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groston

Post subject: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 2:37 am

Addict

Joined: Fri Jun 23, 2023 4:24 am
Posts: 24

This is Daily Hard Killer Sudoku Puzzle from puzzlemadness.co.uk dated 17 July 2023. I have worked on this puzzle for many hours and keep getting stuck. I am certain that I have copied the puzzle properly and have not made any stupid mistakes. However, I cannot figure out what I am doing wrong, so please look at the following (sorry if the notation is quite right) and tell me where my mistake is.

Cleanup - basic -- for simplecage, live N1cage9, get rid of the 9s
45 rule, row 1 -- r1c5 becomes 2
45 rule, col 5 -- r1C5-3c5 lose the 9 Should be r2c5-r4c5 lose 9; r1234c5 total 14
45 rule, row 3 -- r3c1 becomes 4-8 and r3c9 becomes 5-9
cleanup N1cage 9 and N3cage 13 -- N1cage 9 becomes 1-5 and N3cage 13 becomes 4-8
45 rule, N8 -- r7c4-6 become 124, 14, 124
clean up row 7 (since N8 row 7 is only 124) -- remove 124 from N7 row7, N8 rows89, N9 row 7
45 rule on N7-N9 (the three non-cage squares sum to 9) -- r7c5 becomes 1, r7c1 and r7c9 become 35
cleanup row 7 -- remove 35 from r7c2, r7c3, r7c7, r7c8
clean up N5cage 16 -- r5c5 and r6c5 become 6/7/8/9
clean up col 5 -- r2c5, r3c5, and 46c5 r4c5 become 3/4/5
45 rule on sum of row 45 56: The sevencages with their top square in row 5 sum to 95, but (from step 8) 9 are in row 7 and r5c1 and r5c9 must be added to get to 90 -- r5c1 and r5c9 become 13 Ed has already commented on this step with 45 rule row 4 easier
clean up row 5 -- remove 1 and 3
clean up N4cage 11 and N5cages 10 and 10 -- r6c3 loses 8, r6c4 and r6c6 lose 79
since cols 1 and 9 have 13 and 53 -- thus no squares in col 1 or col 9 can have a 3
clean up N1cage 9 -- r3c1 loses 6
clean up N3cage 13 -- r3c9 loses 7 and r2c9 loses 6
45 rule on N5 (can be done since r7c5=1) -- r4c4 and r4c6 become 1-6 and r5c5 becomes 3-5
Cleanup N4cage 23 (since the inner three squares sum to 10) -- r4c3 and r4c7 lose 1-3
45 rule N9 -- r8c6 loses 1-5 This doesn't do anything to r8c6. r7c9 3 more than r7c6 so r7c6 becomes 2 and r7c9 becomes 5
clean up N8cage 16 -- r7c6 becomes 2 and r7c7 and r8c7 become 68 Cannot be 9 and 5 because r7c9 is 5
Only number in a row -- r7c4 becomes 4
cleanup N9 (68 pair) -- basic
cleanup N6 (59 pair) -- basic
cleanup N9cage 7 -- basic
cleanup N3cage 12 -- basic r2c7 becomes 347, r2c8 becomes 589
cleanup N7cage 17 -- r7cw r7c3 becomes 6-8 and r8c3 becomes 5-7
cleanup N5cages 10 -- basic
cleanup N6cage 16 -- basic Unclear what's being cleaned up here. However at this stage 45 rule N6 r7c9 = 5 makes r4c7 become 7
cleanup row 4 (only 4 in N6 is row 4) -- remove 4 from N4 and N5 row 4 Your mistake was in the previous step! N6 cage 16 can also be 1456.
Continue solving with 4 still in N6 cage 16
45 rule on N5 (again) -- r4cr loses 3 and 5
cleanup row 4 (only 5 in N5 is row 4) -- remove 5 from N3 row 4
cleanup N4cage 23 (repeat step 19) -- r3c3 loses 78
cleanup N4cage 13 -- r4c1 and r4c2 lose 67
45 rule N7 (the three squares fromcages that cross into other Ns) -- r6c1 becomes 3
Unique values in squares -- r5c1 becomes 1, r5c9 becomes 3, r7c9 becomes 5
cleanup N6cage 13 -- r4c8 and r4c9 lose 17
only number in a row -- r4c6 becomes 7
cleanup N4cage 23 (repeat step 19) -- r4c3->6
cleanup N6cage 13 -- r4c8 and r4c9 lose 4

And this is the problem! Once done, there are no 4s in N6! Everything above seem legit, but the only one that seems a tad odd is step 12. Is there an error that I simply do not see?

Top

Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 8:19 am

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Attachment:

17-07-23Hard.png [ 64.42 KiB | Viewed 15327 times ]

Thanks for asking! Its very hard to see your own errors!!

groston wrote:

12. 45 rule on sum of row 45: The sevencages with their top square in row 5 sum to 95, but (from step 8) 9 are in row 7 and r5c1 and r5c9 must be added to get to 90 -- r5c1 and r5c9 become 13

This should start "sum of row 56". The 3 cells at r7c159 = 9 as you say. As you say correctly, the cages in r56 sum to "95" which is 5 above 90. Therefore the two innies at r5c19 must be 5 less than r7c159 to get r56 down to 90.

You are using innies and outies to do the calculation. An easier way to do this is to just look at r4. Add those cages up to get the total for the two outies r5c19.

Here's the code for that puzzle.

triple click code:

It gets a score of 0.90.

logic used by SudokuSolver:

NOTE: SudokuSolver has some very weird ways of doing the "45" test.  For example, it can't do "45" on r4 like I suggested but gets this another way (see step 22 below: it will blow your mind!!)

Puzzle Completed.  Step Analysis:
2	Find Hidden Cages	3
5	Find Hidden Cages
84	Naked Singles
8	Naked Pairs
1	Hidden Singles
3	Locked Candidates (Box/Line)
2	Cage Placement	1
4	Cage Combinations
1	Cage Combinations Extended
1	45 Rule Single Innies/Outies
2	45 Rule Two Innies/Outies	2
85	Cage Cleanup	2
2	Cage Cleanup	1
54	Cage Cleanup
4	45 Rule Two Innies&Outies	2
Total solving time (seconds):		0.16
Calculated score:		0.90

Preliminaries
Cage 14(2) n6 - cells only uses 5689
Cage 15(2) n8 - cells only uses 6789
Cage 7(2) n9 - cells do not use 789
Cage 12(2) n8 - cells do not use 126
Cage 12(2) n3 - cells do not use 126
Cage 13(2) n3 - cells do not use 123
Cage 9(2) n7 - cells do not use 9
Cage 9(2) n1 - cells do not use 9
Cage 9(2) n1 - cells do not use 9
Cage 10(2) n5 - cells do not use 5
Cage 10(2) n5 - cells do not use 5
Cage 11(2) n8 - cells do not use 1
Cage 11(2) n4 - cells do not use 1

1. 45 Rule on r1 found single innie r1c5=2
1a. Combinations {1457} no longer valid in cage 17(4) n2

2. Naked Single 2 at r1c5 - removed from peer at r2c5

3. Naked Single 2 at r1c5 - removed from peer at r3c5

4. Naked Single 2 at r1c5 - removed from peer at r4c5

5. Naked Single 2 at r1c5 - removed from peer at r5c5

6. Naked Single 2 at r1c5 - removed from peer at r6c5

7. Naked Single 2 at r1c5 - removed from peer at r7c5
7a. Combinations {259} {268} no longer valid in cage 16(3) n58

8. Naked Single 2 at r1c5 - removed from peer at r1c1

9. Naked Single 2 at r1c5 - removed from peer at r1c2

10. Naked Single 2 at r1c5 - removed from peer at r1c3

11. Naked Single 2 at r1c5 - removed from peer at r1c4
11a. Combinations {2379} {2469} {2478} {2568} no longer valid in cage 21(4) n12

12. Naked Single 2 at r1c5 - removed from peer at r1c6

13. Naked Single 2 at r1c5 - removed from peer at r1c7

14. Naked Single 2 at r1c5 - removed from peer at r1c8

15. Naked Single 2 at r1c5 - removed from peer at r1c9
15a. Combinations {2389} {2479} {2569} {2578} no longer valid in cage 22(4) n23

16. Naked Single 2 at r1c5 - removed from peer at r2c4

17. Naked Single 2 at r1c5 - removed from peer at r2c6

18. Naked Single 2 at r1c5 - removed from peer at r3c4

19. Naked Single 2 at r1c5 - removed from peer at r3c6

20. Candidate 2 locked in r2 for n1 nowhere else in n1
20a. Cage sum in cage 9(2) n1 - removed 7 from r2c1

21. Candidate 1 locked in n8 for r7 nowhere else in r7

22. 45 Rule on r6789 - outies total 41 -> remaining cells r5c19 total 4
22a. Set candidates at r5c1 to 13
22b. Set candidates at r5c9 to 13
22c. Cage sum in cage 11(2) n4 - removed 8 from r6c3
22d. Cage sum in cage 10(2) n5 - removed 79 from r6c4
22e. Cage sum in cage 10(2) n5 - removed 79 from r6c6

23. Combinations {247} {256} no longer valid in cage 13(3) n4

24. Combinations {247} {256} no longer valid in cage 13(3) n6

25. 45 Rule on r3 - innies r3c19 total 13
25a. Removed candidates 13 from r3c1
25b. Removed candidate 4 from r3c9
25c. Cage sum in cage 9(2) n1 - removed 68 from r2c1
25d. Cage sum in cage 13(2) n3 - removed 9 from r2c9

26. 45 Rule on r2 - innies r2c19 total 9
26a. Found a hidden cage h9(2) n13

27. 45 Rule on n7 - outies r7c4 minus innies r7c1 equals 1
27a. Removed candidate 9 from r7c1
27b. Removed candidates 12 from r7c4

28. Candidate 2 locked in c4 for n5 nowhere else in n5
28a. Cage sum in cage 10(2) n5 - removed 8 from r5c6 - removed 8 from r6c6
28b. Combinations {28} no longer valid in cage 10(2) n5

29. 45 Rule on n6 - innies r4c7 minus outies r7c9 equals 2
29a. Removed candidates 123 from r4c7
29b. Removed candidates 89 from r7c9

30. 45 Rule on n4 - innies r4c3 minus outies r7c1 equals 3
30a. Removed candidates 1234 from r4c3
30b. Removed candidates 78 from r7c1
30c. Cage sum in innie/outie cells (r7c4)-(r7c1)=1 - removed 89 from r7c4

31. 45 Rule on n9 - innies r7c9 minus outies r7c6 equals 3
31a. Set candidates at r7c6 to 1234
31b. Removed candidates 23 from r7c9
31c. Cage sum in innie/outie cells (r4c7)-(r7c9)=2 - removed 45 from r4c7

32. 45 Rule on r2 - innies r2c9 equal outies r3c1
32a. Found a hidden innie/outie cells  (r2c9)=(r3c1)

33. 45 Rule on n47 - innies r4c3 minus outies r7c4 equals 2
33a. Found a hidden innie/outie cells (r4c3)-(r7c4)=2

34. 45 Rule on r3 - innies r3c9 minus outies r2c1 equals 4
34a. Found a hidden innie/outie cells (r3c9)-(r2c1)=4

35. 45 Rule on n69 - innies r4c7 minus outies r7c6 equals 5
35a. Found a hidden innie/outie cells (r4c7)-(r7c6)=5

36. Limited placement of candidates in cage 16(3) n89
36a. Removed 2 from r7c7
36b. Removed 12 from r8c7

37. Found a hidden cage h9(3) n789

38. Removed redundant candidates 789 from cage h9(3) n789
38a. Cage sum in innie/outie cells (r4c7)-(r7c9)=2 - removed 9 from r4c7
38b. Cage sum in innie/outie cells (r7c9)-(r7c6)=3 - removed 4 from r7c6

39. Combinations {457} no longer valid in cage 16(3) n89

40. Combinations {23459} no longer valid in cage 23(5) n456

41. Limited placement of candidates in cage 16(3) n89
41a. Removed 3 from r7c7
41b. Removed 3 from r8c7

42. Found a hidden cage h7(3) n8

43. Hidden single 2 found at r7c6 in cage h7(3) n8
43a. Cage sum in cage 16(3) n89 - removed 47 from r7c7 - removed 47 from r8c7
43b. Cage sum in cage h7(3) n8 - removed 3567 from r7c4 - removed 3456 from r7c5
43c. Only combinations {259} {268} valid in cage 16(3) n89
43d. Last cell in innie/outie cells (r7c9)-(r7c6)=3 at r7c9 set to 5
43e. Last cell in innie/outie cells (r4c7)-(r7c6)=5 at r4c7 set to 7

44. Naked Single 1 found at r7c5
44a. Cage sum in cage 16(3) n58 - removed 45 from r5c5 - removed 1345 from r6c5
44b. Last cell in cage h9(3) n789 at r7c1 set to 3
44c. Only combinations {169} {178} valid in cage 16(3) n58
44d. Only combination {135} valid in cage h9(3) n789

45. Naked Single 7 at r4c7 - removed from peer at r1c7

46. Naked Single 7 at r4c7 - removed from peer at r2c7
46a. Cage sum in cage 12(2) n3 - removed 5 from r2c8

47. Naked Single 7 at r4c7 - removed from peer at r3c7

48. Naked Single 7 at r4c7 - removed from peer at r4c1

49. Naked Single 7 at r4c7 - removed from peer at r4c2
49a. Combinations {157} no longer valid in cage 13(3) n4

50. Naked Single 7 at r4c7 - removed from peer at r4c3
50a. Combinations {12389} {12569} {13469} {13568} {23468} no longer valid in cage 23(5) n456
50b. Last cell in innie/outie cells (r4c3)-(r7c1)=3 at r4c3 set to 6
50c. Last cell in innie/outie cells (r4c3)-(r7c4)=2 at r7c4 set to 4

51. Naked Single 6 at r4c3 - removed from peer at r1c3

52. Naked Single 6 at r4c3 - removed from peer at r2c3
52a. Cage sum in cage 9(2) n1 - removed 3 from r2c2

53. Naked Single 6 at r4c3 - removed from peer at r3c3

54. Naked Single 6 at r4c3 - removed from peer at r5c3
54a. Cage sum in cage 11(2) n4 - removed 5 from r6c3

55. Naked Single 6 at r4c3 - removed from peer at r6c3
55a. Cage sum in cage 11(2) n4 - removed 5 from r5c3
55b. Combinations {56} no longer valid in cage 11(2) n4

56. Naked Single 6 at r4c3 - removed from peer at r7c3
56a. Only combinations {458} {467} valid in cage 17(3) n78

57. Naked Single 6 at r4c3 - removed from peer at r8c3
57a. Combinations {467} no longer valid in cage 17(3) n78

58. Naked Single 6 at r4c3 - removed from peer at r9c3
58a. Cage sum in cage 9(2) n7 - removed 3 from r9c2

59. Naked Single 6 at r4c3 - removed from peer at r4c1

60. Naked Single 6 at r4c3 - removed from peer at r4c2
60a. Combinations {346} no longer valid in cage 13(3) n4

61. Naked Single 6 at r4c3 - removed from peer at r4c4
61a. Only combinations {14567} {23567} valid in cage 23(5) n456

62. Naked Single 6 at r4c3 - removed from peer at r4c5

63. Naked Single 6 at r4c3 - removed from peer at r4c6

64. Naked Single 6 at r4c3 - removed from peer at r4c8

65. Naked Single 6 at r4c3 - removed from peer at r4c9
65a. Combinations {346} no longer valid in cage 13(3) n6

66. Naked Single 6 at r4c3 - removed from peer at r5c2
66a. Combinations {1269} {1278} {1458} {1467} {2457} no longer valid in cage 18(4) n47

67. Naked Single 6 at r4c3 - removed from peer at r6c1

68. Naked Single 6 at r4c3 - removed from peer at r6c2
68a. Combinations {1368} {2367} {3456} no longer valid in cage 18(4) n47

69. Naked Single 7 at r4c7 - removed from peer at r4c4

70. Naked Single 7 at r4c7 - removed from peer at r4c5

71. Naked Single 7 at r4c7 - removed from peer at r4c6

72. Naked Single 7 at r4c7 - removed from peer at r4c8

73. Naked Single 7 at r4c7 - removed from peer at r4c9
73a. Combinations {157} no longer valid in cage 13(3) n6

74. Naked Single 7 at r4c7 - removed from peer at r5c8
74a. Combinations {1249} {1267} {1348} {2347} no longer valid in cage 16(4) n69

75. Naked Single 7 at r4c7 - removed from peer at r6c8

76. Naked Single 7 at r4c7 - removed from peer at r6c9
76a. Combinations {1357} no longer valid in cage 16(4) n69

77. Naked Single 3 at r7c1 - removed from peer at r1c1

78. Naked Single 3 at r7c1 - removed from peer at r2c1
78a. Cage sum in cage 9(2) n1 - removed 6 from r3c1
78b. Cage sum in cage h9(2) n13 - removed 6 from r2c9
78c. Combinations {36} no longer valid in cage 9(2) n1
78d. Combinations {36} no longer valid in cage h9(2) n13
78e. Cage sum in innie/outie cells (r3c9)-(r2c1)=4 - removed 7 from r3c9
78f. Combinations {3468} {3567} no longer valid in combined cages 12(2) n3 & h9(2) n13

79. Naked Single 3 at r7c1 - removed from peer at r4c1

80. Naked Single 3 at r7c1 - removed from peer at r5c1
80a. Cage sum in cage h4(2) n46 - removed 1 from r5c9
80b. Combinations {238} no longer valid in cage 13(3) n4

81. Naked Single 1 found at r5c1
81a. Cage sum in cage 13(3) n4 - removed 125 from r4c1 - removed 1259 from r4c2

82. Naked Single 3 found at r5c9
82a. Cage sum in cage 13(3) n6 - removed 345 from r4c8 - removed 345 from r4c9
82b. Combinations {148} no longer valid in cage 13(3) n6

83. Naked Single 1 at r5c1 - removed from peer at r1c1

84. Naked Single 1 at r5c1 - removed from peer at r2c1
84a. Cage sum in cage 9(2) n1 - removed 8 from r3c1
84b. Cage sum in cage h9(2) n13 - removed 8 from r2c9
84c. Combinations {18} no longer valid in cage 9(2) n1
84d. Combinations {18} no longer valid in cage h9(2) n13
84e. Cage sum in innie/outie cells (r3c9)-(r2c1)=4 - removed 5 from r3c9
84f. Combinations {1389} {1578} no longer valid in combined cages 12(2) n3 & h9(2) n13

85. Naked Single 1 at r5c1 - removed from peer at r6c1

86. Naked Single 1 at r5c1 - removed from peer at r8c1

87. Naked Single 1 at r5c1 - removed from peer at r9c1

88. Naked Single 1 at r5c1 - removed from peer at r6c2
88a. Combinations {1359} no longer valid in cage 18(4) n47

89. Naked Single 3 at r5c9 - removed from peer at r1c9

90. Naked Single 3 at r5c9 - removed from peer at r6c9

91. Naked Single 3 at r5c9 - removed from peer at r8c9

92. Naked Single 3 at r5c9 - removed from peer at r9c9

93. Naked Single 3 at r5c9 - removed from peer at r6c8
93a. Combinations {2356} no longer valid in cage 16(4) n69

94. Naked Single 3 at r7c1 - removed from peer at r6c1

95. Naked Single 3 at r7c1 - removed from peer at r8c1

96. Naked Single 3 at r7c1 - removed from peer at r9c1

97. Naked Single 3 at r7c1 - removed from peer at r7c2

98. Naked Single 3 at r7c1 - removed from peer at r7c3

99. Naked Single 3 at r7c1 - removed from peer at r7c8

100. Naked Single 3 at r7c1 - removed from peer at r8c2
100a. Combinations {1379} {2369} {2378} {3458} {3467} no longer valid in cage 20(4) n7

101. Naked Single 3 at r7c1 - removed from peer at r8c3

102. Naked Single 3 at r7c1 - removed from peer at r9c3
102a. Cage sum in cage 9(2) n7 - removed 6 from r9c2
102b. Combinations {36} no longer valid in cage 9(2) n7

103. Naked Single 3 at r7c1 - removed from peer at r6c2

104. Naked Single 4 found at r7c4
104a. Cage sum in cage 17(3) n78 - removed 2479 from r7c3 - removed 12479 from r8c3

105. Naked Single 4 at r7c4 - removed from peer at r1c4

106. Naked Single 4 at r7c4 - removed from peer at r2c4

107. Naked Single 4 at r7c4 - removed from peer at r3c4

108. Naked Single 4 at r7c4 - removed from peer at r4c4

109. Naked Single 4 at r7c4 - removed from peer at r5c4
109a. Cage sum in cage 10(2) n5 - removed 6 from r6c4

110. Naked Single 4 at r7c4 - removed from peer at r6c4
110a. Cage sum in cage 10(2) n5 - removed 6 from r5c4
110b. Combinations {46} no longer valid in cage 10(2) n5
110c. Combinations {3469} {4567} no longer valid in combined cages 10(2) n5 & 12(2) n8

111. Naked Single 4 at r7c4 - removed from peer at r8c4
111a. Cage sum in cage 12(2) n8 - removed 8 from r9c4

112. Naked Single 4 at r7c4 - removed from peer at r9c4
112a. Cage sum in cage 12(2) n8 - removed 8 from r8c4
112b. Combinations {48} no longer valid in cage 12(2) n8
112c. Combinations {1489} {3478} no longer valid in combined cages 10(2) n5 & 12(2) n8
112d. Combinations {4689} no longer valid in combined cages 12(2) n8 & 15(2) n8

113. Naked Single 4 at r7c4 - removed from peer at r7c2

114. Naked Single 4 at r7c4 - removed from peer at r7c8

115. Naked Single 4 at r7c4 - removed from peer at r8c6
115a. Cage sum in cage 11(2) n8 - removed 7 from r9c6

116. Naked Single 4 at r7c4 - removed from peer at r9c6
116a. Cage sum in cage 11(2) n8 - removed 7 from r8c6
116b. Combinations {47} no longer valid in cage 11(2) n8
116c. Combinations {3479} {2489} {4568} no longer valid in combined cages 12(2) n8 & 11(2) n8
116d. Combinations {4679} no longer valid in combined cages 15(2) n8 & 11(2) n8

117. Naked Single 1 at r7c5 - removed from peer at r2c5

118. Naked Single 1 at r7c5 - removed from peer at r3c5

119. Naked Single 1 at r7c5 - removed from peer at r4c5

120. Naked Single 2 at r7c6 - removed from peer at r8c6
120a. Cage sum in cage 11(2) n8 - removed 9 from r9c6

121. Naked Single 2 at r7c6 - removed from peer at r9c6
121a. Cage sum in cage 11(2) n8 - removed 9 from r8c6
121b. Combinations {29} no longer valid in cage 11(2) n8
121c. Combinations {2478} {2568} {2379} {2469} no longer valid in combined cages 10(2) n5 & 11(2) n8
121d. Combinations {2579} no longer valid in combined cages 12(2) n8 & 11(2) n8
121e. Combinations {2789} no longer valid in combined cages 15(2) n8 & 11(2) n8

122. Naked Single 2 at r7c6 - removed from peer at r7c2

123. Naked Single 2 at r7c6 - removed from peer at r7c8

124. Naked Single 5 at r7c9 - removed from peer at r1c9

125. Naked Single 5 at r7c9 - removed from peer at r2c9
125a. Cage sum in cage 13(2) n3 - removed 8 from r3c9
125b. Cage sum in cage h9(2) n13 - removed 4 from r2c1
125c. Combinations {58} no longer valid in cage 13(2) n3
125d. Cage sum in innie/outie cells  (r2c9)=(r3c1) - removed 5 from r3c1

126. Naked Single 5 at r7c9 - removed from peer at r6c9

127. Naked Single 5 at r7c9 - removed from peer at r8c9

128. Naked Single 5 at r7c9 - removed from peer at r9c9

129. Naked Single 5 at r7c9 - removed from peer at r7c2

130. Naked Single 5 at r7c9 - removed from peer at r7c3
130a. Cage sum in cage 17(3) n78 - removed 8 from r8c3

131. Naked Single 8 found at r7c3

132. Naked Single 5 found at r8c3

133. Naked Single 8 at r7c3 - removed from peer at r1c3

134. Naked Single 8 at r7c3 - removed from peer at r2c3
134a. Cage sum in cage 9(2) n1 - removed 1 from r2c2

135. Naked Single 8 at r7c3 - removed from peer at r3c3

136. Naked Single 8 at r7c3 - removed from peer at r5c3
136a. Cage sum in cage 11(2) n4 - removed 3 from r6c3
136b. Combinations {38} no longer valid in cage 11(2) n4

137. Naked Single 8 at r7c3 - removed from peer at r9c3
137a. Cage sum in cage 9(2) n7 - removed 1 from r9c2

138. Naked Single 8 at r7c3 - removed from peer at r7c2

139. Naked Single 8 at r7c3 - removed from peer at r7c7
139a. Cage sum in cage 16(3) n89 - removed 6 from r8c7

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

141. Naked Single 8 at r7c3 - removed from peer at r8c1

142. Naked Single 8 at r7c3 - removed from peer at r8c2

143. Naked Single 8 at r7c3 - removed from peer at r9c1
143a. Only combinations {1469} {2459} {2567} valid in cage 20(4) n7

144. Naked Single 8 at r7c3 - removed from peer at r9c2
144a. Cage sum in cage 9(2) n7 - removed 1 from r9c3
144b. Combinations {18} no longer valid in cage 9(2) n7
144c. Combinations {1258} {1348} no longer valid in combined cages 9(2) n7 & 7(2) n9

145. Naked Single 5 at r7c9 - removed from peer at r7c7
145a. Cage sum in cage 16(3) n89 - removed 9 from r8c7

146. Naked Single 5 at r7c9 - removed from peer at r7c8

147. Naked Single 5 at r7c9 - removed from peer at r8c7
147a. Cage sum in cage 16(3) n89 - removed 9 from r7c7
147b. Combinations {259} no longer valid in cage 16(3) n89

148. Naked Single 6 found at r7c7

149. Naked Single 8 found at r8c7

150. Naked Single 6 at r7c7 - removed from peer at r1c7

151. Naked Single 6 at r7c7 - removed from peer at r3c7

152. Naked Single 6 at r7c7 - removed from peer at r5c7
152a. Cage sum in cage 14(2) n6 - removed 8 from r6c7

153. Naked Single 6 at r7c7 - removed from peer at r6c7
153a. Cage sum in cage 14(2) n6 - removed 8 from r5c7
153b. Combinations {68} no longer valid in cage 14(2) n6

154. Naked Single 6 at r7c7 - removed from peer at r9c7
154a. Cage sum in cage 7(2) n9 - removed 1 from r9c8

155. Naked Single 6 at r7c7 - removed from peer at r7c2

156. Naked Single 6 at r7c7 - removed from peer at r7c8

157. Naked Single 6 at r7c7 - removed from peer at r8c8

158. Naked Single 6 at r7c7 - removed from peer at r8c9

159. Naked Single 6 at r7c7 - removed from peer at r9c8
159a. Cage sum in cage 7(2) n9 - removed 1 from r9c7
159b. Combinations {16} no longer valid in cage 7(2) n9
159c. Only combination {2347} valid in combined cages 9(2) n7 & 7(2) n9

160. Naked Single 6 at r7c7 - removed from peer at r9c9
160a. Combinations {1369} {1468} {1567} {2368} {2467} no longer valid in cage 19(4) n9

161. Naked Single 5 at r7c9 - removed from peer at r8c8
161a. Only combinations {1279} {1378} valid in cage 19(4) n9

162. Naked Single 5 at r7c9 - removed from peer at r9c7
162a. Cage sum in cage 7(2) n9 - removed 2 from r9c8

163. Naked Single 5 at r7c9 - removed from peer at r9c8
163a. Cage sum in cage 7(2) n9 - removed 2 from r9c7
163b. Combinations {25} no longer valid in cage 7(2) n9

164. Naked Single 5 at r7c9 - removed from peer at r5c8

165. Naked Single 5 at r7c9 - removed from peer at r6c8

166. Naked Single 5 at r8c3 - removed from peer at r1c3

167. Naked Single 5 at r8c3 - removed from peer at r2c3
167a. Cage sum in cage 9(2) n1 - removed 4 from r2c2

168. Naked Single 5 at r8c3 - removed from peer at r3c3

169. Naked Single 5 at r8c3 - removed from peer at r9c3
169a. Cage sum in cage 9(2) n7 - removed 4 from r9c2

170. Naked Single 5 at r8c3 - removed from peer at r8c1

171. Naked Single 5 at r8c3 - removed from peer at r8c2

172. Naked Single 5 at r8c3 - removed from peer at r8c4
172a. Cage sum in cage 12(2) n8 - removed 7 from r9c4

173. Naked Single 5 at r8c3 - removed from peer at r8c6
173a. Cage sum in cage 11(2) n8 - removed 6 from r9c6

174. Naked Single 5 at r8c3 - removed from peer at r9c1
174a. Only combination {1469} valid in cage 20(4) n7

175. Naked Single 5 at r8c3 - removed from peer at r9c2
175a. Cage sum in cage 9(2) n7 - removed 4 from r9c3
175b. Combinations {45} no longer valid in cage 9(2) n7

176. Naked Single 8 at r8c7 - removed from peer at r1c7

177. Naked Single 8 at r8c7 - removed from peer at r2c7
177a. Cage sum in cage 12(2) n3 - removed 4 from r2c8

178. Naked Single 8 at r8c7 - removed from peer at r3c7

179. Naked Single 8 at r8c7 - removed from peer at r8c5
179a. Cage sum in cage 15(2) n8 - removed 7 from r9c5

180. Naked Single 8 at r8c7 - removed from peer at r8c6
180a. Cage sum in cage 11(2) n8 - removed 3 from r9c6

181. Naked Single 8 at r8c7 - removed from peer at r8c8

182. Naked Single 8 at r8c7 - removed from peer at r8c9

183. Naked Single 8 at r8c7 - removed from peer at r9c9
183a. Combinations {1378} no longer valid in cage 19(4) n9

184. Naked pair {34} found at r9c78
184a. Cage sum in cage 12(2) n8 - removed 9 from r8c4

185. Naked pair {27} found at r9c23

186. Naked Single 9 found at r7c2

187. Naked Single 9 at r7c2 - removed from peer at r1c2

188. Naked Single 9 at r7c2 - removed from peer at r3c2

189. Naked Single 9 at r7c2 - removed from peer at r5c2

190. Naked Single 9 at r7c2 - removed from peer at r6c2

191. Naked Single 9 at r7c2 - removed from peer at r8c2

192. Naked Single 9 at r7c2 - removed from peer at r7c8

193. Naked Single 7 found at r7c8

194. Naked Single 9 at r7c2 - removed from peer at r8c1

195. Naked Single 9 at r7c2 - removed from peer at r9c1

196. Naked Single 7 at r7c8 - removed from peer at r1c8

197. Naked Single 7 at r7c8 - removed from peer at r2c8
197a. Cage sum in cage 12(2) n3 - removed 5 from r2c7
197b. Combinations {57} no longer valid in cage 12(2) n3
197c. Combinations {3589} {4579} no longer valid in combined cages 12(2) n3 & 13(2) n3

198. Naked Single 7 at r7c8 - removed from peer at r3c8

199. Naked Single 7 at r7c8 - removed from peer at r8c8

200. Naked Single 7 at r7c8 - removed from peer at r8c9

201. Naked Single 6 found at r9c1
201a. Cage sum in cage 20(4) n7 - removed 6 from r8c1 - removed 46 from r8c2

202. Naked Single 4 found at r8c1

203. Naked Single 1 found at r8c2

204. Naked Single 4 at r8c1 - removed from peer at r1c1

205. Naked Single 4 at r8c1 - removed from peer at r3c1
205a. Cage sum in cage 9(2) n1 - removed 5 from r2c1
205b. Cage sum in cage h13(2) n13 - removed 9 from r3c9
205c. Combinations {45} no longer valid in cage 9(2) n1
205d. Only combination {67} valid in cage h13(2) n13
205e. Cage sum in innie/outie cells  (r2c9)=(r3c1) - removed 4 from r2c9
205f. Combinations {1368} {1458} {3456} no longer valid in combined cages 9(2) n1 & 9(2) n1

206. Naked Single 2 found at r2c1

207. Naked Single 7 found at r2c9

208. Naked Single 7 found at r3c1

209. Naked Single 6 found at r3c9

210. Naked Single 2 at r2c1 - removed from peer at r6c1

211. Naked Single 2 at r2c1 - removed from peer at r2c2
211a. Cage sum in cage 9(2) n1 - removed 7 from r2c3

212. Naked Single 2 at r2c1 - removed from peer at r2c3
212a. Cage sum in cage 9(2) n1 - removed 7 from r2c2
212b. Combinations {27} no longer valid in cage 9(2) n1
212c. Only combinations {1389} {3468} {3459} valid in combined cages 9(2) n1 & 12(2) n3

213. Naked Single 7 at r2c9 - removed from peer at r1c9

214. Naked Single 7 at r2c9 - removed from peer at r2c4

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

216. Naked Single 7 at r2c9 - removed from peer at r2c6
216a. Combinations {2357} no longer valid in cage 17(4) n2
216b. Combinations {357} no longer valid in split cage 15(3) n2

217. Naked Single 7 at r3c1 - removed from peer at r1c1

218. Naked Single 7 at r3c1 - removed from peer at r6c1

219. Naked Single 7 at r3c1 - removed from peer at r3c2

220. Naked Single 7 at r3c1 - removed from peer at r3c3

221. Naked Single 7 at r3c1 - removed from peer at r3c4

222. Naked Single 7 at r3c1 - removed from peer at r3c5

223. Naked Single 7 at r3c1 - removed from peer at r3c6
223a. Only combination {1234589} valid in cage 32(7) n123

224. Naked Single 7 at r3c1 - removed from peer at r1c2

225. Naked Single 7 at r3c1 - removed from peer at r1c3

226. Naked Single 6 at r3c9 - removed from peer at r1c9

227. Naked Single 6 at r3c9 - removed from peer at r6c9

228. Naked Single 6 at r3c9 - removed from peer at r3c2

229. Naked Single 6 at r3c9 - removed from peer at r3c4

230. Naked Single 6 at r3c9 - removed from peer at r3c5

231. Naked Single 6 at r3c9 - removed from peer at r3c6

232. Naked Single 6 at r3c9 - removed from peer at r3c8

233. Naked Single 6 at r3c9 - removed from peer at r1c8

234. Naked Single 4 at r8c1 - removed from peer at r4c1
234a. Cage sum in cage 13(3) n4 - removed 8 from r4c2

235. Naked Single 4 at r8c1 - removed from peer at r6c1

236. Naked Single 1 at r8c2 - removed from peer at r1c2

237. Naked Single 1 at r8c2 - removed from peer at r3c2

238. Naked Single 1 at r8c2 - removed from peer at r8c8

239. Naked Single 1 at r8c2 - removed from peer at r8c9

240. Naked Single 6 at r9c1 - removed from peer at r1c1

241. Naked Single 6 at r9c1 - removed from peer at r9c5
241a. Cage sum in cage 15(2) n8 - removed 9 from r8c5

242. Naked pair {59} found at r56c7
242a. Cage sum in cage 12(2) n3 - removed 3 from r2c8
242b. Cage sum in cage 13(3) n6 - removed 1 from r4c8 - removed 1 from r4c9
242c. Combinations {139} no longer valid in cage 13(3) n6

243. Naked pair {28} found at r4c89
243a. Cage sum in cage 13(3) n4 - removed 4 from r4c2
243b. Combinations {148} no longer valid in cage 13(3) n4
243c. Combinations {23567} no longer valid in cage 23(5) n456
243d. Combinations {1258} no longer valid in cage 16(4) n69

244. Naked Single 9 found at r4c1

245. Naked Single 3 found at r4c2

246. Naked Single 9 at r4c1 - removed from peer at r1c1

247. Naked Single 9 at r4c1 - removed from peer at r6c1
247a. Combinations {2349} no longer valid in cage 18(4) n47

248. Naked Single 9 at r4c1 - removed from peer at r4c4

249. Naked Single 9 at r4c1 - removed from peer at r4c5

250. Naked Single 9 at r4c1 - removed from peer at r4c6

251. Naked Single 9 at r4c1 - removed from peer at r5c3
251a. Cage sum in cage 11(2) n4 - removed 2 from r6c3

252. Naked Single 9 at r4c1 - removed from peer at r6c3
252a. Cage sum in cage 11(2) n4 - removed 2 from r5c3
252b. Combinations {29} no longer valid in cage 11(2) n4

253. Naked Single 3 at r4c2 - removed from peer at r1c2

254. Naked Single 3 at r4c2 - removed from peer at r3c2

255. Naked Single 3 at r4c2 - removed from peer at r4c4

256. Naked Single 3 at r4c2 - removed from peer at r4c5

257. Naked Single 3 at r4c2 - removed from peer at r4c6

258. Naked pair {47} found at r56c3
258a. Cage sum in cage 9(2) n1 - removed 5 from r2c2
258b. Cage sum in cage 9(2) n7 - removed 2 from r9c2
258c. Combinations {45} no longer valid in cage 9(2) n1
258d. Combinations {3459} no longer valid in combined cages 9(2) n1 & 12(2) n3

259. Naked Single 7 found at r9c2

260. Naked Single 2 found at r9c3

261. Naked pair {29} found at r8c89

262. Naked Single 1 found at r9c9

263. Naked Single 1 at r9c9 - removed from peer at r1c9

264. Naked Single 1 at r9c9 - removed from peer at r6c9

265. Naked Single 4 found at r6c9
265a. Cage sum in cage 16(4) n69 - removed 4 from r5c8 - removed 46 from r6c8

266. Naked Single 6 found at r5c8

267. Naked Single 1 found at r6c8

268. Naked Single 6 at r5c8 - removed from peer at r5c5
268a. Cage sum in cage 16(3) n58 - removed 9 from r6c5

269. Naked Single 6 at r5c8 - removed from peer at r5c6
269a. Cage sum in cage 10(2) n5 - removed 4 from r6c6

270. Naked Single 1 at r6c8 - removed from peer at r1c8

271. Naked Single 1 at r6c8 - removed from peer at r3c8

272. Naked Single 1 at r6c8 - removed from peer at r6c4
272a. Cage sum in cage 10(2) n5 - removed 9 from r5c4
272b. Combinations {19} no longer valid in cage 10(2) n5
272c. Combinations {1579} no longer valid in combined cages 10(2) n5 & 12(2) n8

273. Naked Single 1 at r6c8 - removed from peer at r6c6
273a. Cage sum in cage 10(2) n5 - removed 9 from r5c6
273b. Combinations {19} no longer valid in cage 10(2) n5
273c. Combinations {1289} {1379} {1469} no longer valid in combined cages 10(2) n5 & 10(2) n5
273d. Only combinations {3567} {3468} valid in combined cages 10(2) n5 & 11(2) n8

274. Naked Single 4 at r6c9 - removed from peer at r1c9

275. Naked Single 4 at r6c9 - removed from peer at r6c3
275a. Cage sum in cage 11(2) n4 - removed 7 from r5c3

276. Naked Single 4 found at r5c3

277. Naked Single 7 found at r6c3

278. Naked Single 4 at r5c3 - removed from peer at r5c6
278a. Cage sum in cage 10(2) n5 - removed 6 from r6c6
278b. Combinations {46} no longer valid in cage 10(2) n5
278c. Only combination {2378} valid in combined cages 10(2) n5 & 10(2) n5
278d. Combinations {3468} no longer valid in combined cages 10(2) n5 & 11(2) n8

279. Naked Single 7 found at r5c6

280. Naked Single 3 found at r6c6

281. Naked Single 7 at r5c6 - removed from peer at r1c6
281a. Only combinations {1489} {3469} {3568} valid in cage 22(4) n23

282. Naked Single 7 at r5c6 - removed from peer at r5c4
282a. Cage sum in cage 10(2) n5 - removed 3 from r6c4
282b. Combinations {37} no longer valid in cage 10(2) n5

283. Naked Single 7 at r5c6 - removed from peer at r5c5
283a. Cage sum in cage 16(3) n58 - removed 8 from r6c5

284. Naked Single 7 at r5c6 - removed from peer at r6c5
284a. Cage sum in cage 16(3) n58 - removed 8 from r5c5
284b. Combinations {178} no longer valid in cage 16(3) n58

285. Naked Single 9 found at r5c5

286. Naked Single 6 found at r6c5

287. Naked Single 9 at r5c5 - removed from peer at r2c5

288. Naked Single 9 at r5c5 - removed from peer at r3c5

289. Naked Single 9 at r5c5 - removed from peer at r9c5
289a. Cage sum in cage 15(2) n8 - removed 6 from r8c5
289b. Combinations {69} no longer valid in cage 15(2) n8
289c. Combinations {5679} no longer valid in combined cages 12(2) n8 & 15(2) n8
289d. Combinations {3689} no longer valid in combined cages 15(2) n8 & 11(2) n8

290. Naked Single 7 found at r8c5

291. Naked Single 8 found at r9c5

292. Naked Single 9 at r5c5 - removed from peer at r5c7
292a. Cage sum in cage 14(2) n6 - removed 5 from r6c7

293. Naked Single 5 found at r5c7

294. Naked Single 9 found at r6c7

295. Naked Single 5 at r5c7 - removed from peer at r5c2

296. Naked Single 6 at r6c5 - removed from peer at r2c5

297. Naked Single 3 at r6c6 - removed from peer at r1c6

298. Naked Single 3 at r6c6 - removed from peer at r2c6

299. Naked Single 3 at r6c6 - removed from peer at r3c6

300. Naked Single 3 at r6c6 - removed from peer at r8c6
300a. Cage sum in cage 11(2) n8 - removed 8 from r9c6
300b. Combinations {38} no longer valid in cage 11(2) n8
300c. Combinations {3578} no longer valid in combined cages 12(2) n8 & 11(2) n8

301. Naked Single 6 found at r8c6

302. Naked Single 5 found at r9c6

303. Naked Single 7 at r8c5 - removed from peer at r8c4
303a. Cage sum in cage 12(2) n8 - removed 5 from r9c4
303b. Combinations {57} no longer valid in cage 12(2) n8
303c. Combinations {2578} no longer valid in combined cages 10(2) n5 & 12(2) n8

304. Naked Single 3 found at r8c4

305. Naked Single 9 found at r9c4

306. Naked Single 3 at r8c4 - removed from peer at r1c4

307. Naked Single 3 at r8c4 - removed from peer at r2c4

308. Naked Single 3 at r8c4 - removed from peer at r3c4

309. Naked Single 6 at r8c6 - removed from peer at r1c6
309a. Only combination {1489} valid in cage 22(4) n23

310. Naked Single 6 at r8c6 - removed from peer at r2c6

311. Naked Single 9 at r9c4 - removed from peer at r1c4

312. Naked Single 9 at r9c4 - removed from peer at r2c4

313. Naked Single 9 at r9c4 - removed from peer at r3c4

314. Naked Single 8 at r9c5 - removed from peer at r2c5

315. Naked Single 8 at r9c5 - removed from peer at r3c5

316. Naked Single 5 at r9c6 - removed from peer at r1c6

317. Naked Single 5 at r9c6 - removed from peer at r2c6

318. Naked Single 5 at r9c6 - removed from peer at r3c6

319. Naked Single 5 at r9c6 - removed from peer at r4c6

320. Naked pair {28} found at r56c4

321. Naked pair {15} found at r34c4
321a. Combinations {1259} {2348} no longer valid in cage 17(4) n2
321b. Combinations {159} {348} no longer valid in split cage 15(3) n2

322. Naked Single 6 found at r2c4
322a. Cage sum in cage 17(4) n2 - removed 34 from r2c5 - removed 189 from r2c6
322b. Combinations {1268} no longer valid in cage 17(4) n2
322c. Combinations {168} no longer valid in split cage 15(3) n2

323. Naked Single 5 found at r2c5

324. Naked Single 4 found at r2c6

325. Naked Single 6 at r2c4 - removed from peer at r1c4
325a. Only combinations {1479} {1578} {3567} valid in cage 21(4) n12

326. Naked Single 7 found at r1c4

327. Naked Single 6 at r2c4 - removed from peer at r2c2
327a. Cage sum in cage 9(2) n1 - removed 3 from r2c3
327b. Combinations {36} no longer valid in cage 9(2) n1
327c. Combinations {3468} no longer valid in combined cages 9(2) n1 & 12(2) n3

328. Naked Single 8 found at r2c2

329. Naked Single 1 found at r2c3

330. Naked Single 8 at r2c2 - removed from peer at r1c2

331. Naked Single 8 at r2c2 - removed from peer at r3c2

332. Naked Single 8 at r2c2 - removed from peer at r5c2

333. Naked Single 8 at r2c2 - removed from peer at r6c2

334. Naked Single 8 at r2c2 - removed from peer at r2c8
334a. Cage sum in cage 12(2) n3 - removed 4 from r2c7
334b. Combinations {48} no longer valid in cage 12(2) n3

335. Naked Single 3 found at r2c7

336. Naked Single 9 found at r2c8

337. Naked Single 8 at r2c2 - removed from peer at r1c1
337a. Only combination {3567} valid in cage 21(4) n12

338. Naked Single 5 found at r1c1
338a. Cage sum in cage 21(4) n12 - removed 45 from r1c2 - removed 19 from r1c3

339. Naked Single 6 found at r1c2

340. Naked Single 3 found at r1c3

341. Naked Single 5 at r1c1 - removed from peer at r6c1

342. Naked Single 8 found at r6c1
342a. Cage sum in cage 18(4) n47 - removed 2 from r6c2

343. Naked Single 2 found at r5c2

344. Naked Single 5 found at r6c2

345. Naked Single 5 at r1c1 - removed from peer at r1c8

346. Naked Single 5 at r1c1 - removed from peer at r3c2

347. Naked Single 4 found at r3c2

348. Naked Single 3 at r1c3 - removed from peer at r3c3

349. Naked Single 3 at r1c3 - removed from peer at r1c7

350. Naked Single 3 at r1c3 - removed from peer at r1c8

351. Naked Single 1 at r2c3 - removed from peer at r3c3

352. Naked Single 9 found at r3c3

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

354. Naked Single 5 at r2c5 - removed from peer at r4c5

355. Naked Single 5 at r2c5 - removed from peer at r3c4

356. Naked Single 4 at r2c6 - removed from peer at r1c6

357. Naked Single 4 at r2c6 - removed from peer at r3c6

358. Naked Single 4 at r2c6 - removed from peer at r4c6

359. Naked Single 4 found at r4c5
359a. Cage sum in cage 23(5) n456 - removed 1 from r4c4

360. Naked Single 1 found at r3c4

361. Naked Single 5 found at r4c4

362. Naked Single 1 found at r4c6

363. Naked Single 4 at r2c6 - removed from peer at r3c5

364. Naked Single 3 found at r3c5

365. Naked Single 3 at r2c7 - removed from peer at r3c7

366. Naked Single 3 at r2c7 - removed from peer at r9c7
366a. Cage sum in cage 7(2) n9 - removed 4 from r9c8

367. Naked Single 4 found at r9c7

368. Naked Single 3 found at r9c8

369. Naked Single 3 at r2c7 - removed from peer at r3c8

370. Naked Single 9 at r2c8 - removed from peer at r1c8

371. Naked Single 9 at r2c8 - removed from peer at r3c8

372. Naked Single 9 at r2c8 - removed from peer at r8c8
372a. Cage sum in cage 19(4) n9 - removed 2 from r8c9

373. Naked Single 2 found at r8c8

374. Naked Single 9 found at r8c9

375. Naked Single 9 at r2c8 - removed from peer at r1c9

376. Naked Single 8 found at r1c9

377. Naked Single 8 at r1c9 - removed from peer at r4c9
377a. Cage sum in cage 13(3) n6 - removed 2 from r4c8

378. Naked Single 8 found at r4c8

379. Naked Single 2 found at r4c9

380. Naked Single 8 at r1c9 - removed from peer at r1c6

381. Naked Single 8 at r1c9 - removed from peer at r1c8

382. Naked Single 4 found at r1c8
382a. Cage sum in cage 22(4) n23 - removed 1 from r1c6 - removed 4 from r1c7

383. Naked Single 9 found at r1c6

384. Naked Single 1 found at r1c7

385. Naked Single 9 at r1c6 - removed from peer at r3c6

386. Naked Single 1 at r1c7 - removed from peer at r3c7

387. Naked Single 4 at r1c8 - removed from peer at r3c8

388. Naked Single 4 at r1c8 - removed from peer at r3c7

389. Naked Single 2 found at r3c7
389a. Cage sum in cage 32(7) n123 - removed 1 from r3c6 - removed 28 from r3c8

390. Naked Single 8 found at r3c6

391. Naked Single 5 found at r3c8

392. Naked Single 2 at r5c2 - removed from peer at r5c4
392a. Cage sum in cage 10(2) n5 - removed 8 from r6c4

393. Naked Single 8 found at r5c4

394. Naked Single 2 found at r6c4

Puzzle Complete

Don't hesitate to post again for further clarification. Innies +/- outies are mind bending!!

Cheers
Ed

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groston

Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 2:29 pm

Addict

Joined: Fri Jun 23, 2023 4:24 am
Posts: 24

Ed - Thank you. You are correct, I could have looked at just row 4 instead of rows 5 and 6. However, in both cases, squares r5c1 and r5c9 sum to 4, and as I had posted they become 1/3. So, this does not seem to be the actual mistake. Any further suggestions?

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Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 9:21 pm

Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia

Sorry. I thought "13" was the hidden cage sum rather than a combination list (we normally put these in brackets to make this clear, eg {13} for unordered sets).

Can you have a look at step 29? What is the "basic cleanup" you do in the 16(4)r5c8? How did you get rid of the 4s? Why not {146}[5]?

This is what I have at the end of step 28

.-------------------------------.-------------------------------.-------------------------------.
| 1456789   13456789  13456789  | 1356789   2         13456789  | 1347      13456789  1456789   |
| 1245      12345678  12345678  | 1356789   345       13456789  | 347       589       4578      |
| 4578      123456789 123456789 | 1356789   345       13456789  | 12347     123456789 5689      |
:-------------------------------+-------------------------------+-------------------------------:
| 12456789  123456789 456789    | 12356     345       13456     | 47        1234678   124678    |
| 13        2456789   2456789   | 2789      6789      4679      | 59        24678     13        |
| 12456789  123456789 2345679   | 1238      6789      1346      | 59        1234678   124678    |
:-------------------------------+-------------------------------+-------------------------------:
| 35        6789      678       | 4         1         2         | 68        79        35        |
| 12456789  123456789 567       | 35789     6789      356789    | 68        1234579   124579    |
| 12456789  12345678  12345678  | 35789     6789      356789    | 1234      1345      124579    |
'-------------------------------.-------------------------------.-------------------------------'

.-----------------------------------------------------------------------.
|(21)   :       :       :       |(17)   |(22)   :       :       :       |
|  1    :  1 3  :  1 3  :  1 3  |       |  1 3  :  1 3  :  1 3  :  1    |
|  456  :  456  :  456  :   56  |   2   |  456  :  4    :  456  :  456  |
|  789  :  789  :  789  :  789  |       |  789  :  7    :  789  :  789  |
|-------------------------------|.......|-------------------------------|
|( 9)   |( 9)   :       |       :       :       |(12)   :       |(13)   |
|  12   |  123  :  123  |  1 3  :    3  :  1 3  |    3  :       |       |
|  45   |  456  :  456  |   56  :  45   :  456  |  4    :   5   |  45   |
|       |  78   :  78   |  789  :       :  789  |  7    :   89  |  78   |
|.......|---------------|-----------------------|---------------|.......|
|       |(32)   :       :       :       :       :       :       |       |
|       |  123  :  123  :  1 3  :    3  :  1 3  :  123  :  123  |       |
|  45   |  456  :  456  :   56  :  45   :  456  :  4    :  456  |   56  |
|  78   |  789  :  789  :  789  :       :  789  :  7    :  789  |   89  |
|-------|-------------------------------------------------------|-------|
|(13)   :       |(23)   :       :       :       :       |(13)   :       |
|  12   :  123  |       :  123  :    3  :  1 3  :       |  123  :  12   |
|  456  :  456  |  456  :   56  :  45   :  456  :  4    |  4 6  :  4 6  |
|  789  :  789  |  789  :       :       :       :  7    |  78   :  78   |
|.......--------|---------------------------------------|-------:.......|
|       |(18)   |(11)   |(10)   |(16)   |(10)   |(14)   |(16)   |       |
|  1 3  |   2   |   2   |   2   |       |       |       |   2   |  1 3  |
|       |  456  |  456  |       |    6  |  4 6  |   5   |  4 6  |       |
|       |  789  |  789  |  789  |  789  |  7 9  |    9  |  78   |       |
|-------|.......|.......|.......|.......|.......|.......|.......|-------|
|       :       |       |       |       |       |       |       :       |
|  12   :  123  |   23  |  123  |       |  1 3  |       |  123  :  12   |
|  456  :  456  |  456  |       |    6  |  4 6  |   5   |  4 6  :  4 6  |
|  789  :  789  |  7 9  |   8   |  789  |       |    9  |  78   :  78   |
|.......--------|-------|-------|.......|-------|-------|-------:.......|
|       |(20)   |(17)   :       |       |(16)   :       |(19)   |       |
|    3  |       |       :       |       |       :       |       |    3  |
|   5   |    6  |    6  :   4   |   1   |   2   :    6  |       |   5   |
|       |  789  |  78   :       |       |       :   8   |  7 9  |       |
|-------|.......|.......--------|-------|-------:.......|.......|-------|
|       :       |       |(12)   |(15)   |(11)   |       |       :       |
|  12   :  123  |       |    3  |       |    3  |       |  123  :  12   |
|  456  :  456  |   56  |   5   |    6  |   56  |    6  |  45   :  45   |
|  789  :  789  |  7    |  789  |  789  |  789  |   8   |  7 9  :  7 9  |
|.......--------|-------|.......|.......|.......|-------|-------:.......|
|       |( 9)   :       |       |       |       |( 7)   :       |       |
|  12   |  123  :  123  |    3  |       |    3  |  123  :  1 3  |  12   |
|  456  |  456  :  456  |   5   |    6  |   56  |  4    :  45   |  45   |
|  789  |  78   :  78   |  789  |  789  |  789  |       :       |  7 9  |
.-----------------------------------------------------------------------.

Cheers
Ed

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groston

Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 10:05 pm

Addict

Joined: Fri Jun 23, 2023 4:24 am
Posts: 24

It took a while, but I think you found my screw-up. For reasons of pure stupidity, I believe that I removed the 4s from N6cage 16 because I only looked at three squares, not all 4. also, sorry for all of the typos in my original posting...

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Andrew

Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Wed Jul 19, 2023 10:07 pm

Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada

Good to see that you found your error.

As you will see, I've just gone through your steps and added comments in your original post.

And I see that Ed has also gone through and found the same error.

Cheers,

Andrew

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HATMAN

Post subject: Re: Cannot figure out what I am doing wrong...

Posted: Thu Jul 20, 2023 7:45 am

Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia

I'm surprised by the SS score of 0.9 if you start innies R1, innies N8 it just rolls out.

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