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groston
 Post subject: How hard?
PostPosted: Sat Jul 29, 2023 3:48 am 
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Joined: Fri Jun 23, 2023 4:24 am
Posts: 24
I truly hope that some can truthfully tell me that the puzzlemadness.co.uk Daily Hard Killer Sudoku Puzzle dated 27 July 2023 was a hard one because it took quite a bit of effort to solve...
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Ed
 Post subject: Re: How hard?
PostPosted: Sat Jul 29, 2023 6:52 pm 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
I often have that feeling I missed something important. This wasn't one of them for me.

27 July Hard killer
Attachment:
27-07-23Hard.png
27-07-23Hard.png [ 67.2 KiB | Viewed 12380 times ]
triple click code:
3x3::k:3072:3072:1537:1537:4866:4866:4866:4355:4355:1796:1796:6405:1537:3590:3590:3335:3335:4355:2824:6405:6405:2057:2057:5130:3335:3335:4875:2824:6405:2572:2572:4109:5130:5130:1806:4875:3087:3856:2572:3089:4109:4109:2578:1806:4875:3087:3856:4373:3089:3089:4627:2578:2836:2836:3087:1558:4373:4373:4627:4627:5911:5911:2836:5400:1558:1558:3353:3353:5911:5911:2330:3355:5400:5400:4636:4636:4636:797:797:2330:3355:
Here's the SudokuSolver log. It's cracked by step 11. It gets 0.85.
SS log using Scoring solver order:
Preliminaries
Cage 3(2) n89 - cells ={12}
Cage 14(2) n2 - cells only uses 5689
Cage 15(2) n4 - cells only uses 6789
Cage 7(2) n6 - cells do not use 789
Cage 7(2) n1 - cells do not use 789
Cage 8(2) n2 - cells do not use 489
Cage 12(2) n1 - cells do not use 126
Cage 13(2) n8 - cells do not use 123
Cage 13(2) n9 - cells do not use 123
Cage 9(2) n9 - cells do not use 9
Cage 10(2) n6 - cells do not use 5
Cage 11(2) n14 - cells do not use 1
Cage 6(3) n12 - cells ={123}
Cage 6(3) n7 - cells ={123}
Cage 21(3) n7 - cells do not use 123
Cage 10(3) n45 - cells do not use 89
Cage 20(3) n256 - cells do not use 12
Cage 11(3) n69 - cells do not use 9
Cage 19(3) n36 - cells do not use 1
Cage 19(3) n23 - cells do not use 1
Cage 13(4) n3 - cells do not use 89

1. Naked pair {12} found at r9c67
1a. Cage sum in cage 9(2) n9 - removed 78 from r8c8
1b. Combinations {189} {279} no longer valid in cage 18(3) n78

2. Naked triple {123} found at r1c34 r2c4

3. Naked triple {123} found at r8c23 r7c2

4. 45 Rule on n3 - innies r1c7 r3c9 total 15
4a. Removed candidates 2345 from r1c7
4b. Removed candidates 2345 from r3c9
4c. Combinations {289} {379} no longer valid in cage 19(3) n23

5. 45 Rule on c9 - outies r16c8 total 15
5a. Set candidates at r1c8 to 789
5b. Set candidates at r6c8 to 678

6. Combinations {245} no longer valid in cage 11(3) n69
6a. Removed redundant candidates 5

7. 45 Rule on r1 - outies r2c49 total 9
7a. Set candidates at r2c9 to 678

8. Naked quad {6789} found at r1c78 r23c9
8a. Only combination {1345} valid in cage 13(4) n3

9. Combinations {359} no longer valid in cage 17(3) n3

10. Removed redundant candidates 2 from cage 13(4) n3

11. Naked quad {1345} found at r2c78 r3c78
11a. Only combinations {269} {278} valid in cage 17(3) n3

12. Naked Single 2 found at r1c9

13. Naked Single 2 at r1c9 - removed from peer at r4c9

14. Naked Single 2 at r1c9 - removed from peer at r5c9
14a. Combinations {289} no longer valid in cage 19(3) n36

15. Naked Single 2 at r1c9 - removed from peer at r6c9

16. Naked Single 2 at r1c9 - removed from peer at r7c9
16a. Combinations {128} {236} no longer valid in cage 11(3) n69

17. Naked Single 2 at r1c9 - removed from peer at r1c3

18. Naked Single 2 at r1c9 - removed from peer at r1c4

19. Naked pair {13} found at r1c34
19a. Cage sum in cage 12(2) n1 - removed 9 from r1c1 - removed 9 from r1c2
19b. Cage sum in cage h9(2) n23 - removed 68 from r2c9
19c. Combinations {39} no longer valid in cage 12(2) n1
19d. Only combination {27} valid in cage h9(2) n23
19e. Combinations {1369} {2359} no longer valid in combined cages 12(2) n1 & 7(2) n1
19f. Only combinations {1267} {2347} valid in combined cages 7(2) n1 & h9(2) n23
19g. Combinations {1589} {3569} no longer valid in combined cages 14(2) n2 & h9(2) n23

20. Naked Single 2 found at r2c4

21. Naked Single 2 at r2c4 - removed from peer at r3c4
21a. Cage sum in cage 8(2) n2 - removed 6 from r3c5

22. Naked Single 2 at r2c4 - removed from peer at r4c4

23. Naked Single 2 at r2c4 - removed from peer at r5c4

24. Naked Single 2 at r2c4 - removed from peer at r6c4

25. Naked Single 2 at r2c4 - removed from peer at r7c4

26. Naked Single 2 at r2c4 - removed from peer at r2c1
26a. Cage sum in cage 7(2) n1 - removed 5 from r2c2

27. Naked Single 2 at r2c4 - removed from peer at r2c2
27a. Cage sum in cage 7(2) n1 - removed 5 from r2c1
27b. Combinations {25} no longer valid in cage 7(2) n1
27c. Combinations {2458} no longer valid in combined cages 12(2) n1 & 7(2) n1
27d. Combinations {2568} no longer valid in combined cages 7(2) n1 & 14(2) n2

28. Naked Single 2 at r2c4 - removed from peer at r2c3

29. Naked Single 2 at r2c4 - removed from peer at r3c5
29a. Cage sum in cage 8(2) n2 - removed 6 from r3c4
29b. Combinations {26} no longer valid in cage 8(2) n2
29c. Combinations {2569} no longer valid in combined cages 14(2) n2 & 8(2) n2

30. Naked Single 7 found at r2c9
30a. Last cell in cage 17(3) n3 at r1c8 set to 8
30b. Combinations {269} no longer valid in cage 17(3) n3

31. Naked Single 8 at r1c8 - removed from peer at r6c8
31a. Last cell in cage h15(2) n36 at r6c8 set to 7
31b. Combinations {146} no longer valid in cage 11(3) n69
31c. Combinations {69} no longer valid in cage h15(2) n36
31d. Combinations {2569} {3469} no longer valid in combined cages 7(2) n6 & h15(2) n36
31e. Only combinations {3678} {4578} valid in combined cages 9(2) n9 & h15(2) n36

32. Naked Single 8 at r1c8 - removed from peer at r7c8

33. Naked Single 8 at r1c8 - removed from peer at r9c8
33a. Cage sum in cage 9(2) n9 - removed 1 from r8c8
33b. Combinations {18} no longer valid in cage 9(2) n9
33c. Combinations {1258} {1348} no longer valid in combined cages 7(2) n6 & 9(2) n9
33d. Combinations {1489} {1678} no longer valid in combined cages 9(2) n9 & 13(2) n9

34. Naked Single 8 at r1c8 - removed from peer at r1c1
34a. Cage sum in cage 12(2) n1 - removed 4 from r1c2

35. Naked Single 8 at r1c8 - removed from peer at r1c2
35a. Cage sum in cage 12(2) n1 - removed 4 from r1c1
35b. Combinations {48} no longer valid in cage 12(2) n1
35c. Combinations {1468} no longer valid in combined cages 12(2) n1 & 7(2) n1

36. Naked Single 8 at r1c8 - removed from peer at r1c5

37. Naked Single 8 at r1c8 - removed from peer at r1c6

38. Naked Single 8 at r1c8 - removed from peer at r1c7
38a. Cage sum in cage h15(2) n3 - removed 7 from r3c9
38b. Only combination {469} valid in cage 19(3) n23

39. Naked Single 8 at r1c8 - removed from peer at r3c9
39a. Cage sum in cage h15(2) n3 - removed 7 from r1c7
39b. Combinations {78} no longer valid in cage h15(2) n3

40. Naked Single 7 at r2c9 - removed from peer at r4c9

41. Naked Single 7 at r2c9 - removed from peer at r5c9
41a. Combinations {379} {478} no longer valid in cage 19(3) n36

42. Naked Single 7 at r2c9 - removed from peer at r6c9
42a. Cage sum in cage 11(3) n69 - removed 468 from r6c9 - removed 4678 from r7c9

43. Naked Single 7 at r2c9 - removed from peer at r8c9
43a. Cage sum in cage 13(2) n9 - removed 6 from r9c9

44. Naked Single 7 at r2c9 - removed from peer at r9c9
44a. Cage sum in cage 13(2) n9 - removed 6 from r8c9
44b. Combinations {67} no longer valid in cage 13(2) n9

45. Naked Single 7 at r2c9 - removed from peer at r2c3

46. Naked Single 7 at r6c8 - removed from peer at r7c8

47. Naked Single 7 at r6c8 - removed from peer at r9c8
47a. Cage sum in cage 9(2) n9 - removed 2 from r8c8
47b. Combinations {27} no longer valid in cage 9(2) n9
47c. Combinations {1267} {2347} no longer valid in combined cages 7(2) n6 & 9(2) n9
47d. Only combinations {3469} {3568} valid in combined cages 9(2) n9 & 13(2) n9

48. Naked Single 7 at r6c8 - removed from peer at r6c1

49. Naked Single 7 at r6c8 - removed from peer at r6c2
49a. Cage sum in cage 15(2) n4 - removed 8 from r5c2

50. Naked Single 7 at r6c8 - removed from peer at r6c3

51. Naked Single 7 at r6c8 - removed from peer at r6c4

52. Naked Single 7 at r6c8 - removed from peer at r6c5

53. Naked Single 7 at r6c8 - removed from peer at r6c6

54. Naked Single 7 at r6c8 - removed from peer at r6c7
54a. Cage sum in cage 10(2) n6 - removed 3 from r5c7

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

56. Naked Single 7 at r6c8 - removed from peer at r5c7
56a. Cage sum in cage 10(2) n6 - removed 3 from r6c7
56b. Combinations {37} no longer valid in cage 10(2) n6
56c. Combinations {1367} {2357} no longer valid in combined cages 7(2) n6 & 10(2) n6

57. Naked pair {57} found at r1c12
57a. Cage sum in cage 11(2) n14 - removed 46 from r4c1

58. Naked pair {13} found at r67c9

59. Hidden single 9 found at r7c8 in c8
59a. Combinations {2678} {3578} {4568} no longer valid in cage 23(4) n89

60. Naked Single 9 at r7c8 - removed from peer at r7c1

61. Naked Single 9 at r7c8 - removed from peer at r7c3

62. Naked Single 9 at r7c8 - removed from peer at r7c4

63. Naked Single 9 at r7c8 - removed from peer at r7c5

64. Naked Single 9 at r7c8 - removed from peer at r7c6

65. Naked Single 9 at r7c8 - removed from peer at r7c7

66. Naked Single 9 at r7c8 - removed from peer at r8c7

67. Naked Single 9 at r7c8 - removed from peer at r8c9
67a. Cage sum in cage 13(2) n9 - removed 4 from r9c9

68. Naked Single 9 at r7c8 - removed from peer at r9c9
68a. Cage sum in cage 13(2) n9 - removed 4 from r8c9
68b. Combinations {49} no longer valid in cage 13(2) n9
68c. Combinations {3469} no longer valid in combined cages 9(2) n9 & 13(2) n9

69. Naked Single 9 at r7c8 - removed from peer at r8c6

70. Naked pair {58} found at r89c9
70a. Cage sum in cage 9(2) n9 - removed 4 from r8c8 - removed 4 from r9c8
70b. Combinations {568} no longer valid in cage 19(3) n36
70c. Combinations {45} no longer valid in cage 9(2) n9

71. Naked pair {36} found at r89c8
71a. Cage sum in cage 7(2) n6 - removed 14 from r4c8 - removed 14 from r5c8
71b. Cage sum in cage 11(3) n69 - removed 1 from r6c9
71c. Only combination {25} valid in cage 7(2) n6
71d. Combinations {1349} {2348} no longer valid in combined cages 7(2) n6 & 10(2) n6
71e. Combinations {1456} no longer valid in combined cages 7(2) n6 & 9(2) n9

72. Naked Single 3 found at r6c9

73. Naked Single 1 found at r7c9

74. Naked Single 3 at r6c9 - removed from peer at r6c1

75. Naked Single 3 at r6c9 - removed from peer at r6c3

76. Naked Single 3 at r6c9 - removed from peer at r6c4

77. Naked Single 3 at r6c9 - removed from peer at r6c5

78. Naked Single 3 at r6c9 - removed from peer at r6c6

79. Naked Single 3 at r6c9 - removed from peer at r4c7

80. Naked Single 1 at r7c9 - removed from peer at r7c2

81. Naked Single 1 at r7c9 - removed from peer at r7c4

82. Naked Single 1 at r7c9 - removed from peer at r7c5

83. Naked Single 1 at r7c9 - removed from peer at r7c6

84. Naked Single 1 at r7c9 - removed from peer at r7c7

85. Naked Single 1 at r7c9 - removed from peer at r8c7

86. Naked Single 1 at r7c9 - removed from peer at r9c7
86a. Cage sum in cage 3(2) n89 - removed 2 from r9c6

87. Naked Single 1 found at r9c6

88. Naked Single 2 found at r9c7

89. Naked Single 1 at r9c6 - removed from peer at r5c6

90. Naked Single 1 at r9c6 - removed from peer at r6c6
90a. Combinations {189} no longer valid in cage 18(3) n58

91. Naked Single 1 at r9c6 - removed from peer at r8c6
91a. Combinations {1589} {1679} no longer valid in cage 23(4) n89

92. Naked Single 2 at r9c7 - removed from peer at r5c7
92a. Cage sum in cage 10(2) n6 - removed 8 from r6c7

93. Naked Single 2 at r9c7 - removed from peer at r6c7
93a. Cage sum in cage 10(2) n6 - removed 8 from r5c7
93b. Combinations {28} no longer valid in cage 10(2) n6
93c. Combinations {1268} no longer valid in combined cages 7(2) n6 & 10(2) n6

94. Naked Single 2 at r9c7 - removed from peer at r7c7

95. Naked Single 2 at r9c7 - removed from peer at r8c7

96. Naked pair {25} found at r45c8

97. Naked pair {14} found at r23c8

98. Naked pair {47} found at r78c7
98a. Cage sum in cage 10(2) n6 - removed 6 from r5c7 - removed 6 from r6c7
98b. Combinations {46} no longer valid in cage 10(2) n6
98c. Combinations {2456} no longer valid in combined cages 7(2) n6 & 10(2) n6

99. Naked pair {19} found at r56c7
99a. Cage sum in cage h15(2) n3 - removed 6 from r3c9

100. Naked Single 6 found at r1c7
100a. Cage sum in cage 19(3) n23 - removed 6 from r1c5 - removed 6 from r1c6

101. Naked Single 9 found at r3c9

102. Naked Single 6 at r1c7 - removed from peer at r4c7
102a. Combinations {479} {569} no longer valid in cage 20(3) n256

103. Naked Single 8 found at r4c7
103a. Cage sum in cage 20(3) n256 - removed 468 from r3c6 - removed 468 from r4c6

104. Naked Single 9 at r3c9 - removed from peer at r3c1
104a. Cage sum in cage 11(2) n14 - removed 2 from r4c1

105. Naked Single 9 at r3c9 - removed from peer at r3c2

106. Naked Single 9 at r3c9 - removed from peer at r3c3

107. Naked Single 9 at r3c9 - removed from peer at r3c6
107a. Cage sum in cage 20(3) n256 - removed 3 from r4c6

108. Naked Single 8 at r4c7 - removed from peer at r4c1
108a. Cage sum in cage 11(2) n14 - removed 3 from r3c1

109. Naked Single 8 at r4c7 - removed from peer at r4c2

110. Naked Single 8 at r4c7 - removed from peer at r4c5

111. Naked pair {49} found at r1c56
111a. Cage sum in cage 14(2) n2 - removed 5 from r2c5 - removed 5 from r2c6
111b. Combinations {59} no longer valid in cage 14(2) n2
111c. Only combination {3468} valid in combined cages 7(2) n1 & 14(2) n2
111d. Combinations {1579} no longer valid in combined cages 14(2) n2 & 8(2) n2

112. Naked pair {68} found at r2c56
112a. Cage sum in cage 7(2) n1 - removed 1 from r2c1 - removed 1 from r2c2
112b. Combinations {16} no longer valid in cage 7(2) n1
112c. Combinations {1567} no longer valid in combined cages 12(2) n1 & 7(2) n1

113. Naked pair {34} found at r2c12
113a. Cage sum in cage 6(3) n12 - removed 1 from r1c4
113b. Cage sum in cage 11(2) n14 - removed 7 from r4c1
113c. Combinations {47} no longer valid in cage 11(2) n14

114. Naked Single 1 found at r1c3

115. Naked Single 3 found at r1c4

116. Naked Single 5 found at r2c7

117. Naked Single 1 at r1c3 - removed from peer at r2c3
117a. Combinations {4678} no longer valid in cage 25(4) n14

118. Naked Single 9 found at r2c3

119. Naked Single 1 found at r2c8
119a. Cage sum in cage 13(4) n3 - removed 5 from r3c7 - removed 1 from r3c8

120. Naked Single 3 found at r3c7

121. Naked Single 4 found at r3c8

122. Naked Single 1 at r1c3 - removed from peer at r3c3

123. Naked Single 1 at r1c3 - removed from peer at r4c3

124. Naked Single 1 at r1c3 - removed from peer at r5c3

125. Naked Single 1 at r1c3 - removed from peer at r6c3
125a. Combinations {179} no longer valid in cage 17(3) n478

126. Naked Single 1 at r1c3 - removed from peer at r8c3

127. Naked Single 1 at r1c3 - removed from peer at r3c2

128. Naked Single 3 at r1c4 - removed from peer at r3c4
128a. Cage sum in cage 8(2) n2 - removed 5 from r3c5

129. Naked Single 3 at r1c4 - removed from peer at r4c4

130. Naked Single 3 at r1c4 - removed from peer at r5c4
130a. Combinations {138} {237} {345} no longer valid in cage 12(3) n5

131. Naked Single 3 at r1c4 - removed from peer at r7c4
131a. Combinations {359} {368} no longer valid in cage 17(3) n478

132. Naked Single 3 at r1c4 - removed from peer at r9c4

133. Naked Single 3 at r1c4 - removed from peer at r3c5
133a. Cage sum in cage 8(2) n2 - removed 5 from r3c4
133b. Combinations {35} no longer valid in cage 8(2) n2
133c. Combinations {3568} no longer valid in combined cages 14(2) n2 & 8(2) n2

134. Naked Single 3 at r1c4 - removed from peer at r3c6
134a. Cage sum in cage 20(3) n256 - removed 9 from r4c6
134b. Combinations {389} no longer valid in cage 20(3) n256

135. Naked Single 9 at r2c3 - removed from peer at r6c3
135a. Combinations {269} no longer valid in cage 17(3) n478

136. Naked Single 9 at r2c3 - removed from peer at r9c3

137. Naked Single 9 at r2c3 - removed from peer at r4c2

138. Naked pair {17} found at r3c45
138a. Cage sum in cage 20(3) n256 - removed 5 from r4c6

139. Naked Single 5 found at r3c6

140. Naked Single 7 found at r4c6

141. Naked Single 5 at r3c6 - removed from peer at r5c6

142. Naked Single 5 at r3c6 - removed from peer at r6c6

143. Naked Single 5 at r3c6 - removed from peer at r7c6

144. Naked Single 5 at r3c6 - removed from peer at r8c6
144a. Combinations {2579} {3569} no longer valid in cage 23(4) n89

145. Naked Single 7 at r4c6 - removed from peer at r5c6

146. Naked Single 7 at r4c6 - removed from peer at r7c6

147. Naked Single 7 at r4c6 - removed from peer at r4c2
147a. Only combinations {2689} {3589} valid in cage 25(4) n14

148. Naked Single 7 at r4c6 - removed from peer at r4c3

149. Naked Single 7 at r4c6 - removed from peer at r4c4

150. Naked Single 7 at r4c6 - removed from peer at r4c5

151. Naked Single 7 at r4c6 - removed from peer at r5c4
151a. Combinations {147} no longer valid in cage 12(3) n5

152. Naked Single 7 at r4c6 - removed from peer at r5c5
152a. Combinations {178} {367} {457} no longer valid in cage 16(3) n5

153. Naked pair {23} found at r7c2 r8c3

154. Naked Single 1 found at r8c2

155. Naked Single 1 at r8c2 - removed from peer at r4c2

156. 45 Rule on n9 found single outie r8c6=3
156a. Combinations {2489} no longer valid in cage 23(4) n89

157. Naked Single 3 at r8c6 - removed from peer at r5c6

158. Naked Single 3 at r8c6 - removed from peer at r7c6

159. Naked Single 3 at r8c6 - removed from peer at r8c3
159a. Cage sum in cage 6(3) n7 - removed 2 from r7c2

160. Naked Single 3 found at r7c2

161. Naked Single 2 found at r8c3

162. Naked Single 3 at r7c2 - removed from peer at r2c2
162a. Cage sum in cage 7(2) n1 - removed 4 from r2c1

163. Naked Single 3 found at r2c1

164. Naked Single 4 found at r2c2

165. Naked Single 3 at r2c1 - removed from peer at r4c1
165a. Cage sum in cage 11(2) n14 - removed 8 from r3c1
165b. Combinations {38} no longer valid in cage 11(2) n14

166. Naked Single 3 at r2c1 - removed from peer at r5c1
166a. Combinations {138} {237} {345} no longer valid in cage 12(3) n47

167. Naked Single 4 at r2c2 - removed from peer at r4c2

168. Naked Single 4 at r2c2 - removed from peer at r9c2

169. Naked Single 3 at r7c2 - removed from peer at r4c2
169a. Combinations {3589} no longer valid in cage 25(4) n14

170. Naked Single 3 at r7c2 - removed from peer at r7c5
170a. Combinations {369} {378} no longer valid in cage 18(3) n58

171. Naked Single 2 at r8c3 - removed from peer at r3c3

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

173. Naked Single 2 at r8c3 - removed from peer at r5c3
173a. Combinations {127} {235} no longer valid in cage 10(3) n45

174. Naked Single 2 at r8c3 - removed from peer at r6c3
174a. Combinations {278} no longer valid in cage 17(3) n478

175. Naked Single 3 at r8c6 - removed from peer at r8c8
175a. Cage sum in cage 9(2) n9 - removed 6 from r9c8

176. Naked Single 6 found at r8c8

177. Naked Single 3 found at r9c8

178. Naked Single 3 at r8c6 - removed from peer at r9c5
178a. Combinations {369} {378} no longer valid in cage 18(3) n78

179. Naked Single 6 at r8c8 - removed from peer at r8c1

180. Naked Single 6 at r8c8 - removed from peer at r8c4
180a. Cage sum in cage 13(2) n8 - removed 7 from r8c5

181. Naked Single 6 at r8c8 - removed from peer at r8c5
181a. Cage sum in cage 13(2) n8 - removed 7 from r8c4
181b. Combinations {67} no longer valid in cage 13(2) n8

182. 45 Rule on r89 found single innie r8c7=7
182a. Last cell in cage 23(4) n89 at r7c7 set to 4

183. Naked Single 4 at r7c7 - removed from peer at r7c1

184. Naked Single 4 at r7c7 - removed from peer at r7c3

185. Naked Single 4 at r7c7 - removed from peer at r7c4

186. Naked Single 4 at r7c7 - removed from peer at r7c5

187. Naked Single 4 at r7c7 - removed from peer at r7c6

188. Naked Single 7 at r8c7 - removed from peer at r8c1

189. 45 Rule on c12 found single outie r3c3=8
189a. Cage sum in cage 25(4) n14 - removed 8 from r3c2 - removed 5 from r4c2

190. Naked Single 8 at r3c3 - removed from peer at r6c3

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

192. Naked Single 8 at r3c3 - removed from peer at r9c3

193. Naked pair {26} found at r34c2
193a. Cage sum in cage 15(2) n4 - removed 9 from r5c2 - removed 9 from r6c2
193b. Combinations {69} no longer valid in cage 15(2) n4

194. Naked Single 7 found at r5c2

195. Naked Single 8 found at r6c2

196. Naked Single 7 at r5c2 - removed from peer at r1c2
196a. Cage sum in cage 12(2) n1 - removed 5 from r1c1

197. Naked Single 7 found at r1c1

198. Naked Single 5 found at r1c2

199. Naked Single 7 at r1c1 - removed from peer at r5c1

200. Naked Single 7 at r1c1 - removed from peer at r7c1
200a. Combinations {147} no longer valid in cage 12(3) n47

201. Naked Single 7 at r1c1 - removed from peer at r9c1

202. Naked Single 5 at r1c2 - removed from peer at r9c2

203. Naked Single 7 at r5c2 - removed from peer at r9c2
203a. Only combination {489} valid in cage 21(3) n7

204. Naked Single 7 at r5c2 - removed from peer at r5c3

205. Naked Single 8 at r6c2 - removed from peer at r9c2

206. Naked Single 9 found at r9c2
206a. Cage sum in cage 21(3) n7 - removed 59 from r8c1 - removed 569 from r9c1

207. Naked Single 8 at r6c2 - removed from peer at r6c1

208. Naked Single 8 at r6c2 - removed from peer at r6c4

209. Naked Single 8 at r6c2 - removed from peer at r6c5

210. Naked Single 8 at r6c2 - removed from peer at r6c6

211. Naked Single 8 at r6c2 - removed from peer at r5c1

212. Naked Single 9 at r9c2 - removed from peer at r9c4

213. Naked Single 9 at r9c2 - removed from peer at r9c5
213a. Combinations {459} no longer valid in cage 18(3) n78

214. Naked pair {48} found at r89c1
214a. Combinations {246} no longer valid in cage 12(3) n47

215. Hidden single 1 found at r4c4 in cage 10(3) n45

216. Naked Single 1 at r4c4 - removed from peer at r3c4
216a. Cage sum in cage 8(2) n2 - removed 7 from r3c5

217. Naked Single 7 found at r3c4

218. Naked Single 1 found at r3c5

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

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

221. Naked Single 1 at r3c5 - removed from peer at r4c5

222. Naked Single 1 at r3c5 - removed from peer at r5c5
222a. Combinations {169} no longer valid in cage 16(3) n5

223. Naked Single 1 at r3c5 - removed from peer at r6c5

224. Naked Single 1 at r4c4 - removed from peer at r5c4

225. Naked Single 1 at r4c4 - removed from peer at r6c4
225a. Only combination {246} valid in cage 12(3) n5

226. 45 Rule on n5 found single innie r6c6=9
226a. Cage sum in cage 18(3) n58 - removed 2568 from r7c5 - removed 68 from r7c6
226b. Only combination {279} valid in cage 18(3) n58
226c. Combinations {45} no longer valid in split cage 9(2) n8

227. Naked Single 7 found at r7c5

228. Naked Single 2 found at r7c6

229. Naked Single 9 at r6c6 - removed from peer at r1c6
229a. Cage sum in cage 19(3) n23 - removed 4 from r1c5

230. Naked Single 9 found at r1c5

231. Naked Single 4 found at r1c6

232. Naked Single 9 at r1c5 - removed from peer at r4c5

233. Naked Single 9 at r1c5 - removed from peer at r5c5

234. Naked Single 9 at r1c5 - removed from peer at r6c5

235. Naked Single 9 at r1c5 - removed from peer at r8c5
235a. Cage sum in cage 13(2) n8 - removed 4 from r8c4

236. Naked Single 4 at r1c6 - removed from peer at r5c6

237. Naked Single 9 at r6c6 - removed from peer at r5c6
237a. Combinations {259} {349} no longer valid in cage 16(3) n5

238. Naked Single 9 at r6c6 - removed from peer at r6c1

239. Naked Single 9 at r6c6 - removed from peer at r6c4

240. Naked Single 9 at r6c6 - removed from peer at r6c7
240a. Cage sum in cage 10(2) n6 - removed 1 from r5c7

241. Naked Single 9 found at r5c7

242. Naked Single 1 found at r6c7

243. Naked Single 9 at r5c7 - removed from peer at r5c1
243a. Combinations {129} no longer valid in cage 12(3) n47

244. Naked Single 9 at r5c7 - removed from peer at r5c4

245. Naked Single 1 at r6c7 - removed from peer at r6c1

246. Naked Single 7 at r7c5 - removed from peer at r9c5

247. Naked Single 7 at r7c5 - removed from peer at r7c3
247a. Combinations {467} no longer valid in cage 17(3) n478

248. Naked Single 2 at r7c6 - removed from peer at r5c6

249. Naked pair {56} found at r7c13
249a. Combinations {468} no longer valid in cage 18(3) n78

250. Naked Single 8 found at r7c4
250a. Cage sum in cage 17(3) n478 - removed 56 from r6c3 - removed 6 from r7c3

251. Naked Single 4 found at r6c3

252. Naked Single 5 found at r7c3

253. Naked Single 7 found at r9c3
253a. Cage sum in cage 18(3) n78 - removed 48 from r9c4 - removed 48 from r9c5

254. Naked Single 4 at r6c3 - removed from peer at r4c3
254a. Cage sum in cage 10(3) n45 - removed 5 from r5c3

255. Naked Single 4 at r6c3 - removed from peer at r5c3
255a. Cage sum in cage 10(3) n45 - removed 5 from r4c3
255b. Combinations {145} no longer valid in cage 10(3) n45

256. Naked Single 4 at r6c3 - removed from peer at r6c4

257. Naked Single 4 at r6c3 - removed from peer at r6c5

258. Naked Single 5 at r7c3 - removed from peer at r7c1

259. Naked Single 6 found at r7c1
259a. Cage sum in cage 12(3) n47 - removed 256 from r5c1 - removed 26 from r6c1

260. Naked Single 1 found at r5c1

261. Naked Single 5 found at r6c1

262. Naked Single 5 at r6c1 - removed from peer at r4c1
262a. Cage sum in cage 11(2) n14 - removed 6 from r3c1
262b. Combinations {56} no longer valid in cage 11(2) n14

263. Naked Single 2 found at r3c1

264. Naked Single 9 found at r4c1

265. Naked Single 2 at r3c1 - removed from peer at r3c2
265a. Cage sum in cage 25(4) n14 - removed 6 from r4c2

266. Naked Single 6 found at r3c2

267. Naked Single 2 found at r4c2

268. Naked Single 2 at r4c2 - removed from peer at r4c5

269. Naked Single 2 at r4c2 - removed from peer at r4c8
269a. Cage sum in cage 7(2) n6 - removed 5 from r5c8

270. Naked Single 5 found at r4c8

271. Naked Single 2 found at r5c8

272. Naked Single 5 at r4c8 - removed from peer at r4c5

273. Naked Single 2 at r5c8 - removed from peer at r5c5
273a. Combinations {268} no longer valid in cage 16(3) n5

274. Naked Single 5 at r6c1 - removed from peer at r6c4

275. Naked Single 5 at r6c1 - removed from peer at r6c5

276. Naked Single 6 found at r6c4
276a. Cage sum in cage 12(3) n5 - removed 568 from r5c4 - removed 6 from r6c5

277. Naked Single 4 found at r5c4

278. Naked Single 2 found at r6c5

279. Naked Single 4 at r5c4 - removed from peer at r5c5

280. Naked Single 4 at r5c4 - removed from peer at r5c9
280a. Cage sum in cage 19(3) n36 - removed 6 from r4c9

281. Naked Single 4 found at r4c9

282. Naked Single 6 found at r5c9

283. Naked Single 4 at r4c9 - removed from peer at r4c5

284. Naked Single 6 at r5c9 - removed from peer at r5c3
284a. Cage sum in cage 10(3) n45 - removed 3 from r4c3

285. Naked Single 6 found at r4c3

286. Naked Single 3 found at r5c3

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

288. Naked Single 3 found at r4c5
288a. Cage sum in cage 16(3) n5 - removed 368 from r5c5 - removed 6 from r5c6

289. Naked Single 5 found at r5c5

290. Naked Single 8 found at r5c6

291. Naked Single 5 at r5c5 - removed from peer at r8c5
291a. Cage sum in cage 13(2) n8 - removed 8 from r8c4

292. Naked Single 5 at r5c5 - removed from peer at r9c5
292a. Cage sum in cage 18(3) n78 - removed 6 from r9c4

293. Naked Single 5 found at r9c4

294. Naked Single 6 found at r9c5

295. Naked Single 8 at r5c6 - removed from peer at r2c6
295a. Cage sum in cage 14(2) n2 - removed 6 from r2c5

296. Naked Single 8 found at r2c5

297. Naked Single 6 found at r2c6

298. Naked Single 8 at r2c5 - removed from peer at r8c5
298a. Cage sum in cage 13(2) n8 - removed 5 from r8c4
298b. Combinations {58} no longer valid in cage 13(2) n8

299. Naked Single 9 found at r8c4

300. Naked Single 4 found at r8c5

301. Naked Single 4 at r8c5 - removed from peer at r8c1
301a. Cage sum in cage 21(3) n7 - removed 8 from r9c1

302. Naked Single 8 found at r8c1

303. Naked Single 4 found at r9c1

304. Naked Single 8 at r8c1 - removed from peer at r8c9
304a. Cage sum in cage 13(2) n9 - removed 5 from r9c9

305. Naked Single 5 found at r8c9

306. Naked Single 8 found at r9c9

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