3

273. Naked Single 6 at r3c3 - removed from peer at r9c3
273a. Combinations {1469} {2468} no longer valid in cage 20(4) n78

274. Naked Single 7 at r3c4 - removed from peer at r7c4

275. Naked Single 7 at r3c4 - removed from peer at r8c4

276. Naked Single 7 at r3c4 - removed from peer at r9c4

277. Naked Single 1 at r3c9 - removed from peer at r8c9

278. Naked Single 2 found at r8c9
278a. Cage sum in cage 11(3) n9 - removed 4 from r8c8

279. Naked Single 6 at r7c6 - removed from peer at r7c2

280. Naked Single 6 at r7c6 - removed from peer at r7c5

281. Naked Single 6 at r7c6 - removed from peer at r8c5

282. Naked Single 6 at r7c6 - removed from peer at r9c5

283. Naked Single 2 at r8c9 - removed from peer at r8c1

284. Naked Single 2 at r8c9 - removed from peer at r8c2

285. Naked Single 2 at r8c9 - removed from peer at r8c4

286. Naked Single 2 at r8c9 - removed from peer at r8c5

287. Naked Single 3 at r9c1 - removed from peer at r2c1
287a. Cage sum in cage 14(3) n1 - removed 2 from r2c2

288. Naked Single 2 found at r2c1

289. Naked Single 3 found at r2c2

290. Naked Single 2 at r2c1 - removed from peer at r2c5

291. Naked Single 6 found at r2c5

292. Naked Single 3 at r2c2 - removed from peer at r8c2

293. Naked Single 3 at r9c1 - removed from peer at r8c1

294. Naked Single 5 found at r8c1
294a. Cage sum in cage 16(3) n7 - removed 9 from r7c2 - removed 6 from r8c2

295. Naked Single 2 found at r7c2

296. Naked Single 9 found at r8c2

297. Naked Single 2 at r7c2 - removed from peer at r7c4

298. Naked Single 2 at r7c2 - removed from peer at r7c5

299. Naked Single 5 at r8c1 - removed from peer at r8c6
299a. Cage sum in cage 13(2) n8 - removed 8 from r9c6

300. Naked Single 8 found at r8c6

301. Naked Single 5 found at r9c6

302. Naked Single 9 at r8c2 - removed from peer at r8c4

303. Naked Single 9 at r8c2 - removed from peer at r8c5

304. Naked Single 3 found at r8c5

305. Naked Single 3 at r8c5 - removed from peer at r9c5

306. Naked Single 8 at r8c6 - removed from peer at r8c3

307. Naked Single 8 at r8c6 - removed from peer at r8c8
307a. Cage sum in cage 11(3) n9 - removed 1 from r7c8

308. Naked Single 8 found at r7c8

309. Naked Single 1 found at r8c8

310. Naked Single 8 at r7c8 - removed from peer at r7c3

311. Naked Single 1 at r8c8 - removed from peer at r8c3
311a. Combinations {1289} no longer valid in cage 20(4) n78

312. Naked Single 7 found at r8c3
312a. Cage sum in cage h20(4) n7 - removed 7 from r7c3 - removed 17 from r9c3

313. Naked Single 1 found at r7c3

314. Naked Single 8 found at r9c3
314a. Cage sum in cage 20(4) n78 - removed 29 from r9c4

315. Naked Single 1 at r7c3 - removed from peer at r7c4

316. Naked Single 9 found at r7c4
316a. Cage sum in cage 33(7) n789 - removed 9 from r7c5 - removed 9 from r9c5

317. Naked Single 7 found at r7c5

318. Naked Single 2 found at r9c5

319. Naked Single 9 at r7c4 - removed from peer at r1c4
319a. Cage sum in cage 20(4) n2 - removed 2 from r1c5

320. Naked Single 2 found at r1c4

321. Naked Single 9 found at r1c5

322. Naked Single 7 at r8c3 - removed from peer at r8c7
322a. Cage sum in cage 13(2) n9 - removed 6 from r9c7

323. Naked Single 6 found at r8c7

324. Naked Single 7 found at r9c7

325. Naked Single 1 at r8c8 - removed from peer at r8c4
325a. Cage sum in cage 20(4) n78 - removed 4 from r9c4

326. Naked Single 4 found at r8c4

327. Naked Single 1 found at r9c4

Puzzle Complete
Much easier to step through with SudokuSolver for me rather try to read a log. But enjoy!

Cheers
Ed
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groston
 Post subject: Re: Bad puzzle?
PostPosted: Sat Jul 08, 2023 3:17 am 
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Joined: Fri Jun 23, 2023 4:24 am
Posts: 24
Thank you.

I am still trying to figure out the terminology used in the log (perhaps you can point me to a page that explains it?) In item 4, I understand the 45 rule, but do not understand "on c12 split cage 25(5) n12". I see that the cells r1c12 should sum to 9 since the 16 cells beneath them sum to 81...

Also, thanks for pointing out a mistake I made, but I don't understand. I re-added the cages in the bottom three nonets and still came up with 127. Thus cells r7c1 and r7c9 should sum to 8. What's wrong?
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Ed
 Post subject: Re: Bad puzzle?
PostPosted: Sat Jul 08, 2023 8:06 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
groston wrote:
What's wrong?
Nothing with your maths! The image is wrong. Should be a 9(2) at r9c12. That makes the cages total in n789 = 128

Hopefully that now makes sense of the solver log step 4a.

A very general introduction to killer techniques here

Cheers
Ed
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groston
 Post subject: Re: Bad puzzle?
PostPosted: Sat Jul 08, 2023 2:38 pm 
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Unreal - I would have sworn that I checked that. Damn! And thanks for pointing out my idiotic mistake.
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