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rcbroughton Expert
Joined: 15 Nov 2006 Posts: 143 Location: London

Posted: Sat Nov 25, 2006 10:21 pm Post subject: Completed walkthrough 


Reposting the walkthrough . . .
[edited to reflect most recent version which removed a couple of bugs in the printed output]
1. Must use 9 in cage 27(4) at r1c8
> Removed candidate 9 from r1c7 r2c9 r3c7 r3c8 r3c9
2. Must use 9 in cage 27(4) at r2c1
> Removed candidate 9 from r1c2 r2c2
3. 45 rule on row 9. Excluded cells r8c3 r8c5 r8c7 equal 21
> Only combinations {489} {579} {678} allowed
> Removed candidates 123 from r8c3
> Removed candidates 123 from r8c5
> Removed candidates 123 from r8c7
> Found a hidden cage 21(3) at r8c3 r8c5 r8c7
4. 45 rule on N2. Included cells r3c5 minus excluded cells r1c3 r1c7 equals 2
> Min of included cells is 5. Set min candidate in r3c5
> Max of excluded cells is 7. Set max candidate in r1c3 r1c7
5. 45 rule on column 5
> Found a hidden cage 22(4) at r3c5 r4c5 r8c5 r9c5
6. 45 rule on N3. Included cells r1c7 r3c7 equal excluded cells r4c8
> Min of excluded cells is 3. Set min candidate in r4c8
7. 45 rule on N7. Included cells r7c2 r7c3 minus excluded cells r6c1 equals 1
> Min of excluded cells is 4. Set min candidate in r6c1
> Max of included cells is 8. Set max candidate in r7c2 r7c3
8. 45 rule on N7
> Found a hidden cage 18(3) at r6c1 r6c3 r6c4
9. 45 rule on N8 found single cell at r7c5 value 5
> Removed combinations {127} {136} from cage 10(3) at r5c5
> Removed candidates 67 from r5c5
> Removed candidates 67 from r6c5
10. From value 5 found at r7c5
> Removed 5 from r7c12346789 r12345689c5 r8c4 r8c6 r9c4 r9c6
11. Only combinations {49} {67} allowed in cage 13(2) at r1c5
> Removed candidate 8 from r1c5
> Removed candidate 8 from r2c5
12. Only combinations {18} {27} {36} allowed in cage 9(2) at r7c4
> Removed candidate 4 from r7c4
> Removed candidate 4 from r8c4
13. Only combinations {18} {27} {36} allowed in cage 9(2) at r7c6
> Removed candidate 4 from r7c6
> Removed candidate 4 from r8c6
14. 45 rule on column 5. Included cells r3c5 r4c5 r8c5 r9c5 equal 22
> Cage 13(2) at r1c5 doesn't allow permutations with {46}, {47}
> Combined cages 9(2) at r7c6 & 9(2) at r7c4 doesn't allow permutations in r8c5 r9c5 with {78}, {17}, {68}, {16}, {67}, {38}, {28}
> Only combinations {1489} {1678} {2389} allowed
> Removed candidates 67 from r8c5
> Removed candidates 67 from r9c5
15. 45 rule on N9
> Found a hidden cage 15(3) at r6c6 r6c7 r6c9
16. 45 rule on columns 1 to 2. Included cells r7c2 minus excluded cells r2c3 r8c3 r9c3 equals 20
> Only combinations {1489} {1579} {2589} {1678} {2679} {3689} {4789} allowed
> Removed candidates 123 from r2c3
> Removed candidates 67 from r7c2
> Removed candidates 123 from r9c3
17. 45 rule on N3, N6, N9. Included cells r1c7 minus excluded cells r5c6 r6c6 equals 13
> Min of excluded cells is 14. Set min candidate in r5c6 r6c6
> Max of included cells is 4. Set max candidate in r1c7
18. 45 rule on N3
> Found a hidden cage 18(5) at r1c7 r2c9 r3c8 r3c9 r3c7
19. 45 rule on rows 6 to 9
> Found a hidden cage 12(3) at r6c2 r6c8 r6c5
20. 45 rule on columns 1 to 4. Included cells r4c4 r9c4 equal 13
> Only combinations {49} {58} {67} allowed
> Removed candidates 1238 from r4c4
> Removed candidates 123 from r9c4
> Found a hidden cage 13(2) at r4c4 r9c4
21. 45 rule on columns 6 to 9. Included cells r4c6 r9c6 equal 8
> Only combinations {17} {26} {35} allowed
> Removed candidates 3489 from r4c6
> Removed candidates 489 from r9c6
> Found a hidden cage 8(2) at r4c6 r9c6
22. Value 4 locked for column 6 in N2
> Removed 4 from r1c4 r1c5 r2c4 r2c5 r3c4 r1c7
23. Naked pair 67 found in combined cages 10(3) at r5c5 & 13(2) at r1c5 at r1c5 r2c5
> Removed value 6 from r3c5 r4c5 r1c4 r1c6 r2c4 r2c6 r3c4 r3c6
> Removed value 7 from r3c5 r4c5 r1c4 r1c6 r2c4 r2c6 r3c4 r3c6
> Removed combination {3567} from cage 21(4) at r3c5
> Removed combinations {1257} {1347} {2346} from cage 15(4) at r1c3
> Removed combinations {1257} {1347} {1356} {2346} from cage 15(4) at r1c6
> Removed candidate 5 from r1c6
> Removed candidate 5 from r2c6
> Removed candidate 5 from r3c6
24. Only combinations {1239} {1248} {1356} allowed in cage 15(4) at r1c3
> Removed candidate 5 from r1c3
25. Only combinations {2478} {3468} {1578} {2568} {1389} {1479} {2469} {3459} {1569} {2379} with r3c5 {89} allowed in cage 21(4) at r3c5
> Removed candidates 89 from r4c5
26. Must use 1 in cage 15(4) at r1c3
> Removed candidate 1 from r1c6
27. Must use 12 in cage 15(4) at r1c6
> Removed candidate 1 from r1c4
> Removed candidate 2 from r1c4
28. Only combinations {1239} {1248} {1356} allowed in cage 15(4) at r1c3
> Removed candidate 8 from r2c4
> Removed candidate 8 from r3c4
29. Value 5 locked in column 4 of N2
> Removed 5 from r4c4 r5c4 r6c4
30. Only combinations {49} {67} allowed in cage h13(2) at r4c4
> Removed candidate 8 from r9c4
31. 45 rule on column 4. Included cells r5c4 r4c4 r6c4 r9c4 minus excluded cells r1c3 equals 21
> Cage 9(2) at r7c4 doesn't allow permutations in r5c4 r4c4 r6c4 r9c4 with {1876}, {873}
> Cage h5(2) at r5c5 doesn't allow permutations in r5c4 r4c4 r6c4 with {24}, {34}
> Only combinations {11489} {46689} {12479} {13469} {23679} {33489} {13689} allowed
> Removed candidates 24 from r1c3
32. Only combinations {1239} {1356} allowed in cage 15(4) at r1c3
> Removed candidate 8 from r1c4
33. Must use 13 in cage 15(4) at r1c3
> Removed candidate 3 from r1c6
34. 45 rule on column 5. Excluded cells r4c4 r4c6 r9c4 r9c6 equal 21
> Cage 9(2) at r7c6 doesn't allow permutations in r4c6 r9c4 r9c6 with {176}
> Combined cages 9(2) at r7c6 & 9(2) at r7c4 doesn't allow permutations in r9c4 r9c6 with {37}, {67}, {16}
> Cage h5(2) at r5c5 doesn't allow permutations in r4c4 r4c6 with {24}
> Only combinations {1479} {3459} {2469} {4566} {1569} {2379} {3567} allowed
> Removed candidate 7 from r9c4
35. Only combinations {49} {67} allowed in cage h13(2) at r4c4
> Removed candidate 6 from r4c4
36. 45 rule on column 6. Included cells r4c6 r5c6 r6c6 r9c6 minus excluded cells r1c7 equals 21
> Cage 9(2) at r7c6 doesn't allow permutations in r4c6 r5c6 r6c6 r9c6 with {1876}, {823}, {176}, {8276}, {873}
> Only combinations {11579} {22579} {23569} {12578} {12569} {12589} {13568} with r1c7 {12} allowed
> Removed candidate 3 from r1c7
37. Must use 1356 in cage 15(4) at r1c3
> Removed candidate 6 from r1c1 r1c2 r1c5>7 r1c8 r1c9 r2c3 r3c3 r4c3 r5c3 r6c3 r7c3 r8c3 r9c3 r2c1 r2c2 r3c1 r3c2
38. From value 7 found at r1c5
> Removed 7 from r1c1289 r2c5 r2c5>6
39. From value 6 found at r2c5
> Removed 6 from r2c789
40. Only combination {3789} allowed in cage 27(4) at r1c8
> Removed candidates 45 from r1c8
> Removed candidates 45 from r1c9
> Removed candidates 45 from r2c7
> Removed candidates 45 from r2c8
41. Only combinations {3789} {4689} {5679} allowed in cage 27(4) at r2c1
> Removed candidates 45 from r4c2
42. Naked quad 3897 found in N3 at r1c8 r1c9 r2c7 r2c8
> Removed value 3 from r3c8 r2c9 r3c7 r3c9
> Removed value 8 from r3c8 r2c9 r3c7 r3c9
> Removed value 7 from r3c8 r2c9 r3c7 r3c9
> Removed combinations {1278} {1359} {1368} {2349} {2358} {2367} from cage 18(4) at r2c9
43. Only combinations {1269} {1458} {1467} {2457} {3456} allowed in cage 18(4) at r2c9
> Removed candidates 456 from r4c8
44. Must use 3789 in cage 27(4) at r1c8
> Removed candidate 7 from r2c1 r2c2 r2c3
45. Value 6 only occurs at r1c3 in that row
46. Only combinations {1356} with 6 locked in r1c3, r1c4 {35} allowed in cage 15(4) at r1c3
> Removed candidate 9 from r1c4
> Removed candidates 29 from r2c4
> Removed candidates 29 from r3c4
47. Naked triple 351 found in cage 15(4) at r1c3 at r1c4 r2c4 r3c4
> Removed value 3 from r5c4 r6c4 r7c4 r8c4 r2c6 r3c6
> Removed value 1 from r5c4 r6c4 r7c4 r8c4 r2c6 r3c6
> Removed combinations {18} {36} from cage 9(2) at r7c4
> Removed candidates 68 from r7c4
> Removed candidates 68 from r8c4
> Removed combination {1239} from cage 15(4) at r1c6
> Removed candidate 9 from r1c6
> Removed candidate 9 from r2c6
> Removed candidate 9 from r3c6
48. Only combinations {1248} with 1 locked in r1c7 allowed in cage 15(4) at r1c6
> Set candidate 1 in r1c7
49. From value 1 found at r1c7
> Removed 1 from r1c12 r345679c7 r2c9 r3c8 r3c9
50. Only combinations {2348} {1259} {1349} {1358} allowed in cage 17(4) at r1c1
> Removed candidate 5 from r2c2
51. Only combinations {2457} {3456} with r4c8 {73} allowed in cage 18(4) at r2c9
> Removed candidates 89 from r4c8
52. Only combinations {258} {357} {456} {159} {267} {168} {348} {249} allowed in cage h15(3) at r6c6
> Removed candidate 9 from r6c9
53. Naked pair 27 found in combined cages 9(2) at r7c6 & 9(2) at r7c4 at r7c4 r8c4
> Removed value 2 from r5c4 r6c4 r7c6 r8c6 r9c5 r9c6
> Removed value 7 from r4c4 r5c4 r6c4 r7c6 r8c6 r9c6
> Removed combinations {1578} {2379} from cage 21(4) at r3c5
> Removed combination {1357} from cage 16(4) at r3c3
> Removed combination {2357} from cage 17(4) at r6c3
> Removed combinations {2479} {3478} {1678} {2389} from cage 22(4) at r8c5
> Removed combination {27} from cage 9(2) at r7c6
54. Only combinations {2478} {3468} {1389} {1479} {2469} {3459} with r3c5 {89}, r4c4 {49} allowed in cage 21(4) at r3c5
> Removed candidate 4 from r4c5
> Removed candidate 2 from r4c6
55. Only combinations {3469} {1489} allowed in cage 22(4) at r8c5
> Removed candidate 1 from r9c5
56. Only combinations {1489} {2389} with r3c5 {89}, r4c5 {12} allowed in cage h22(4) at r3c5
> Removed candidate 3 from r4c5
57. Only combinations {2478} {1479} {2469} with r3c5 {89}, 4 locked in r4c4, r4c5 {21}, r4c6 {76} allowed in cage 21(4) at r3c5
> Set candidate 4 in r4c4
> Removed candidates 15 from r4c6
58. From value 4 found at r4c4
> Removed 4 from r4c1379 r569c4 r5c5 r6c5
59. Only combinations {1249} {1258} {1267} {1348} {1456} {2356} allowed in cage 16(4) at r3c3
> Removed candidates 89 from r3c3
> Removed candidates 89 from r4c3
> Removed candidates 89 from r5c3
60. Only combinations {235} with 5 locked in r7c5 allowed in cage 10(3) at r5c5
> Removed candidate 1 from r5c5
> Removed candidate 1 from r6c5
61. Only combinations {1367} {1349} {2348} {2456} {1358} {1259} {1268} allowed in cage 17(4) at r6c3
> Removed candidate 9 from r6c3
62. Only combination {49} allowed in cage h13(2) at r4c4
> Set candidate 9 in r9c4
63. From value 9 found at r9c4
> Removed 9 from r9c1235789 r56c4 r8c5
64. Only combinations {3469} {1489} with r8c5 {48}, 9 locked in r9c4, r9c6 {61} allowed in cage 22(4) at r8c5
> Removed candidate 3 from r9c6
65. Only combinations {489} {678} allowed in cage h21(3) at r8c3
> Removed candidate 5 from r8c3
> Removed candidates 57 from r8c7
66. Only combinations {1489} {2389} with 9 locked in r3c5, r4c5 {12}, r8c5 {48} allowed in cage h22(4) at r3c5
> Set candidate 9 in r3c5
67. From value 9 found at r3c5
> Removed 9 from r3c12
68. Only combinations {3789} {4689} {5679} allowed in cage 27(4) at r2c1
> Removed candidates 45 from r2c1
69. Only combinations {468} {567} {378} {189} {369} allowed in cage h18(3) at r6c1
> Removed candidate 2 from r6c3
70. Only combination {17} allowed in cage h8(2) at r4c6
> Set candidate 7 in r4c6
> Set candidate 1 in r9c6
71. From value 7 found at r4c6
> Removed 7 from r4c123789 r4c8>3 r56c6
72. From value 3 found at r4c8
> Removed 3 from r4c12379 r1256789c8 r5c7 r5c9 r6c7 r6c9
73. From value 1 found at r9c6
> Removed 1 from r9c1289 r78c6
74. Only combinations {3456} with r2c9 {45}, 3 locked in r4c8 allowed in cage 18(4) at r2c9
> Removed candidate 2 from r2c9
> Removed candidate 2 from r3c8
> Removed candidate 2 from r3c9
75. Only combinations {1479} with 9 locked in r3c5, 4 locked in r4c4, 1 locked in r4c5, 7 locked in r4c6 allowed in cage 21(4) at r3c5
> Set candidate 1 in r4c5
76. From value 1 found at r4c5
> Removed 1 from r4c139
77. Only combination {36} allowed in cage 9(2) at r7c6
> Removed candidate 8 from r7c6
> Removed candidate 8 from r8c6
78. Only combinations {1489} with r8c5 {48}, 9 locked in r9c4, r9c5 {84}, 1 locked in r9c6 allowed in cage 22(4) at r8c5
> Removed candidate 3 from r9c5
79. Only combinations {12456} with 1 locked in r1c7, r2c9 {45}, 2 locked in r3c7 allowed in cage h18(5) at r1c7
> Set candidate 2 in r3c7
80. From value 2 found at r3c7
> Removed 2 from r3c36 r45679c7
81. Only combinations {2567} {2459} {2468} with 2 locked in r3c7, r5c7 {74} allowed in cage 20(4) at r3c7
> Removed candidates 5689 from r5c7
82. Only combinations {456} {258} {159} {267} {168} {249} allowed in cage h15(3) at r6c6
> Removed candidates 78 from r6c9
83. Naked pair 36 found in combined cages 9(2) at r7c6 & 9(2) at r7c4 at r7c6 r8c6
> Removed value 6 from r5c6 r6c6
84. Only combinations {2459} {2567} {2468} with 2 locked in r3c7, r5c7 {47} allowed in cage 20(4) at r3c7
> Removed candidate 8 from r4c7
85. Only combinations {456} {258} {159} {168} {249} allowed in cage h15(3) at r6c6
> Removed candidate 7 from r6c7
> Removed candidate 5 from r6c9
86. Naked pair 68 found in column 4 at r5c4 r6c4
> Removed value 8 from r5c6 r6c6
> Removed combination {2468} from cage 20(4) at r3c7
> Removed combination {2678} from cage 23(4) at r6c6
87. Must use 9 in cage 27(4) at r2c1
> Removed candidate 9 from r4c1 r5c1 r6c1
88. Only combinations {468} {567} {378} allowed in cage h18(3) at r6c1
> Removed candidate 1 from r6c3
89. Must use 25 in cage 20(4) at r3c7
> Removed candidate 5 from r5c8 r5c9
90. Value 9 locked in column 2 of N4
> Removed 9 from r8c2
91. Value 8 locked in row 8 of cage h21(3) at r8c3
> Removed 8 from r8c1 r8c2 r8c8 r8c9
92. 45 rule on row 4
> Found a hidden cage 33(6) at r4c2 r4c8 r4c3 r4c7 r4c1 r4c9
93. 45 rule on column 4
> Found a hidden cage 23(3) at r5c4 r6c4 r9c4
94. 45 rule on column 6
> Found a hidden cage 15(3) at r5c6 r6c6 r9c6
95. 45 rule on N1. Included cells r1c3 r3c3 minus excluded cells r4c2 equals 1
> Max of included cells is 10. Set max candidate in r3c3
96. Only combinations {1258} {1267} {1456} {2356} with r4c3 {25}, r5c4 {86} allowed in cage 16(4) at r3c3
> Removed candidate 3 from r5c3
97. 45 rule on N1. Included cells r1c3 r2c1 r3c1 r3c2 r3c3 equal 28
> Only combinations {34678} {15679} with 6 locked in r1c3, r3c3 {41} allowed
> Removed candidate 4 from r3c1
> Removed candidate 4 from r3c2
> Removed candidate 3 from r3c3
> Found a hidden cage 28(5) at r1c3 r2c1 r3c1 r3c2 r3c3
98. Value 3 locked for column 3 in cage 17(4) at r6c3
> Removed 3 from r7c2
99. Must use 1 in cage 16(4) at r3c3
> Removed candidate 1 from r7c3
100. 45 rule on N1. Included cells r1c3 r3c3 minus excluded cells r4c2 equals 1
> Only combinations {166} {469} with 6 locked in r1c3 allowed
> Removed candidate 8 from r4c2
101. 45 rule on N3
> Found a hidden cage 3(2) at r1c7 r3c7
102. 45 rule on N4. Included cells r4c2 r6c1 r6c3 minus excluded cells r3c3 r5c4 equals 9
> Cage 20(4) at r4c1 doesn't allow permutations in r4c2 r6c1 r6c3 with {864}, {865}
> Cage h15(3) at r6c6 doesn't allow permutations in r6c1 r6c3 with {45}
> Only combinations {13667} {34679} {15678} {13689} {13469} with r4c2 {69}, r3c3 {14}, r5c4 {68} allowed
> Removed candidate 8 from r6c1
> Removed candidates 48 from r6c3
103. Only combinations {567} {378} allowed in cage h18(3) at r6c1
> Removed candidates 46 from r6c1
104. Only combinations {1579} {2569} {4567} {2578} {3568} {2479} {1678} {3478} with r6c1 {57} allowed in cage 22(4) at r6c1
> Removed candidate 3 from r7c1
105. Value 7 locked in row 6 of cage h18(3) at r6c1
> Removed 7 from r6c2 r6c8
106. Only combinations {138} {129} {345} {246} allowed in cage h12(3) at r6c2
> Removed candidates 23 from r6c2
> Removed candidate 2 from r6c8
107. Value 7 locked in row 5 of N6
> Removed 7 from r5c1 r5c2 r5c3
108. Must use 15 in cage 16(4) at r3c3
> Removed candidate 5 from r2c3 r6c3 r9c3 r4c1 r5c1 r5c2 r6c1>7 r6c2
109. From value 7 found at r6c1
> Removed 7 from r6c3 r6c3>3 r3789c1 r8c2
110. From value 3 found at r6c3
> Removed 3 from r6c5 r6c5>2 r7c3 r5c1 r5c2
111. From value 2 found at r6c5
> Removed 2 from r6c9 r5c5 r5c5>3
112. Only combinations {3789} {5679} with 7 locked in r3c2, r4c2 {96} allowed in cage 27(4) at r2c1
> Set candidate 7 in r3c2
113. From value 7 found at r3c2
> Removed 7 from r9c2
114. Only combinations {378} with 7 locked in r6c1, 3 locked in r6c3, 8 locked in r6c4 allowed in cage h18(3) at r6c1
> Set candidate 8 in r6c4
115. From value 8 found at r6c4
> Removed 8 from r6c278 r5c4 r5c4>6
116. From value 6 found at r5c4
> Removed 6 from r5c1289
117. Only combinations {1456} with r3c3 {14}, 5 locked in r4c3, r5c3 {41}, 6 locked in r5c4 allowed in cage 16(4) at r3c3
> Set candidate 5 in r4c3
> Removed candidates 25 from r5c3
118. From value 5 found at r4c3
> Removed 5 from r4c79
119. Only combinations {2567} {2459} with 2 locked in r3c7, r4c7 {69}, 5 locked in r5c6, r5c7 {74} allowed in cage 20(4) at r3c7
> Set candidate 5 in r5c6
120. From value 5 found at r5c6
> Removed 5 from r6c6 r6c6>9
121. From value 9 found at r6c6
> Removed 9 from r6c278 r7c7 r7c8
122. Only combinations {2468} {1289} {1469} allowed in cage 20(4) at r4c1
> Removed candidate 1 from r5c2
123. Only combinations {2348} with 3 locked in r6c3, 8 locked in r6c4, r7c2 {24}, r7c3 {42} allowed in cage 17(4) at r6c3
> Removed candidate 1 from r7c2
> Removed candidate 7 from r7c3
124. Only combinations {3479} {2489} {3569} {2579} {1589} {1679} with 9 locked in r6c6 allowed in cage 23(4) at r6c6
> Removed candidates 46 from r7c7
> Removed candidates 48 from r7c8
125. Only combinations {159} with 9 locked in r6c6, 5 locked in r6c7, 1 locked in r6c9 allowed in cage h15(3) at r6c6
> Set candidate 5 in r6c7
> Set candidate 1 in r6c9
126. From value 5 found at r6c7
> Removed 5 from r6c8 r9c7
127. From value 1 found at r6c9
> Removed 1 from r6c28 r578c9 r5c8 r8c8
128. Only combinations {2678} {2489} with r6c8 {64} allowed in cage 23(4) at r4c9
> Removed candidate 6 from r4c9
> Removed candidate 4 from r5c8
> Removed candidate 4 from r5c9
129. Only combinations {3569} {2579} {1589} with 9 locked in r6c6, 5 locked in r6c7 allowed in cage 23(4) at r6c6
> Removed candidate 7 from r7c8
130. Naked pair 14 found in cage 16(4) at r3c3 at r3c3 r5c3
> Removed value 4 from r2c3 r7c3>2 r8c3 r9c3
> Removed combination {4569} from cage 24(4) at r8c3
131. From value 2 found at r7c3
> Removed 2 from r7c12489 r7c2>4 r7c4>7 r8c1 r8c2 r9c1 r9c2
132. From value 4 found at r7c2
> Removed 4 from r7c19 r125689c2 r6c2>6 r8c1 r9c1
133. From value 6 found at r6c2
> Removed 6 from r6c8 r6c8>4 r489c2 r4c2>9 r4c1
134. From value 9 found at r4c2
> Removed 9 from r4c79 r4c7>6 r5c2 r2c1
135. From value 6 found at r4c7
> Removed 6 from r89c7
136. From value 4 found at r6c8
> Removed 4 from r389c8 r5c7>7
137. From value 7 found at r5c7
> Removed 7 from r5c89 r279c7
138. From value 7 found at r7c4
> Removed 7 from r7c9 r8c4 r8c4>2
139. From value 2 found at r8c4
> Removed 2 from r8c89
140. Only combinations {1259} {1358} {2348} {1349} with r2c3 {98} allowed in cage 17(4) at r1c1
> Removed candidates 89 from r1c1
> Removed candidate 8 from r1c2
> Removed candidate 8 from r2c2
141. Only combinations {3789} with r1c8 {89}, 7 locked in r2c8 allowed in cage 27(4) at r1c8
> Set candidate 7 in r2c8
142. From value 7 found at r2c8
> Removed 7 from r89c8
143. Only combinations {3789} with r2c1 {38}, r3c1 {83}, 7 locked in r3c2, 9 locked in r4c2 allowed in cage 27(4) at r2c1
> Removed candidate 5 from r3c1
144. Only combinations {2468} with r4c1 {28}, 4 locked in r5c1, r5c2 {82}, 6 locked in r6c2 allowed in cage 20(4) at r4c1
> Set candidate 4 in r5c1
145. From value 4 found at r5c1
> Removed 4 from r5c3 r5c3>1 r1c1
146. From value 1 found at r5c3
> Removed 1 from r3c3 r3c3>4
147. From value 4 found at r3c3
> Removed 4 from r3c69 r3c6>8
148. From value 8 found at r3c6
> Removed 8 from r3c1 r3c1>3 r12c6
149. From value 3 found at r3c1
> Removed 3 from r3c4 r1289c1 r2c1>8 r1c2 r2c2
150. From value 8 found at r2c1
> Removed 8 from r2c37 r2c3>9 r479c1 r4c1>2
151. From value 9 found at r2c3
> Removed 9 from r2c7 r2c7>3 r8c3
152. From value 3 found at r2c7
> Removed 3 from r2c4 r79c7 r7c7>8 r1c9
153. From value 2 found at r4c1
> Removed 2 from r4c9 r4c9>8 r1c1 r1c1>5 r5c2>8
154. From value 5 found at r1c1
> Removed 5 from r1c24 r1c2>2 r1c4>3 r89c1 r9c1>6
155. From value 2 found at r1c2
> Removed 2 from r1c6 r1c6>4 r2c2 r2c2>1
156. From value 4 found at r1c6
> Removed 4 from r2c6 r2c6>2
157. From value 1 found at r2c2
> Removed 1 from r2c4 r2c4>5 r8c2
158. From value 5 found at r2c4
> Removed 5 from r2c9 r2c9>4 r3c4 r3c4>1
159. From value 4 found at r2c9
> Removed 4 from r89c9
160. From value 8 found at r4c9
> Removed 8 from r1579c9 r1c9>9 r5c8
161. From value 9 found at r1c9
> Removed 9 from r1c8 r1c8>8 r578c9 r5c9>2
162. From value 8 found at r1c8
> Removed 8 from r9c8
163. From value 8 found at r5c2
> Removed 8 from r9c2
164. From value 2 found at r5c9
> Removed 2 from r5c8 r5c8>9 r9c9
165. From value 9 found at r5c8
> Removed 9 from r8c8
166. From value 8 found at r7c7
> Removed 8 from r89c7 r9c7>4
167. From value 6 found at r9c1
> Removed 6 from r9c89 r78c1
168. From value 4 found at r9c7
> Removed 4 from r9c5 r9c5>8 r8c7 r8c7>9
169. From value 9 found at r8c7
> Removed 9 from r8c1 r8c1>1
170. From value 1 found at r8c1
> Removed 1 from r7c1 r7c1>9
171. From value 8 found at r9c5
> Removed 8 from r9c3 r9c3>7 r8c5 r8c5>4
172. From value 7 found at r9c3
> Removed 7 from r9c9 r8c3 r8c3>8
173. Only combinations {1579} with 7 locked in r6c1, 9 locked in r7c1, 1 locked in r8c1, 5 locked in r8c2 allowed in cage 22(4) at r6c1
> Set candidate 5 in r8c2
174. From value 5 found at r8c2
> Removed 5 from r8c89 r8c8>6 r9c2 r9c2>3
175. From value 6 found at r8c8
> Removed 6 from r8c69 r8c6>3 r37c8 r3c8>5 r7c8>1 r7c9>3
176. From value 5 found at r3c8
> Removed 5 from r3c9 r3c9>6 r9c8 r9c8>2
177. From value 3 found at r7c9
> Removed 3 from r7c6 r7c6>6 r89c9 r8c9>7 r9c9>5 

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Andrew Grandmaster
Joined: 11 Aug 2006 Posts: 300 Location: Lethbridge, Alberta

Posted: Sat Apr 10, 2010 3:46 am Post subject: 


When I first solved this puzzle I wasn't satisfied with how I had completed it so had kept it in my Unfinished folder to have another go at it. Now that I'm working fairly regularly at puzzles in that folder I've had another go at it.
I'll rate my new walkthrough for A24 at Hard 1.25 because of the combination analysis I used in steps 33 and 34.
Here is my new walkthrough for A24.
Prelims
a) R12C5 = {49/58/67}, no 1,2,3
b) R78C4 = {18/27/36/45}, no 9
c) R78C6 = {18/27/36/45}, no 9
d) 10(3) cage at R5C5 = {127/136/145/235}, no 8,9
e) 27(4) cage at R2C1 = {3789/4689/5679}, no 1,2
f) 27(4) cage at R1C8 = {3789/4689/5679}, no 1,2
1. 45 rule on N8 1 innie R7C5 = 5, R56C5 = 5 = {14/23}, cleanup: no 8 in R12C5, no 4 in R78C4, no 4 in R78C6
2. 45 rule on R9 3 outies R8C357 = 21 = {489/579/678}, no 1,2,3
3. 45 rule on C1234 2 innies R49C4 = 13 = {49/67}[58], no 1,2,3, no 8 in R4C4
4. 45 rule on C6789 2 innies R49C6 = 8 = {17/26}[53], no 4,8,9, no 3 in R4C6
5. 4,9 in N8 only in R8C5 + R9C45 > R89C5 must contain at least one of 4,9
5a. R12C5 = {67} (only remaining combination, cannot be {49} which clashes with R89C5), locked for C5 and N2
6. 45 rule on N2 1 innie R3C5 = 2 outies R1C37 + 2
6a. Min R1C37 = 3 > min R3C5 = 5 > R3C5 = {89}
6b. Max R1C37 = 7, no 7,8,9 in R1C37
7. 4,9 in N8 only in 22(4) cage = {1489/2479/3469}
7a. 1 of {1489} must be in R9C6 > no 1 in R9C5
7b. 1 in C5 only in R456C5, locked for N5, cleanup: no 7 in R9C6 (step 4)
7c. 2 of {2479} must be in R9C6 > no 2 in R9C5
7d. 2 in C5 only in R456C5, locked for N5, cleanup: no 6 in R9C6 (step 4)
7e. 3 of {3469} must be in R9C6 > no 3 in R9C5
7f. 3 in C5 only in R456C5, locked for N5
8. Naked triple {489} in R389C5, locked for C5, 4 also locked for N8, cleanup: no 9 in R4C4 (step 3), no 1 in R56C5
8a. R4C5 = 1 (hidden single in C5)
9. 45 rule on C789 2 outies R56C6 = 1 innie R1C7 + 13
9a. Min R56C6 = 14, no 4
9b. Max R56C6 = 17 > max R1C7 = 4
10. 4 in C6 only in R123C6, locked for N2 and 15(4) cage at R1C6, no 4 in R1C7
10a. 15(4) cage at R1C6 must contain 4 = {1248} (only remaining combination), 8 locked for C6 and N2 > R3C5 = 9, CPE no 1 in R1C4, cleanup: no 1 in R78C6
11. Naked pair {48} in R89C5, locked for N8, cleanup: no 5 in R4C4 (step 3), no 1 in R78C4
11a. Naked quad {2367} in R78C46, locked for N8 > R9C4 = 9, R4C4 = 4 (step 3), R9C6 = 1, R4C6 = 7 (step 4), cleanup: no 2 in R78C6
11b. Naked pair {36} in R78C6, locked for C6 and N8
12. Naked triple {248} in R123C6, locked for N2 and 15(4) cage at R1C6 > R1C7 = 1
12a. Naked triple {135} in R123C4, locked for C4
12b. R123C4 = {135} = 9 > R1C3 = 6 (cage sum), R12C5 = [76]
13. 27(4) cage at R1C8 = {3789} (only remaining combination), locked for N3, 7 also locked for R2
14. 45 rule on N1 1 outie R4C2 = 1 remaining innie R3C3 + 5, no 2,5,7,8 in R3C3, no 3,5 in R4C2
15. 45 rule on N3 1 outie R4C8 = 1 remaining innie R3C7 + 1, no 6 in R3C7, no 2,8,9 in R4C8
16. 6 in R3 only in R3C89 > 18(4) cage at R2C9 = {3456} (only remaining combination) > R4C8 = 3, R3C7 = 2 (step 15)
17. 20(4) cage at R3C7 = {2459/2567} (cannot be {2468} because R5C6 only contains 5,9), no 8
17a. 4,7 only in R5C7 > R5C7 = {47}
18. R8C357 (step 2) = {489/678} (cannot be {579} because R8C5 only contains 4,8), no 5, 8 locked for R8
18a. 6 of {678} must be in R8C7 > no 7 in R8C7
19. 45 rule on C12 3 innies R7C2 + R9C12 = 1 outie R2C3 + 4
19a. Min R7C2 + R9C12 = 6 > min R2C3 = 2
20. 45 rule on C12 3 outies R289C3 = 1 innie R7C2 + 20
[This was the innieoutie difference which I missed when I originally tried this puzzle. Step 19 isn’t necessary but I’ve kept it in because I think it’s the more obvious of the 45s on C12.]
20a. Min R289C3 = 21, no 2,3 in R29C3
20b. Max R289C3 = 24 > max R7C2 = 4
20c. R289C3 = 21..24 = {489/579/589/789}, 9 locked for C3
20d. R289C3 cannot be 23 > no 3 in R7C2
21. 16(4) cage at R3C3 = {1258/1267/1348/1456/2356} (cannot be {1357/2347} because R5C4 only contains 6,8)
21a. R5C4 = {68} > no 8 in R45C3
21b. 16(4) cage at R3C3 = {1258/1267/1456/2356} (cannot be {1348} because R4C3 only contains 2,5)
21c. 3 of {2356} must be in R3C3 > no 3 in R5C3
22. R289C3 (step 20c) = {489/589/789} (cannot be {579} which clashes with 16(4) cage at R3C3), 8 locked for C4
23. 45 rule on N6 4 remaining innies R456C7 + R6C9 = 19 = {1459/1468/1567/2458/2467} (cannot be {1279} because 1,2 only in R6C9)
23a. 1,2 only in R6C9 > R6C9 = {12}
24. 45 rule on N9 3 outies R6C679 = 15 = {159/249/258} (cannot be {168} which clashes with R6C4, cannot be {267} because R6C6 only contains 5,9, cannot be {456} because R6C9 only contains 1,2), no 6,7
25. 45 rule on N9 2 innies R7C78 = 1 outie R6C9 + 8
25a. Max R6C9 = 2 > max R7C78 = 10, no 8,9 in R7C8
26. 45 rule on R6789 3 innies R6C258 = 12 = {138/237/246} (cannot be {129} which clashes with R6C9, cannot be {147/156} because R6C5 only contains 2,3, cannot be {345} which clashes with R6C679), no 5,9
26a. Killer pair 1,2 in R6C258 and R6C9, locked for R6
26b. R6C679 (step 24) = {159/249} (cannot be {258} which clashes with R6C258), no 8, 9 locked for R6 and 23(4) cage at R6C6, no 9 in R7C7
27. 45 rule on N7 3 outies R6C134 = 18 = {378/468/567}
27a. 4 of {468} must be in R6C3 > no 4 in R6C1
28. 45 rule on N7 1 outie R6C1 = 2 innies R7C23 + 1
28a. Min R7C23 = 3 > no 3 in R6C1
28b. Max R6C1 = 8 > max R7C23 = 7, no 7 in R7C3
29. 23(4) cage at R6C6 must contain 9 = {1589/2489/3479} (cannot be {1679} because 1,6,7 only in R7C78, cannot be {2579} which clashes with R7C4, cannot be {3569} which clashes with R7C6), no 6
29a. 4,9 of {2489/3479} must be in R6C67 > no 4 in R7C78
29b. 3 of {3479} must be in R7C7 > no 7 in R7C7
30. 7 in R3 only in R3C12 > 27(4) cage at R2C1 = {3789/5679}, no 4, CPE no 9 in R12C2 + R45C1
30a. 6,9 of {5679} must be in R2C1 + R4C2 > no 5 in R2C1
30b. 9 in N4 only in R45C2, locked for C2
31. 45 rule on N1 4 innies R2C1 + R3C123 = 22 (must contain 7) = {1579/3478}
31a. 1,4 only in R3C3 > R3C3 = {14}, cleanup: no 8 in R4C2 (step 14)
31b. 17(4) cage in N1 = {1259/2348} (cannot be {1349/1358} which clash with R2C1 + R3C123)
31c. 1 of {1259} must be in R2C2 > no 5 in R2C2
32. 16(4) cage at R3C3 (step 21b) = {1258/1267/1456}, 1 locked for C3
33. R6C134 (step 27) = {378/468/567}
33a. 3 in C3 only in R67C3 > 17(4) cage at R6C3 = {1367/2348} (cannot be {2357} because R6C4 only contains 6,8, cannot be {1358} which clashes with the combinations for R6C134), no 5
33b. R6C34 = [38/48/76] > R6C134 = [738/648/576], no 8 in R6C1
[Alternatively R7C23 cannot be [43] (because 2 of 17(4) cage at R6C3 because 2 of {2348} must be in R7C23) > max R7C23 = 6 > max R6C1 = 7]
34. R6C134 (step 33b) = [738/648/576] > R6C13 = [57/64/73]
34a. 8 in N4 only in 20(4) cage = {1289/1568/2378/2468} (cannot be {1478/3458} which clash with R6C13)
34b. Killer pair 2,5 in 20(4) cage and R4C3, locked for N4
35. R6C134 (step 33b) = [738/648] > R6C4 = 8, R6C3 = {34}, R5C4 = 6
36. R6C258 (step 26) = {237/246}, 2 locked for R6 > R6C9 = 1
36a. Killer pair 3,4 in R6C258 and R6C3, locked for R6
37. 23(4) cage at R6C6 (step 29) = {1589} (only remaining combination) > R7C78 = [81]
38. Naked triple {234} in R6C3 + R7C23, 2 locked for R7 and N7, CPE no 4 in R89C3
39. 45 rule on N4 5 innies R4C23 + R5C3 + R6C13 = 25 = {13579/14569/23479/34567} (cannot be {12679/23569} which clash with 20(4) cage)
39a. 1 of {13579} must be in R5C3, 3,4 of {23479/34567} must be in R56C3 > no 7 in R5C3
40. Naked pair {14} in R35C3, locked for C3 > R67C3 = [32], R4C3 = 5, R7C2 = 4, R6C1 = 7 (step 34), R56C5 = [32], R6C2 = 6, R6C8 = 4, R4C2 = 9, R3C3 = 4 (step 14), R3C6 = 8, R5C3 = 1, R45C7 = [67], R6C5 = 5 (step 17), R6C67 = [95], R78C4 = [72]
41. Naked pair {56} in R3C89, locked for R3 and N3 > R2C9 = 4, R3C12 = [37], R2C1 = 8, R2C3 = 9, R4C1 = 2, R5C12 = [48], R4C9 = 8, R2C7 = 3, R1C9 = 9, R12C8 = [87], R12C6 = [42], R2C2 = 1
42. Naked pair {35} in R89C2, locked for C2 and N7 > R9C1 = 6, R7C1 = 9, R8C1 = 1, R8C2 = 5 (cage sum)
and the rest is naked singles.
Unfortunately because of a rework with simpler steps, after I realised that I’d missed some eliminations, I was unable to use the interesting
45 rule on R12 2 innies R2C19 = 2 outies R3C46 + 3
R3C4 is odd, R3C6 is even > R3C46 must be odd > R2C19 must be even > no 8 in R2C9 (R2C19 cannot be [88] and all other combinations for R2C19 with 8 in R2C9 are odd) 

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Andrew Grandmaster
Joined: 11 Aug 2006 Posts: 300 Location: Lethbridge, Alberta

Posted: Sat Apr 10, 2010 3:59 am Post subject: 


Back in November 2006 Richard posted the SudokuSolver log from the then current version of his solver.
Ed kindly provided me with the log from the current version of SS and I was impressed at the improvements which Richard has made, including making the first placement in step 1, so I'm posting this log.
I was also interested to see that the latest version of SS solved A24 without needing to use 45 rule on C12, something which Ed and I had considered an important step and which had also been used in the earlier SS log.
Here is the SSv3.3.1 log for A24. I've taken the liberty of doing minor editing for clarity.
Preliminaries
Cage 13(2) n2  cells do not use 123
Cage 9(2) n8  cells do not use 9
Cage 9(2) n8  cells do not use 9
Cage 10(3) n58  cells do not use 89
Cage 27(4) n14  cells do not use 12
Cage 27(4) n3  cells do not use 12
1. 45 Rule on n8 found single innie r7c5=5
1a. Cage sum in cage 13(2) n2  removed 8 from r1c5  removed 8 from r2c5
1b. Cage sum in cage 10(3) n58  removed 67 from r5c5  removed 67 from r6c5
1c. Cage sum in cage 9(2) n8  removed 4 from r7c4  removed 4 from r8c4
1d. Cage sum in cage 9(2) n8  removed 4 from r7c6  removed 4 from r8c6
1e. Combinations {58} no longer valid in cage 13(2) n2
1f. Combinations {45} no longer valid in cage 9(2) n8
1g. Combinations {45} no longer valid in cage 9(2) n8
1h. Combinations {1579} {2569} {2578} {3568} {4567} no longer valid in cage 22(4) n8
1i. Combinations {1458} {2457} {3456} no longer valid in combined cages 9(2) n8 & 9(2) n8
2. 45 Rule on c6789  innies r49c6 total 8
2a. Removed candidates 3489 from r4c6
2b. Removed candidates 489 from r9c6
2c. Found a hidden cage h8(2) n58
3. 45 Rule on c1234  innies r49c4 total 13
3a. Removed candidates 1238 from r4c4
3b. Removed candidates 123 from r9c4
3c. Found a hidden cage h13(2) n58
4. Candidate 9 locked in cage 27(4) n3 for n3 nowhere else in n3
5. Candidate 4 in n8 must be in cage 22(4) n8
5a. Removed combinations {1678} {2389}
6. Candidate 9 in n8 must be in cage 22(4) n8
6a. Removed combination {3478}
7. Must use candidate 9 in cage 27(4) n14
7a. Removed 9 from r12c2
8. Split cage 5(2) n5 restricts combinations in cage 21(4) n25
8a. Removed combination {1389}  blocked by {13}
8b. Removed combination {2469}  blocked by {24}
8c. Removed combination {2478}  blocked by {24}
8d. Removed combination {3459}  blocked by {34}
8e. Removed combination {3468}  blocked by {34}
9. 45 Rule on n79  outies total 33 > remaining cells r6c258 total 12
9a. Found a hidden cage h12(3) n456
10. 45 Rule on r9  outies r8c357 total 21
10a. Removed candidates 123 from r8c3
10b. Removed candidates 123 from r8c5
10c. Removed candidates 123 from r8c7
10d. Found a hidden cage h21(3) n789
11. Limited placement of candidates in cage 22(4) n8
11a. Removed 1 from r9c5
12. 45 Rule on n7  outies r6c134 total 18
12a. Found a hidden cage h18(3) n45
13. 45 Rule on n9  outies r6c679 total 15
13a. Found a hidden cage h15(3) n56
14. 45 Rule on n3  innies r13c7 equal outies r4c8
14a. Removed candidates 12 from r4c8
15. 45 Rule on n7  outies r6c1 minus innies r7c23 equals 1
15a. Removed candidates 123 from r6c1
15b. Removed candidates 89 from r7c2
15c. Removed candidates 89 from r7c3
16. 45 Rule on n1  innies r13c3 minus outies r4c2 equals 1
16a. Found a hidden cage innie/outie cells (r13c3)(r4c2)=1
17. 45 Rule on n2  innies r3c5 minus outies r1c37 equals 2
17a. Removed candidates 789 from r1c3
17b. Removed candidates 78 from r1c7
17c. Removed candidates 1234 from r3c5
18. Candidate 1 locked in c5 for n5 nowhere else in n5
18a. Cage sum in cage h8(2) n58  removed 7 from r9c6
19. Limited placement of candidates in cage 22(4) n8
19a. Removed 2 from r9c5
20. Candidate 2 locked in c5 for n5 nowhere else in n5
20a. Cage sum in cage h8(2) n58  removed 6 from r9c6
21. Limited placement of candidates in cage 22(4) n8
21a. Removed 3 from r9c5
22. Candidate 3 locked in c5 for n5 nowhere else in n5
23. Hidden triple {123} found at r456c5 in c5
23a. Cage sum in cage 10(3) n58  removed 1 from r5c5  removed 1 from r6c5
23b. Only combination {235} valid in cage 10(3) n58
23c. Combinations {14} no longer valid in split cage 5(2) n5
23d. Combinations {1467} no longer valid in combined cages 13(2) n2 & s5(2) n5
24. Naked pair {23} found at r56c5, locked for c5
24a. Combinations {2379} {2568} {3567} no longer valid in cage 21(4) n25
25. Naked Single 1 found at r4c5
26. Combinations {147} {156} no longer valid in cage h12(3) n456
27. Limited placement of candidates in cage 21(4) n25
27a. Removed 7 from r3c5
28. Cage h12(3) n456 restricts combinations in cage h18(3) n45
28a. Removed combination {369}  blocked by {369}
29. Cage h12(3) n456 restricts combinations in cage h15(3) n56
29a. Removed combination {258}  blocked by {258}
30. 45 Rule on c5  innies r389c5 total 21
30a. Found a hidden cage h21(3) n28
31. 45 Rule on n9  innies r7c78 minus outies r6c9 equals 8
31a. Found a hidden cage innie/outie cells (r7c78)(r6c9)=8
32. 45 Rule on n147  outies r56c4 minus innies r1c3 equals 8
32a. Found a hidden cage innie/outie cells (r56c4)(r1c3)=8
33. 45 Rule on n369  outies r56c6 minus innies r1c7 equals 13
33a. Removed candidates 56 from r1c7
33b. Removed candidate 4 from r5c6
33c. Removed candidate 4 from r6c6
34. Candidate 4 locked in c6 for n2 nowhere else in n2
34a. Cage sum in cage 13(2) n2  removed 9 from r1c5  removed 9 from r2c5
34b. Combinations {49} no longer valid in cage 13(2) n2
34c. Combinations {2349} no longer valid in combined cages 13(2) n2 & s5(2) n5
35. Naked pair {67} found at r12c5, locked for c5 and n2
35a. Combinations {1257} {1347} no longer valid in cage 15(4) n12
35b. Only combinations {1239} {1248} valid in cage 15(4) n23
35c. Combinations {678} no longer valid in cage h21(3) n28
36. Removed redundant candidates 5 from cage 15(4) n23
37. Candidate 5 locked in n2 for c4 nowhere else in c4
37a. Cage sum in cage h13(2) n58  removed 8 from r9c4
37b. Combinations {58} no longer valid in cage h13(2) n58
37c. Combinations {2578} {3568} no longer valid in combined cages 9(2) n8 & h13(2) n58
38. Candidate 4 locked in n5 for c4 nowhere else in c4
38a. Cage sum in cage h13(2) n58  removed 9 from r4c4
39. Candidate 4 in c6 must be in cage 15(4) n23
39a. Removed combination {1239}  cells ={1248}
40. Naked quad {1248} found at r1c67 r23c6
41. Combinations {1248} no longer valid in cage 15(4) n12
41a. Removed redundant candidates 8
42. Candidate 3 locked in n2 for c4 nowhere else in c4
42a. Cage sum in cage 9(2) n8  removed 6 from r7c4  removed 6 from r8c4
42b. Combinations {36} no longer valid in cage 9(2) n8
42c. Combinations {3469} no longer valid in combined cages 9(2) n8 & h13(2) n58
43. Candidate 9 locked in c6 for n5 nowhere else in n5
44. Combinations {1259} no longer valid in cage 17(4) n457
45. Candidate 4 locked in c6 for cage 15(4) n23 & n2 nowhere else in cage 15(4) n23 or n2
46. Candidate 8 locked in cage 15(4) n23 for c6 & n2 nowhere else in c6 or n2
46a. Cage sum in cage 9(2) n8  removed 1 from r7c6  removed 1 from r8c6
46b. Combinations {1578} no longer valid in cage 21(4) n25
46c. Combinations {18} no longer valid in cage 9(2) n8
46d. Combinations {1268} {1358} no longer valid in combined cages 9(2) n8 & h8(2) n58
47. Naked Single 9 found at r3c5
47a. Cage sum in cage 21(4) n25  removed 7 from r4c4  removed 6 from r4c6
47b. Combinations {1239} no longer valid in cage 15(4) n12
47c. Cage sum in innie/outie cells (r3c5)(r1c37)=2  removed 1234 from r1c3
48. Naked pair {48} found at r89c5, locked for n8
48a. Cage sum in cage 9(2) n8  removed 1 from r7c4  removed 1 from r8c4
48b. Combinations {18} no longer valid in cage 9(2) n8
48c. Only combination {2367} valid in combined cages 9(2) n8 & 9(2) n8
48d. Only combination {2479} valid in combined cages 9(2) n8 & h13(2) n58
49. Naked pair {27} found at r78c4, locked for c4 and n8
49a. Cage sum in cage h13(2) n58  removed 6 from r4c4  removed 6 from r9c4
49b. Combinations {2346} no longer valid in cage 15(4) n12
49c. Combinations {27} no longer valid in cage 9(2) n8
49d. Only combination {1489} valid in cage 22(4) n8
49e. Combinations {26} no longer valid in cage h8(2) n58
49f. Combinations {67} no longer valid in cage h13(2) n58
49g. Combinations {2357} no longer valid in combined cages 9(2) n8 & h8(2) n58
50. Naked Single 4 found at r4c4
50a. Last cell in cage 21(4) n25 at r4c6 set to 7
50b. Combinations {1569} no longer valid in cage 21(4) n25
51. Naked Single 9 found at r9c4
52. Naked pair {36} found at r78c6, locked for c6
53. Naked Single 1 found at r9c6
53a. Combinations {1689} no longer valid in cage 24(4) n7
53b. Combinations {1289} {1379} {1469} {1478} {1568} no longer valid in cage 20(4) n9
54. Naked triple {248} found at r123c6, locked for cage 15(4) n23
54a. Cage sum in innie/outie cells (r3c5)(r1c37)=2  removed 5 from r1c3
55. Naked Single 6 found at r1c3
55a. Cage sum in cage 13(2) n2  removed 7 from r2c5
55b. Combinations {1268} {1367} {2456} no longer valid in cage 17(4) n1
55c. Cage sum in innie/outie cells (r13c3)(r4c2)=1  removed 2578 from r3c3  removed 35 from r4c2
56. Naked Single 7 found at r1c5
57. Naked Single 1 found at r1c7
57a. Only combinations {2349} {2358} {2367} {2457} {3456} valid in cage 18(4) n36
57b. Combinations {1289} {1379} {1469} {1478} {1568} no longer valid in cage 20(4) n356
57c. Cage sum in innie/outie cells (r13c7)=(r4c8)  removed 36 from r3c7
58. Naked Single 6 found at r2c5
58a. Only combination {3789} valid in cage 27(4) n3
59. Removed redundant candidates 45 from cage 27(4) n3
60. Naked quad {3789} found at r1c89 r2c78, locked for n3 (but not 7 locked for r2, those eliminations are made in step 69)
60a. Combinations {2367} {2457} no longer valid in cage 18(4) n36
60b. Cage sum in innie/outie cells (r13c7)=(r4c8)  removed 89 from r4c8
61. Hidden single 3 found at r4c8 in cage 18(4) n36
61a. Only combination {3456} valid in cage 18(4) n36
61b. Only combinations {2459} {2468} {2567} valid in cage 20(4) n356
61c. Combinations {3479} {3569} {3578} no longer valid in cage 23(4) n6
61d. Combinations {348} {357} no longer valid in cage h15(3) n56
61e. Last cell in innie/outie cells (r13c7)=(r4c8) at r3c7 set to 2
62. Combinations {2468} no longer valid in cage 20(4) n356
62a. Removed redundant candidates 8
63. Combinations {1249} {1357} {2347} no longer valid in cage 16(4) n145
63a. Removed redundant candidates 9
64. Combinations {1349} {1457} {2357} no longer valid in cage 17(4) n457
64a. Removed redundant candidates 9
65. Combinations {2678} no longer valid in cage 23(4) n569
66. Combinations {579} no longer valid in cage h21(3) n789
66a. Removed redundant candidates 5
67. Combinations {168} {267} no longer valid in cage h15(3) n56
67a. Removed redundant candidates 78
68. Combinations {279} {459} no longer valid in cage h18(3) n45
68a. Removed redundant candidates 2
69. Candidate 7 locked in r3 for n1 nowhere else in n1
69a. Combinations {1457} {2357} no longer valid in cage 17(4) n1
70. 45 Rule on n147  outies r56c4 total 14
70a. Found a hidden cage h14(2) n5
71. 45 Rule on n5  innies r56c6 total 14
71a. After removing cage h14(2) n5
71b. Found a hidden cage h14(2) n5
72. 45 Rule on n1  outies r4c2 minus innies r3c3 equals 5
72a. Found a hidden cage innie/outie cells (r4c2)(r3c3)=5
73. Candidate 8 locked in cage h21(3) n789 for r8 nowhere else in r8
74. Candidate 7 in r3 must be in cage 27(4) n14
74a. Removed combination {4689}  cells do not use 124
75. Candidate 2 in n1 must be in cage 17(4) n1
75a. Removed combinations {1349} {1358}
76. Candidate 8 in n6 must be in cage 23(4) n6
76a. Removed combinations {1679} {2579}
77. Must use candidate 5 in cage 20(4) n356
77a. Removed 5 from r5c89
78. Must use candidate 9 in cage 27(4) n14
78a. Removed 9 from r456c1
78b. Combinations {189} no longer valid in cage h18(3) n45
79. Combinations {1379} no longer valid in cage 20(4) n4
80. Removed redundant candidates 1 from cage h18(3) n45
81. Candidate 9 locked in n4 for c2 nowhere else in c2
82. Limited placement of candidates in cage 20(4) n356
82a. Removed 569 from r5c7
83. Limited placement of candidates in cage 27(4) n14
83a. Removed 5 from r2c1
84. Limited placement of candidates in cage 16(4) n145
84a. Removed combination {1348}  no valid placement
84b. Removed 8 from r4c3
84c. Removed 38 from r5c3
85. Limited placement of candidates in cage 17(4) n457
85a. Removed 6 from r7c2
86. Limited placement of candidates in cage 23(4) n569
86a. Removed combination {3578}  no valid placement
86b. Removed 9 from r7c7
87. Cell at r4c3 restricts combinations in cage 20(4) n4
87a. Removed combination {2459}  blocked by {25}
87b. Removed combination {2567}  blocked by {25}
88. Cage 20(4) n356 restricts combinations in cage 23(4) n6
88a. Removed combination {4568}  blocked by {46}
89. Cage 23(4) n569 restricts combinations in cage 20(4) n9
89a. Removed combination {2378}  blocked by {378}
90. Cage h18(3) n45 restricts combinations in cage 20(4) n4
90a. Removed combination {1478}  blocked by {47}
90b. Removed combination {3467}  blocked by {47}
90c. Removed combination {3458}  blocked by {345}
91. Cage h15(3) n56 restricts combinations in cage h12(3) n456
91a. Removed combination {345}  blocked by {45}
91b. Removed redundant candidates 5
92. Hidden Killer Pair {35} in n1 using cage 27(4) n14 and cage 17(4) n1
92a. Removed {3} from r3c3
92b. Combinations {2356} no longer valid in cage 16(4) n145
92c. Cage sum in innie/outie cells (r13c3)(r4c2)=1  removed 8 from r4c2
93. Candidate 1 locked in cage 16(4) n145 for c3 nowhere else in c3
94. Limited placement of candidates in cage 17(4) n1
94a. Removed 5 from r2c2
95. Limited placement of candidates in cage 17(4) n457
95a. Removed 7 from r7c2
96. Cell at r4c2 restricts combinations in cage 20(4) n4
96a. Removed combination {1469}  blocked by {69}
96b. Removed combination {2369}  blocked by {69}
97. Candidate 8 locked in cage 20(4) n4 for n4 nowhere else in n4
98. Combinations {1268} no longer valid in cage 17(4) n457
99. Combinations {2389} no longer valid in cage 22(4) n47
100. Killer Pair {25} in n4 using r4c3 and cage 20(4) n4
100a. Removed {25} from r6c13 r5c3
100b. Combinations {1358} {2456} no longer valid in cage 17(4) n457
100c. Combinations {567} no longer valid in cage h18(3) n45
101. Hidden single 8 found at r6c4 in cage h18(3) n45
101a. Cage sum in cage h18(3) n45  removed 4 from r6c1  removed 7 from r6c3
101b. Combinations {1258} no longer valid in cage 16(4) n145
101c. Combinations {1367} no longer valid in cage 17(4) n457
101d. Combinations {138} no longer valid in cage h12(3) n456
102. Naked Single 6 found at r5c4
103. Removed redundant candidates 17 from cage 17(4) n457
104. Naked triple {234} found at r7c23 r6c3
105. Combinations {1489} no longer valid in cage 22(4) n47
106. 45 Rule on n7  outies r6c13 total 10
106a. Found a hidden cage h10(2) n4
107. Candidate 2 locked in cage 17(4) n457 for r7 & n7 nowhere else in r7 or n7
107a. Cage sum in cage 9(2) n8  removed 7 from r8c4
107b. Combinations {2479} {2569} {2578} no longer valid in cage 22(4) n47
107c. Combinations {2489} {2579} no longer valid in cage 23(4) n569
107d. Combinations {2589} {2679} no longer valid in cage 24(4) n7
108. Naked Single 7 found at r7c4
108a. Combinations {1679} {3479} no longer valid in cage 23(4) n569
109. Naked Single 2 found at r8c4
110. Candidate 5 locked in cage 23(4) n569 for r6 nowhere else in r6
111. Candidate 2 locked in cage h12(3) n456 for r6 nowhere else in r6
111a. Only combinations {1349} {1358} {1367} {1457} valid in cage 17(4) n69
111b. Combinations {249} no longer valid in cage h15(3) n56
112. Candidate 2 in n6 must be in cage 23(4) n6
112a. Removed combination {1589}  cells do not use 15
113. Hidden single 1 found at r6c9 in n6
113a. Cage sum in cage h15(3) n56  removed 46 from r6c7
113b. Cage sum in innie/outie cells (r7c78)(r6c9)=8  removed 46 from r7c7  removed 489 from r7c8
113c. Combinations {129} no longer valid in cage h12(3) n456
113d. Combinations {456} no longer valid in cage h15(3) n56
114. Naked pair {59} found at r6c67, locked for r6
115. Hidden single 1 found at r7c8 in c8
115a. Only combination {1589} valid in cage 23(4) n569
115b. Last cell in innie/outie cells (r7c78)(r6c9)=8 at r7c7 set to 8
116. Combinations {1358} no longer valid in cage 17(4) n69
117. Combinations {2468} {3458} no longer valid in cage 20(4) n9
118. Combinations {1678} {3478} {3568} no longer valid in cage 22(4) n47
119. Candidate 5 locked in n6 for c7 nowhere else in c7
120. 45 Rule on n6  innies r6c7 equal outies r5c6
120a. Found a hidden cage innie/outie cells (r6c7)=(r5c6)
121. Candidate 1 in r8 must be in cage 22(4) n47
121a. Removed combinations {3469} {4567}  cells ={1579}
121b. Cage sum in cage h10(2) n4  removed 4 from r6c3
121c. Combinations {46} no longer valid in cage h10(2) n4
121d. Combinations {468} no longer valid in cage h18(3) n45
122. Naked Single 7 found at r6c1
122a. Combinations {1267} no longer valid in cage 16(4) n145
122b. Combinations {2378} no longer valid in cage 20(4) n4
122c. Combinations {237} no longer valid in cage h12(3) n456
123. Naked Single 3 found at r6c3
123a. Cage sum in cage 10(3) n58  removed 2 from r5c5
124. Naked Single 3 found at r5c5
125. Naked Single 2 found at r6c5
126. Naked Single 9 found at r7c1
126a. Only combinations {3678} {4578} valid in cage 24(4) n7
127. Naked pair {14} found at r35c3, locked for c3
127a. Cage sum in cage 17(4) n457  removed 2 from r7c2
128. Naked Single 4 found at r7c2
128a. Cage sum in cage h12(3) n456  removed 6 from r6c8
128b. Combinations {1289} no longer valid in cage 20(4) n4
128c. Combinations {4578} no longer valid in cage 24(4) n7
129. Naked Single 6 found at r6c2
129a. Combinations {5679} no longer valid in cage 27(4) n14
129b. Cage sum in innie/outie cells (r4c2)(r3c3)=5  removed 1 from r3c3
130. Naked Single 4 found at r3c3
130a. Cage sum in cage 16(4) n145  removed 2 from r4c3
130b. Combinations {2348} no longer valid in cage 17(4) n1
131. Naked Single 8 found at r3c6
132. Naked Single 9 found at r4c2
132a. Combinations {2678} no longer valid in cage 23(4) n6
133. Naked Single 5 found at r4c3
133a. Combinations {2459} no longer valid in cage 20(4) n356
133b. Combinations {1568} no longer valid in cage 20(4) n4
134. Naked Single 6 found at r4c7
134a. Cage sum in cage 20(4) n356  removed 9 from r5c6  removed 4 from r5c7
134b. Combinations {678} no longer valid in cage h21(3) n789
135. Naked Single 1 found at r5c3
136. Naked Single 5 found at r5c6
136a. Cage sum in cage 23(4) n569  removed 9 from r6c7
136b. Last cell in innie/outie cells (r6c7)=(r5c6) at r6c7 set to 5
137. Naked single 9 found at r6c6
138. Naked Single 7 found at r5c7
139. Naked Single 4 found at r6c8
140. Naked Single 2 found at r7c3
141. Naked pair {56} found at r3c89, locked for r3 and n3
142. Naked Single 4 found at r2c9
142a. Cage sum in cage 15(4) n23  removed 2 from r1c6
142b. Only combination {1367} valid in cage 17(4) n69
143. Naked Single 4 found at r1c6
144. Naked Single 2 found at r2c6
145. Naked Single 3 found at r3c1
146. Naked Single 8 found at r2c1
147. Naked Single 1 found at r2c2
147a. Cage sum in cage 22(4) n47  removed 5 from r8c1
148. Naked Singles 1 found at: r3c4 r8c1
149. Naked Single 9 found at r2c3
150. Naked Single 3 found at r2c7
150a. Cage sum in cage 15(4) n12  removed 5 from r1c4
150b. Combinations {2369} {2567} no longer valid in cage 20(4) n9
151. Naked Singles 35 found at: r12c4
152. Naked Single 7 found at r2c8
153. Naked Single 7 found at r3c2
154. Naked Single 2 found at r4c1
154a. Cage sum in cage 17(4) n1  removed 5 from r1c2
155. Naked Singles 24 found at:r1c2 r5c1
156. Naked Single 5 found at r1c1
157. Naked Single 8 found at r4c9
157a. Cage sum in cage 27(4) n3  removed 9 from r1c8
158. Naked Single 8 found at r1c8
159. Naked Single 9 found at r1c9
159a. Cage sum in cage 23(4) n6  removed 2 from r5c8
160. Naked Single 8 found at r5c2
161. Naked Single 9 found at r5c8
162. Naked Single 2 found at r5c9
163. Naked Single 5 found at r8c2
164. Naked Single 6 found at r8c8
164a. Cage sum in cage 18(4) n36  removed 5 from r3c9
164b. Cage sum in cage 17(4) n69  removed 3 from r8c9
164c. Cage sum in cage 9(2) n8  removed 3 from r7c6
164d. Combinations {3467} no longer valid in cage 20(4) n9
165. Naked Singles found at: r78c6 r3c9 r9c1
166. Naked Single 5 found at r3c8
167. Naked Single 2 found at r9c8
168. Naked Single 3 found at r7c9
169. Naked Single 3 found at r9c2
170. Naked Single 7 found at r8c9
170a. Cage sum in cage 24(4) n7  removed 8 from r9c3
171. Naked Singles 75 found at: r9c39
171a. Cage sum in cage 20(4) n9  removed 4 from r8c7
172. Naked Single 9 found at r8c7
172a. Cage sum in cage h21(3) n789  removed 8 from r8c5
173. Naked Single 8 found at r8c3
174. Naked Single 4 found at r8c5
175. Naked Singles 84 found at: r9c57
Puzzle Complete 

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