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Billabob

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Feb 24th, 2025
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  1. Cages are numbered top-down left-right starting from 0. If this is hard to understand, here is a key: https://i.imgur.com/lrmzXpE.png
  2.  
  3. Max difficulty: 4.8; total difficulty: 351.9
  4.  
  5. 0: Filled in initial combinations & candidates
  6. 1: (0) Naked single: 7 in r1c6
  7. 2: (0) Naked single: 4 in r1c8
  8. 3: (0) Naked single: 4 in r3c1
  9. 4: (0) Naked single: 7 in r7c3
  10. 5: (0) Naked single: 4 in r7c4
  11. 6: (0) Naked single: 2 in r7c7
  12. 7: (0) Naked single: 7 in r8c4
  13. 8: (0) Naked single: 2 in r8c8
  14. 9: (1) Hidden single: 4 in r8c5
  15. 10: (1.5) Pointing candidates: all combinations for cage 13 contain 1c1,2c1; eliminations in r1c1, r2c1, r6c1
  16. 11: (0) Naked single: 7 in r6c1
  17. 12: (0) Naked single: 3 in r7c1
  18. 13: (1.5) Pointing candidates: all combinations for cage 15 contain 4c6; eliminations in r2c6, r6c6
  19. 14: (1.5) Pointing candidates: all combinations for cage 16 contain 1r4,5r4; eliminations in r4c1, r4c2, r4c5, r4c6
  20. 15: (0) Naked single: 2 in r4c1
  21. 16: (0) Naked single: 1 in r5c1
  22. 17: (1.5) Pointing candidates: all combinations for cage 23 contain 5c8,8c8; eliminations in r2c8, r3c8, r4c8, r5c8
  23. 18: (0) Naked single: 5 in r4c7
  24. 19: (0) Naked single: 1 in r4c8
  25. 20: (3.2) Region parity: Cols 7, 8 must sum to Even number; cage 12's cells within this region must sum to Odd number; reduced from 8 combinations to 4
  26. 21: (3.4) Region sum: Cols 7, 8 must sum to 72; cages 12, 30's cells within this region must sum to 16; cages 12 reduced from 4 combinations to 3
  27. 22: (1.5) Claiming candidates: cage 10 must contain 1 in r3c3, r3c4: from 16 combinations to 10
  28. 23: (1.5) Pointing candidates: all combinations for cage 12 contain 7r3; eliminations in r3c5
  29. 24: (4) Cage comparison: cages 23, 17 interact such that cage 17 has incongruous combinations; reduced from 71 to 65 combinations
  30. 25: (4) Cage comparison: cages 26, 2 interact such that cage 2 has incongruous combinations; reduced from 56 to 54 combinations
  31. 26: (4) Cage comparison: cages 30, 22 interact such that cage 22 has incongruous combinations; reduced from 11 to 10 combinations
  32. 27: (4) Cage comparison: cages 20, 4 interact such that cage 4 has incongruous combinations; reduced from 7 to 5 combinations
  33. 28: (4) Cage comparison: cages 20, 17 interact such that cage 17 has incongruous combinations; reduced from 65 to 62 combinations
  34. 29: (4) Cage comparison: cages 0, 2 interact such that cage 2 has incongruous combinations; reduced from 54 to 47 combinations
  35. 30: (4) Cage comparison: cages 4, 2 interact such that cage 2 has incongruous combinations; reduced from 47 to 46 combinations
  36. 31: (4) Cage comparison: cages 11, 19 interact such that cage 19 has incongruous combinations; reduced from 16 to 12 combinations
  37. 32: (4) Cage comparison: cages 11, 2 interact such that cage 2 has incongruous combinations; reduced from 46 to 39 combinations
  38. 33: (4) Cage comparison: cages 14, 1 interact such that cage 1 has incongruous combinations; reduced from 19 to 17 combinations
  39. 34: (4.2) Cage comparison: cages 23, 26, 22 interact such that cage 22 has incongruous combinations; reduced from 10 to 9 combinations
  40. 35: (4.2) Cage comparison: cages 23, 26, 17 interact such that cage 17 has incongruous combinations; reduced from 62 to 55 combinations
  41. 36: (4.2) Cage comparison: cages 26, 11, 2 interact such that cage 2 has incongruous combinations; reduced from 39 to 34 combinations
  42. 37: (4.2) Cage comparison: cages 30, 22, 7 interact such that cage 7 has incongruous combinations; reduced from 14 to 12 combinations
  43. 38: (4.2) Cage comparison: cages 12, 4, 20 interact such that cage 12 has incongruous combinations; reduced from 3 to 2 combinations
  44. 39: (4.2) Cage comparison: cages 4, 0, 2 interact such that cage 2 has incongruous combinations; reduced from 34 to 30 combinations
  45. 40: (4.2) Cage comparison: cages 20, 14, 18 interact such that cage 18 has incongruous combinations; reduced from 11 to 9 combinations
  46. 41: (4) Cage comparison: cages 18, 2 interact such that cage 2 has incongruous combinations; reduced from 30 to 29 combinations
  47. 42: (4.2) Cage comparison: cages 20, 14, 17 interact such that cage 17 has incongruous combinations; reduced from 55 to 54 combinations
  48. 43: (4.2) Cage comparison: cages 0, 28, 17 interact such that cage 17 has incongruous combinations; reduced from 54 to 53 combinations
  49. 44: (4.2) Cage comparison: cages 28, 14, 17 interact such that cage 17 has incongruous combinations; reduced from 53 to 52 combinations
  50. 45: (4.2) Cage comparison: cages 28, 9, 17 interact such that cages 9, 17 have incongruous combinations; reduced from 12, 52 to 10, 42 combinations respectively
  51. 46: (4.2) Cage comparison: cages 11, 19, 2 interact such that cage 2 has incongruous combinations; reduced from 29 to 27 combinations
  52. 47: (4.4) Cage comparison: cages 23, 26, 22, 17 interact such that cage 17 has incongruous combinations; reduced from 42 to 40 combinations
  53. 48: (4.4) Cage comparison: cages 26, 11, 19, 2 interact such that cage 19 has incongruous combinations; reduced from 12 to 10 combinations
  54. 49: (4.4) Cage comparison: cages 4, 0, 6, 2 interact such that cages 0, 6, 2 have incongruous combinations; reduced from 6, 7, 27 to 5, 6, 20 combinations respectively
  55. 50: (4.4) Cage comparison: cages 4, 0, 1, 2 interact such that cages 1, 2 have incongruous combinations; reduced from 17, 20 to 15, 16 combinations respectively
  56. 51: (4.4) Cage comparison: cages 15, 11, 14, 9 interact such that cage 9 has incongruous combinations; reduced from 10 to 9 combinations
  57. 52: (4.4) Cage comparison: cages 0, 28, 9, 17 interact such that cage 17 has incongruous combinations; reduced from 40 to 37 combinations
  58. 53: (4.4) Cage comparison: cages 18, 10, 1, 2 interact such that cages 1, 2 have incongruous combinations; reduced from 15, 16 to 14, 15 combinations respectively
  59. 54: (4.4) Cage comparison: cages 4, 0, 6, 2 interact such that cage 6 has incongruous combinations; reduced from 6 to 4 combinations
  60. 55: (4.4) Cage comparison: cages 4, 0, 1, 2 interact such that cage 1 has incongruous combinations; reduced from 14 to 10 combinations
  61. 56: (4.4) Cage comparison: cages 28, 6, 14, 17 interact such that cage 17 has incongruous combinations; reduced from 37 to 35 combinations
  62. 57: (4.4) Cage comparison: cages 28, 6, 9, 17 interact such that cage 17 has incongruous combinations; reduced from 35 to 33 combinations
  63. 58: (4.4) Cage comparison: cages 12, 4, 6, 7 interact such that cage 7 has incongruous combinations; reduced from 12 to 11 combinations
  64. 59: (4.6) Cage comparison: cages 12, 30, 4, 22, 7 interact such that cages 22, 7 have incongruous combinations; reduced from 9, 11 to 8, 10 combinations respectively
  65. 60: (4.6) Cage comparison: cages 12, 4, 20, 18, 2 interact such that cage 18 has incongruous combinations; reduced from 9 to 8 combinations
  66. 61: (4.6) Cage comparison: cages 12, 15, 20, 11, 14 interact such that cage 11 has incongruous combinations; reduced from 7 to 6 combinations
  67. 62: (4.6) Cage comparison: cages 12, 15, 20, 14, 9 interact such that cage 9 has incongruous combinations; reduced from 9 to 8 combinations
  68. 63: (4.6) Cage comparison: cages 23, 20, 14, 18, 17 interact such that cage 17 has incongruous combinations; reduced from 33 to 32 combinations
  69. 64: (4.6) Cage comparison: cages 23, 22, 18, 19, 17 interact such that cage 17 has incongruous combinations; reduced from 32 to 29 combinations
  70. 65: (4.6) Cage comparison: cages 6, 0, 4, 1, 2 interact such that cage 1 has incongruous combinations; reduced from 10 to 7 combinations
  71. 66: (4.6) Cage comparison: cages 6, 0, 28, 9, 17 interact such that cage 17 has incongruous combinations; reduced from 29 to 25 combinations
  72. 67: (4.6) Cage comparison: cages 6, 20, 28, 14, 17 interact such that cage 17 has incongruous combinations; reduced from 25 to 23 combinations
  73. 68: (4.8) Cage comparison: cages 12, 6, 0, 4, 20, 17 interact such that cage 17 has incongruous combinations; reduced from 23 to 22 combinations
  74. 69: (4.8) Cage comparison: cages 12, 15, 20, 14, 18, 10 interact such that cage 10 has incongruous combinations; reduced from 10 to 9 combinations
  75. 70: (4.8) Cage comparison: cages 23, 26, 18, 22, 19, 17 interact such that cage 17 has incongruous combinations; reduced from 22 to 20 combinations
  76. 71: (4.6) Cage comparison: cages 17, 6, 28, 9, 7 interact such that cage 7 has incongruous combinations; reduced from 10 to 9 combinations
  77. 72: (4.6) Cage comparison: cages 17, 0, 28, 1, 14 interact such that cage 28 has incongruous combinations; reduced from 6 to 5 combinations
  78. 73: (4.8) Cage comparison: cages 23, 20, 28, 14, 18, 17 interact such that cage 17 has incongruous combinations; reduced from 20 to 19 combinations
  79. 74: (4.8) Cage comparison: cages 30, 0, 4, 1, 7, 2 interact such that cage 2 has incongruous combinations; reduced from 15 to 13 combinations
  80. 75: (4.4) Cage comparison: cages 2, 20, 14, 18 interact such that cage 18 has incongruous combinations; reduced from 8 to 7 combinations
  81. 76: (4.6) Cage comparison: cages 2, 6, 0, 4, 7 interact such that cage 7 has incongruous combinations; reduced from 9 to 8 combinations
  82. 77: (4.8) Cage comparison: cages 6, 0, 4, 28, 1, 2 interact such that cages 1, 2 have incongruous combinations; reduced from 7, 13 to 6, 12 combinations respectively
  83. 78: (4.8) Cage comparison: cages 6, 0, 4, 1, 7, 2 interact such that cages 1, 7 have incongruous combinations; reduced from 6, 8 to 5, 7 combinations respectively
  84. 79: (4.6) Cage comparison: cages 1, 4, 18, 10, 2 interact such that cage 2 has incongruous combinations; reduced from 12 to 11 combinations
  85. 80: (1.5) Claiming candidates: cage 4 must contain 7 in r2c7, r2c8: from 5 combinations to 4
  86. 81: (1.5) Claiming candidates: cage 20 must contain 4 in r5c7, r6c7: from 5 combinations to 4
  87. 82: (4.2) Cage comparison: cages 20, 15, 14 interact such that cages 15, 14 have incongruous combinations; reduced from 5, 7 to 4, 6 combinations respectively
  88. 83: (4.2) Cage comparison: cages 14, 2, 10 interact such that cage 10 has incongruous combinations; reduced from 9 to 8 combinations
  89. 84: (4.6) Cage comparison: cages 4, 1, 2, 6, 0 interact such that cage 0 has incongruous combinations; reduced from 5 to 4 combinations
  90. 85: (4.4) Cage comparison: cages 0, 28, 14, 9 interact such that cage 9 has incongruous combinations; reduced from 8 to 7 combinations
  91. 86: (4.4) Cage comparison: cages 0, 9, 28, 17 interact such that cage 28 has incongruous combinations; reduced from 5 to 4 combinations
  92. 87: (4.2) Cage comparison: cages 28, 6, 17 interact such that cage 17 has incongruous combinations; reduced from 19 to 18 combinations
  93. 88: (4.4) Cage comparison: cages 0, 28, 17, 14 interact such that cage 17 has incongruous combinations; reduced from 18 to 17 combinations
  94. 89: (4.6) Cage comparison: cages 0, 15, 9, 2, 11 interact such that cage 2 has incongruous combinations; reduced from 11 to 10 combinations
  95. 90: (4.6) Cage comparison: cages 0, 28, 1, 14, 17 interact such that cage 17 has incongruous combinations; reduced from 17 to 16 combinations
  96. 91: (4.6) Cage comparison: cages 0, 28, 9, 17, 6 interact such that cages 28, 9, 17, 6 have incongruous combinations; reduced from 4, 7, 16, 4 to 2, 6, 10, 3 combinations respectively
  97. 92: (0) Naked single: 8 in r8c2
  98. 93: (0) Naked single: 8 in r2c1
  99. 94: (1.5) Pointing candidates: all combinations for cage 2 contain 5r2; eliminations in r2c6
  100. 95: (4) Cage comparison: cages 4, 2 interact such that cage 2 has incongruous combinations; reduced from 9 to 7 combinations
  101. 96: (4.2) Cage comparison: cages 9, 17, 14 interact such that cage 17 has incongruous combinations; reduced from 10 to 9 combinations
  102. 97: (1.5) Claiming candidates: cage 14 must contain 3 in r4c3, r5c3: from 6 combinations to 4
  103. 98: (4.2) Cage comparison: cages 14, 2, 18 interact such that cage 2 has incongruous combinations; reduced from 7 to 6 combinations
  104. 99: (4.2) Cage comparison: cages 14, 20, 18 interact such that cage 18 has incongruous combinations; reduced from 7 to 6 combinations
  105. 100: (4.2) Cage comparison: cages 2, 0, 1 interact such that cage 1 has incongruous combinations; reduced from 5 to 4 combinations
  106. 101: (4.4) Cage comparison: cages 14, 2, 20, 19 interact such that cage 19 has incongruous combinations; reduced from 10 to 9 combinations
  107. 102: (4.4) Cage comparison: cages 2, 19, 26, 11 interact such that cage 19 has incongruous combinations; reduced from 9 to 8 combinations
  108. 103: (4.4) Cage comparison: cages 9, 17, 15, 20 interact such that cage 17 has incongruous combinations; reduced from 9 to 8 combinations
  109. 104: (1) Hidden single: 4 in r2c3
  110. 105: (2.1) Hidden triple: 3, 4, 7 in r5c2, r6c2
  111. 106: (0) Naked single: 6 in r7c2
  112. 107: (1) Hidden single: 1 in r3c3
  113. 108: (1) Hidden single: 5 in r8c3
  114. 109: (0) Naked single: 6 in r8c1
  115. 110: (0) Naked single: 5 in r1c1
  116. 111: (0) Naked single: 2 in r1c2
  117. 112: (0) Naked single: 8 in r1c3
  118. 113: (0) Naked single: 7 in r2c7
  119. 114: (0) Naked single: 8 in r3c7
  120. 115: (0) Naked single: 7 in r3c8
  121. 116: (0) Naked single: 8 in r4c4
  122. 117: (0) Naked single: 4 in r4c6
  123. 118: (0) Naked single: 5 in r3c2
  124. 119: (0) Naked single: 2 in r2c6
  125. 120: (0) Naked single: 6 in r3c6
  126. 121: (0) Naked single: 3 in r3c5
  127. 122: (0) Naked single: 2 in r3c4
  128. 123: (0) Naked single: 5 in r5c4
  129. 124: (0) Naked single: 8 in r5c6
  130. 125: (0) Naked single: 5 in r2c5
  131. 126: (0) Naked single: 1 in r6c4
  132. 127: (0) Naked single: 5 in r6c6
  133. 128: (0) Naked single: 8 in r6c8
  134. 129: (0) Naked single: 5 in r7c8
  135. 130: (0) Naked single: 1 in r7c6
  136. 131: (0) Naked single: 8 in r7c5
  137. 132: (0) Naked single: 3 in r8c6
  138. 133: (0) Naked single: 1 in r8c7
  139. 134: (0) Naked single: 1 in r1c5
  140. 135: (0) Naked single: 1 in r2c2
  141. 136: (0) Naked single: 5 in r8c3
  142. 137: (1) Hidden single: 2 in r5c5
  143. 138: (0) Naked single: 6 in r6c5
  144. 139: (0) Naked single: 7 in r5c2
  145. 140: (0) Naked single: 3 in r4c2
  146. 141: (0) Naked single: 6 in r4c3
  147. 142: (0) Naked single: 3 in r5c3
  148. 143: (0) Naked single: 4 in r5c7
  149. 144: (0) Naked single: 6 in r5c8
  150. 145: (0) Naked single: 6 in r1c7
  151. 146: (0) Naked single: 3 in r1c4
  152. 147: (0) Naked single: 6 in r2c4
  153. 148: (0) Naked single: 3 in r2c8
  154. 149: (0) Naked single: 3 in r6c7
  155. 150: (0) Naked single: 4 in r6c2
  156. 151: (0) Naked single: 2 in r6c3
  157. 152: (0) Naked single: 7 in r4c5
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