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Billabob

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Billabob
Feb 24th, 2025
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  1. Puzzle string 9:a__ab_4aa__a_6a_5aa_a_aa_c_6aa_4bacaa_a4_aa_4a_3a__a_3a__a__a__a3__a__b_a__a_,m72s2s2a11a15a12m21d2s1m24d3s1s2a14d2s1a11a8s2a13m6a7m504m40a9d3m144m6s1m1344s3s1s1m162a6
  2.  
  3. Time taken 7144655 ms
  4.  
  5. Max difficulty: 5.2; total difficulty: 821.9
  6.  
  7. 0: Filled in initial combinations & candidates
  8. 1: (1.5) Pointing candidates: all combinations for cage 33 contain 3r9,6r9,9r9; eliminations in r9c1, r9c7, r9c8, r9c9
  9. 2: (3.2) Region sum: Row 9 must sum to 45; cages 29, 31's cells within this region must sum to 21; cages 29, 31 reduced from 120, 11 combinations to 108, 10
  10. 3: (4) Cage comparison: cages 9, 31 interact such that cage 31 has incongruous combinations; reduced from 10 to 9 combinations
  11. 4: (4) Cage comparison: cages 9, 0 interact such that cage 0 has incongruous combinations; reduced from 20 to 16 combinations
  12. 5: (4) Cage comparison: cages 20, 12 interact such that cage 12 has incongruous combinations; reduced from 14 to 12 combinations
  13. 6: (4) Cage comparison: cages 20, 28 interact such that cage 28 has incongruous combinations; reduced from 16 to 14 combinations
  14. 7: (4) Cage comparison: cages 27, 11 interact such that cage 11 has incongruous combinations; reduced from 16 to 14 combinations
  15. 8: (4) Cage comparison: cages 34, 29 interact such that cage 29 has incongruous combinations; reduced from 108 to 96 combinations
  16. 9: (4) Cage comparison: cages 25, 24 interact such that cage 24 has incongruous combinations; reduced from 8 to 6 combinations
  17. 10: (4.2) Cage comparison: cages 9, 17, 31 interact such that cage 31 has incongruous combinations; reduced from 9 to 8 combinations
  18. 11: (4.2) Cage comparison: cages 9, 31, 0 interact such that cage 31 has incongruous combinations; reduced from 8 to 7 combinations
  19. 12: (4.2) Cage comparison: cages 20, 12, 28 interact such that cage 28 has incongruous combinations; reduced from 14 to 12 combinations
  20. 13: (4.2) Cage comparison: cages 19, 21, 18 interact such that cage 18 has incongruous combinations; reduced from 14 to 12 combinations
  21. 14: (4.2) Cage comparison: cages 3, 0, 4 interact such that cage 0 has incongruous combinations; reduced from 16 to 14 combinations
  22. 15: (4.4) Cage comparison: cages 9, 5, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 80 to 77 combinations
  23. 16: (4.4) Cage comparison: cages 9, 17, 31, 0 interact such that cage 0 has incongruous combinations; reduced from 14 to 10 combinations
  24. 17: (4.4) Cage comparison: cages 9, 17, 31, 22 interact such that cage 22 has incongruous combinations; reduced from 77 to 69 combinations
  25. 18: (4.4) Cage comparison: cages 20, 17, 21, 18 interact such that cage 18 has incongruous combinations; reduced from 12 to 10 combinations
  26. 19: (4.2) Cage comparison: cages 19, 21, 18 interact such that cage 19 has incongruous combinations; reduced from 6 to 4 combinations
  27. 20: (4.4) Cage comparison: cages 19, 17, 21, 18 interact such that cage 17 has incongruous combinations; reduced from 6 to 5 combinations
  28. 21: (4.4) Cage comparison: cages 19, 21, 18, 15 interact such that cage 15 has incongruous combinations; reduced from 16 to 14 combinations
  29. 22: (4.4) Cage comparison: cages 20, 17, 24, 23 interact such that cage 23 has incongruous combinations; reduced from 12 to 10 combinations
  30. 23: (4.4) Cage comparison: cages 5, 33, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 69 to 65 combinations
  31. 24: (4.4) Cage comparison: cages 3, 0, 1, 4 interact such that cage 1 has incongruous combinations; reduced from 14 to 12 combinations
  32. 25: (4.4) Cage comparison: cages 3, 0, 2, 4 interact such that cage 2 has incongruous combinations; reduced from 14 to 12 combinations
  33. 26: (4.6) Cage comparison: cages 9, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 65 to 61 combinations
  34. 27: (4.6) Cage comparison: cages 9, 17, 31, 0, 22 interact such that cages 31, 22 have incongruous combinations; reduced from 7, 61 to 6, 54 combinations respectively
  35. 28: (4.2) Cage comparison: cages 34, 31, 29 interact such that cage 29 has incongruous combinations; reduced from 96 to 90 combinations
  36. 29: (4.6) Cage comparison: cages 9, 5, 31, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 54 to 50 combinations
  37. 30: (4.6) Cage comparison: cages 9, 5, 33, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 50 to 48 combinations
  38. 31: (4.6) Cage comparison: cages 13, 21, 25, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 90 to 86 combinations
  39. 32: (4.6) Cage comparison: cages 13, 21, 25, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 48 to 47 combinations
  40. 33: (4.6) Cage comparison: cages 13, 25, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 47 to 46 combinations
  41. 34: (4.6) Cage comparison: cages 20, 17, 24, 25, 23 interact such that cages 25, 23 have incongruous combinations; reduced from 6, 10 to 4, 8 combinations respectively
  42. 35: (4.6) Cage comparison: cages 20, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 48 to 43 combinations
  43. 36: (4.6) Cage comparison: cages 25, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 43 to 34 combinations
  44. 37: (4.6) Cage comparison: cages 25, 21, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 86 to 82 combinations
  45. 38: (4.6) Cage comparison: cages 10, 33, 23, 18, 1 interact such that cage 18 has incongruous combinations; reduced from 10 to 9 combinations
  46. 39: (4.6) Cage comparison: cages 13, 25, 21, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 16 to 15 combinations
  47. 40: (4.6) Cage comparison: cages 13, 25, 21, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 46 to 44 combinations
  48. 41: (4.6) Cage comparison: cages 13, 25, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 82 to 74 combinations
  49. 42: (4.6) Cage comparison: cages 20, 25, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 34 to 32 combinations
  50. 43: (4.8) Cage comparison: cages 9, 17, 5, 31, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 32 to 31 combinations
  51. 44: (4.8) Cage comparison: cages 9, 17, 24, 31, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 31 to 30 combinations
  52. 45: (4.8) Cage comparison: cages 9, 17, 24, 23, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 30 to 28 combinations
  53. 46: (4.8) Cage comparison: cages 9, 5, 33, 0, 15, 22 interact such that cage 15 has incongruous combinations; reduced from 14 to 12 combinations
  54. 47: (4.8) Cage comparison: cages 13, 20, 25, 21, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 44 to 43 combinations
  55. 48: (4.8) Cage comparison: cages 13, 20, 25, 24, 23, 29 interact such that cage 29 has incongruous combinations; reduced from 74 to 66 combinations
  56. 49: (4.8) Cage comparison: cages 13, 25, 21, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 43 to 42 combinations
  57. 50: (4.8) Cage comparison: cages 13, 25, 14, 30, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 15 to 14 combinations
  58. 51: (4.8) Cage comparison: cages 13, 25, 14, 30, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 42 to 38 combinations
  59. 52: (4.8) Cage comparison: cages 13, 21, 14, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 38 to 37 combinations
  60. 53: (4.8) Cage comparison: cages 20, 25, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 28 to 21 combinations
  61. 54: (4.8) Cage comparison: cages 20, 17, 21, 24, 23, 18 interact such that cage 18 has incongruous combinations; reduced from 9 to 7 combinations
  62. 55: (4.2) Cage comparison: cages 19, 18, 15 interact such that cage 15 has incongruous combinations; reduced from 12 to 11 combinations
  63. 56: (4.6) Cage comparison: cages 10, 33, 18, 1, 22 interact such that cages 33, 22 have incongruous combinations; reduced from 6, 21 to 5, 20 combinations respectively
  64. 57: (4.6) Cage comparison: cages 33, 5, 0, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 20 to 19 combinations
  65. 58: (5) Cage comparison: cages 9, 13, 25, 31, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 66 to 64 combinations
  66. 59: (5) Cage comparison: cages 9, 13, 6, 10, 14, 16, 12 interact such that cage 14 has incongruous combinations; reduced from 8 to 7 combinations
  67. 60: (5) Cage comparison: cages 9, 13, 6, 10, 16, 12, 11 interact such that cage 11 has incongruous combinations; reduced from 14 to 13 combinations
  68. 61: (5) Cage comparison: cages 9, 17, 33, 5, 31, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 19 to 18 combinations
  69. 62: (5) Cage comparison: cages 9, 17, 5, 31, 0, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 18 to 17 combinations
  70. 63: (4.8) Cage comparison: cages 33, 5, 0, 15, 32, 22 interact such that cage 32 has incongruous combinations; reduced from 16 to 14 combinations
  71. 64: (5) Cage comparison: cages 9, 17, 24, 31, 23, 0, 22 interact such that cages 17, 22 have incongruous combinations; reduced from 5, 17 to 4, 14 combinations respectively
  72. 65: (4.8) Cage comparison: cages 33, 5, 10, 1, 22, 32 interact such that cage 32 has incongruous combinations; reduced from 14 to 13 combinations
  73. 66: (5) Cage comparison: cages 13, 17, 25, 21, 24, 23, 29 interact such that cage 21 has incongruous combinations; reduced from 6 to 5 combinations
  74. 67: (5) Cage comparison: cages 13, 17, 25, 24, 23, 22, 29 interact such that cage 29 has incongruous combinations; reduced from 64 to 63 combinations
  75. 68: (5) Cage comparison: cages 13, 20, 25, 21, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 37 to 36 combinations
  76. 69: (5) Cage comparison: cages 13, 20, 25, 24, 23, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 36 to 35 combinations
  77. 70: (5) Cage comparison: cages 13, 25, 21, 14, 30, 8, 29 interact such that cages 21, 29 have incongruous combinations; reduced from 5, 63 to 4, 48 combinations respectively
  78. 71: (5) Cage comparison: cages 13, 21, 14, 30, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 35 to 34 combinations
  79. 72: (5) Cage comparison: cages 17, 20, 21, 25, 24, 18, 23 interact such that cage 18 has incongruous combinations; reduced from 7 to 6 combinations
  80. 73: (5) Cage comparison: cages 19, 33, 5, 18, 0, 15, 22 interact such that cage 15 has incongruous combinations; reduced from 11 to 10 combinations
  81. 74: (5) Cage comparison: cages 27, 34, 31, 30, 32, 26, 29 interact such that cage 29 has incongruous combinations; reduced from 48 to 46 combinations
  82. 75: (5) Cage comparison: cages 27, 34, 31, 32, 22, 26, 29 interact such that cage 29 has incongruous combinations; reduced from 46 to 42 combinations
  83. 76: (5) Cage comparison: cages 27, 31, 28, 30, 32, 26, 29 interact such that cage 26 has incongruous combinations; reduced from 14 to 12 combinations
  84. 77: (4.8) Cage comparison: cages 27, 26, 30, 32, 22, 29 interact such that cage 29 has incongruous combinations; reduced from 42 to 41 combinations
  85. 78: (5) Cage comparison: cages 27, 26, 28, 30, 32, 22, 29 interact such that cages 30, 29 have incongruous combinations; reduced from 12, 41 to 11, 38 combinations respectively
  86. 79: (5) Cage comparison: cages 34, 31, 30, 26, 28, 32, 29 interact such that cage 29 has incongruous combinations; reduced from 38 to 36 combinations
  87. 80: (5) Cage comparison: cages 33, 10, 18, 1, 26, 32, 22 interact such that cage 32 has incongruous combinations; reduced from 13 to 12 combinations
  88. 81: (5) Cage comparison: cages 5, 6, 3, 0, 1, 2, 4 interact such that cage 0 has incongruous combinations; reduced from 10 to 9 combinations
  89. 82: (5) Cage comparison: cages 3, 7, 0, 1, 2, 8, 4 interact such that cage 0 has incongruous combinations; reduced from 9 to 8 combinations
  90. 83: (4.4) Cage comparison: cages 5, 0, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 14 to 13 combinations
  91. 84: (5) Cage comparison: cages 9, 17, 27, 31, 0, 22, 29 interact such that cage 29 has incongruous combinations; reduced from 36 to 34 combinations
  92. 85: (5) Cage comparison: cages 9, 17, 34, 31, 0, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 14 to 13 combinations
  93. 86: (5) Cage comparison: cages 9, 17, 33, 10, 0, 1, 22 interact such that cage 22 has incongruous combinations; reduced from 13 to 12 combinations
  94. 87: (4.8) Cage comparison: cages 17, 20, 21, 0, 15, 22 interact such that cage 15 has incongruous combinations; reduced from 10 to 9 combinations
  95. 88: (5) Cage comparison: cages 13, 21, 25, 14, 30, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 34 to 33 combinations
  96. 89: (5) Cage comparison: cages 17, 20, 21, 34, 31, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 33 to 32 combinations
  97. 90: (5) Cage comparison: cages 21, 25, 14, 30, 8, 4, 29 interact such that cages 4, 29 have incongruous combinations; reduced from 32, 34 to 29, 30 combinations respectively
  98. 91: (5) Cage comparison: cages 27, 34, 6, 26, 28, 32, 29 interact such that cage 26 has incongruous combinations; reduced from 12 to 11 combinations
  99. 92: (5) Cage comparison: cages 27, 34, 31, 26, 28, 32, 29 interact such that cage 26 has incongruous combinations; reduced from 11 to 10 combinations
  100. 93: (4.8) Cage comparison: cages 5, 0, 15, 26, 22, 32 interact such that cage 32 has incongruous combinations; reduced from 12 to 11 combinations
  101. 94: (5) Cage comparison: cages 27, 31, 26, 30, 32, 22, 29 interact such that cage 30 has incongruous combinations; reduced from 11 to 10 combinations
  102. 95: (4.8) Cage comparison: cages 13, 25, 14, 30, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 13 to 12 combinations
  103. 96: (4.8) Cage comparison: cages 13, 25, 14, 30, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 29 to 27 combinations
  104. 97: (5) Cage comparison: cages 27, 31, 26, 30, 32, 28, 29 interact such that cage 32 has incongruous combinations; reduced from 11 to 10 combinations
  105. 98: (5) Cage comparison: cages 27, 31, 26, 32, 22, 28, 29 interact such that cage 29 has incongruous combinations; reduced from 30 to 29 combinations
  106. 99: (4.8) Cage comparison: cages 21, 25, 14, 30, 8, 29 interact such that cage 30 has incongruous combinations; reduced from 10 to 9 combinations
  107. 100: (5) Cage comparison: cages 27, 23, 30, 26, 22, 28, 29 interact such that cage 29 has incongruous combinations; reduced from 29 to 28 combinations
  108. 101: (5) Cage comparison: cages 33, 5, 10, 18, 15, 1, 22 interact such that cage 15 has incongruous combinations; reduced from 9 to 8 combinations
  109. 102: (5) Cage comparison: cages 9, 17, 33, 5, 0, 15, 22 interact such that cage 33 has incongruous combinations; reduced from 5 to 4 combinations
  110. 103: (5) Cage comparison: cages 20, 21, 25, 14, 30, 4, 29 interact such that cage 29 has incongruous combinations; reduced from 28 to 27 combinations
  111. 104: (5) Cage comparison: cages 21, 25, 14, 30, 8, 4, 29 interact such that cages 4, 29 have incongruous combinations; reduced from 27, 27 to 20, 26 combinations respectively
  112. 105: (5) Cage comparison: cages 27, 34, 31, 30, 26, 32, 29 interact such that cage 26 has incongruous combinations; reduced from 10 to 9 combinations
  113. 106: (5) Cage comparison: cages 13, 21, 25, 14, 8, 4, 29 interact such that cage 29 has incongruous combinations; reduced from 26 to 24 combinations
  114. 107: (5.2) Cage comparison: cages 9, 13, 10, 14, 15, 16, 12, 11 interact such that cage 10 has incongruous combinations; reduced from 6 to 5 combinations
  115. 108: (4.6) Cage comparison: cages 33, 10, 5, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 12 to 9 combinations
  116. 109: (4.6) Cage comparison: cages 20, 25, 24, 23, 22 interact such that cage 23 has incongruous combinations; reduced from 8 to 7 combinations
  117. 110: (4.6) Cage comparison: cages 21, 14, 22, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 24 to 23 combinations
  118. 111: (4.8) Cage comparison: cages 20, 25, 24, 23, 22, 28 interact such that cage 28 has incongruous combinations; reduced from 12 to 11 combinations
  119. 112: (4.8) Cage comparison: cages 20, 22, 26, 30, 28, 29 interact such that cage 29 has incongruous combinations; reduced from 23 to 22 combinations
  120. 113: (4.8) Cage comparison: cages 27, 5, 23, 15, 22, 32 interact such that cage 23 has incongruous combinations; reduced from 7 to 6 combinations
  121. 114: (4.8) Cage comparison: cages 27, 23, 24, 22, 28, 29 interact such that cage 28 has incongruous combinations; reduced from 11 to 10 combinations
  122. 115: (5) Cage comparison: cages 9, 10, 31, 14, 22, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 22 to 21 combinations
  123. 116: (5) Cage comparison: cages 17, 19, 20, 21, 18, 23, 24 interact such that cage 18 has incongruous combinations; reduced from 6 to 5 combinations
  124. 117: (5) Cage comparison: cages 17, 20, 21, 25, 23, 24, 22 interact such that cage 21 has incongruous combinations; reduced from 4 to 3 combinations
  125. 118: (4) Cage comparison: cages 21, 29 interact such that cage 29 has incongruous combinations; reduced from 21 to 20 combinations
  126. 119: (4.2) Cage comparison: cages 21, 19, 18 interact such that cage 18 has incongruous combinations; reduced from 5 to 4 combinations
  127. 120: (4.2) Cage comparison: cages 21, 19, 15 interact such that cage 15 has incongruous combinations; reduced from 8 to 7 combinations
  128. 121: (4.2) Cage comparison: cages 18, 19, 15 interact such that cage 15 has incongruous combinations; reduced from 7 to 6 combinations
  129. 122: (4.4) Cage comparison: cages 21, 25, 14, 8 interact such that cage 8 has incongruous combinations; reduced from 12 to 11 combinations
  130. 123: (4.4) Cage comparison: cages 21, 25, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 20 to 17 combinations
  131. 124: (4.4) Cage comparison: cages 13, 20, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 20 to 19 combinations
  132. 125: (4.4) Cage comparison: cages 33, 5, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 9 to 8 combinations
  133. 126: (4) Cage comparison: cages 0, 22 interact such that cage 0 has incongruous combinations; reduced from 8 to 7 combinations
  134. 127: (4.6) Cage comparison: cages 21, 25, 14, 30, 8 interact such that cage 8 has incongruous combinations; reduced from 11 to 10 combinations
  135. 128: (4.8) Cage comparison: cages 21, 9, 31, 0, 29, 4 interact such that cage 31 has incongruous combinations; reduced from 6 to 5 combinations
  136. 129: (1.5) Claiming candidates: cage 29 must contain 7 in r9c7, r9c8, r9c9: from 17 combinations to 16
  137. 130: (4.8) Cage comparison: cages 9, 10, 31, 14, 30, 29 interact such that cage 30 has incongruous combinations; reduced from 9 to 8 combinations
  138. 131: (4.8) Cage comparison: cages 17, 20, 25, 23, 24, 22 interact such that cage 20 has incongruous combinations; reduced from 4 to 3 combinations
  139. 132: (4.6) Cage comparison: cages 20, 25, 14, 30, 4 interact such that cage 4 has incongruous combinations; reduced from 19 to 18 combinations
  140. 133: (4.8) Cage comparison: cages 20, 21, 25, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 16 to 15 combinations
  141. 134: (4.8) Cage comparison: cages 20, 25, 23, 24, 22, 29 interact such that cage 29 has incongruous combinations; reduced from 15 to 14 combinations
  142. 135: (4.6) Cage comparison: cages 25, 14, 30, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 10 to 9 combinations
  143. 136: (4.8) Cage comparison: cages 20, 21, 14, 30, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 18 to 17 combinations
  144. 137: (4.8) Cage comparison: cages 21, 9, 17, 34, 31, 29 interact such that cage 21 has incongruous combinations; reduced from 3 to 2 combinations
  145. 138: (4.6) Cage comparison: cages 21, 25, 14, 30, 4 interact such that cage 4 has incongruous combinations; reduced from 17 to 16 combinations
  146. 139: (4.8) Cage comparison: cages 21, 20, 25, 14, 30, 4 interact such that cage 4 has incongruous combinations; reduced from 16 to 15 combinations
  147. 140: (4.8) Cage comparison: cages 21, 20, 14, 30, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 15 to 14 combinations
  148. 141: (4.8) Cage comparison: cages 21, 9, 31, 0, 4, 29 interact such that cages 31, 29 have incongruous combinations; reduced from 5, 14 to 4, 13 combinations respectively
  149. 142: (4.6) Cage comparison: cages 17, 31, 23, 24, 22 interact such that cage 22 has incongruous combinations; reduced from 8 to 7 combinations
  150. 143: (1.5) Pointing candidates: all combinations for cage 22 contain 7r7; eliminations in r7c7, r7c9
  151. 144: (4.4) Cage comparison: cages 25, 23, 24, 22 interact such that cages 23, 24 have incongruous combinations; reduced from 6, 6 to 5, 4 combinations respectively
  152. 145: (4.8) Cage comparison: cages 21, 13, 30, 8, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 14 to 13 combinations
  153. 146: (4.2) Cage comparison: cages 0, 3, 4 interact such that cage 3 has incongruous combinations; reduced from 8 to 6 combinations
  154. 147: (4.8) Cage comparison: cages 21, 17, 25, 31, 34, 29 interact such that cage 17 has incongruous combinations; reduced from 4 to 3 combinations
  155. 148: (4.2) Cage comparison: cages 17, 31, 0 interact such that cage 0 has incongruous combinations; reduced from 7 to 6 combinations
  156. 149: (3.6) Region sum: Col 1 must sum to 45; cages 9, 31, 0, 22's cells within this region must sum to 37; cages 31 reduced from 4 combinations to 2
  157. 150: (3.2) Region sum: Row 9 must sum to 45; cages 29, 31's cells within this region must sum to 21; cages 29 reduced from 13 combinations to 12
  158. 151: (4) Cage comparison: cages 13, 29 interact such that cage 13 has incongruous combinations; reduced from 4 to 2 combinations
  159. 152: (1.5) Pointing candidates: all combinations for cage 13 contain 5c8,9c8; eliminations in r2c8, r6c8
  160. 153: (4.4) Cage comparison: cages 31, 27, 34, 29 interact such that cage 27 has incongruous combinations; reduced from 4 to 3 combinations
  161. 154: (4.4) Cage comparison: cages 31, 34, 32, 29 interact such that cage 32 has incongruous combinations; reduced from 10 to 7 combinations
  162. 155: (4.4) Cage comparison: cages 17, 20, 24, 23 interact such that cage 20 has incongruous combinations; reduced from 3 to 2 combinations
  163. 156: (4.2) Cage comparison: cages 20, 25, 4 interact such that cage 4 has incongruous combinations; reduced from 13 to 12 combinations
  164. 157: (4.4) Cage comparison: cages 25, 24, 23, 29 interact such that cage 23 has incongruous combinations; reduced from 5 to 3 combinations
  165. 158: (1.5) Pointing candidates: all combinations for cage 23 contain 5c4; eliminations in r1c4, r2c4, r4c4
  166. 159: (4.4) Cage comparison: cages 23, 27, 22, 30 interact such that cage 30 has incongruous combinations; reduced from 7 to 6 combinations
  167. 160: (4.4) Cage comparison: cages 23, 27, 22, 26 interact such that cage 26 has incongruous combinations; reduced from 9 to 7 combinations
  168. 161: (4.4) Cage comparison: cages 30, 26, 32, 29 interact such that cage 30 has incongruous combinations; reduced from 6 to 5 combinations
  169. 162: (4.6) Cage comparison: cages 20, 21, 25, 30, 14 interact such that cage 25 has incongruous combinations; reduced from 3 to 2 combinations
  170. 163: (4.4) Cage comparison: cages 21, 25, 4, 29 interact such that cage 29 has incongruous combinations; reduced from 12 to 10 combinations
  171. 164: (4.6) Cage comparison: cages 20, 21, 25, 28, 4 interact such that cage 28 has incongruous combinations; reduced from 9 to 8 combinations
  172. 165: (4.6) Cage comparison: cages 21, 25, 15, 22, 29 interact such that cage 15 has incongruous combinations; reduced from 6 to 5 combinations
  173. 166: (4.6) Cage comparison: cages 21, 27, 19, 30, 26 interact such that cage 30 has incongruous combinations; reduced from 5 to 4 combinations
  174. 167: (4.2) Cage comparison: cages 21, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 10 to 9 combinations
  175. 168: (4.6) Cage comparison: cages 21, 25, 30, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 12 to 11 combinations
  176. 169: (4.6) Cage comparison: cages 21, 30, 14, 8, 29 interact such that cages 14, 8 have incongruous combinations; reduced from 7, 8 to 6, 7 combinations respectively
  177. 170: (4.2) Cage comparison: cages 30, 14, 4 interact such that cage 4 has incongruous combinations; reduced from 11 to 9 combinations
  178. 171: (4.4) Cage comparison: cages 30, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 9 to 8 combinations
  179. 172: (4.6) Cage comparison: cages 20, 25, 4, 28, 29 interact such that cage 29 has incongruous combinations; reduced from 9 to 7 combinations
  180. 173: (4.4) Cage comparison: cages 31, 27, 29, 7 interact such that cage 7 has incongruous combinations; reduced from 8 to 7 combinations
  181. 174: (4.4) Cage comparison: cages 20, 25, 7, 8 interact such that cage 8 has incongruous combinations; reduced from 7 to 6 combinations
  182. 175: (4.4) Cage comparison: cages 20, 7, 28, 12 interact such that cage 12 has incongruous combinations; reduced from 12 to 8 combinations
  183. 176: (4.4) Cage comparison: cages 23, 30, 22, 29 interact such that cage 30 has incongruous combinations; reduced from 4 to 3 combinations
  184. 177: (4.4) Cage comparison: cages 27, 30, 26, 28 interact such that cage 28 has incongruous combinations; reduced from 8 to 7 combinations
  185. 178: (4.4) Cage comparison: cages 30, 8, 14, 29 interact such that cage 8 has incongruous combinations; reduced from 6 to 5 combinations
  186. 179: (4.4) Cage comparison: cages 30, 26, 28, 32 interact such that cage 28 has incongruous combinations; reduced from 7 to 6 combinations
  187. 180: (4.6) Cage comparison: cages 20, 25, 28, 4, 12 interact such that cage 4 has incongruous combinations; reduced from 8 to 7 combinations
  188. 181: (1) Hidden single: 1 in r7c8
  189. 182: (0) Naked single: 6 in r8c8
  190. 183: (0) Naked single: 1 in r8c1
  191. 184: (0) Naked single: 3 in r5c1
  192. 185: (0) Naked single: 2 in r5c8
  193. 186: (0) Naked single: 1 in r5c7
  194. 187: (0) Naked single: 6 in r6c7
  195. 188: (0) Naked single: 3 in r6c8
  196. 189: (0) Naked single: 9 in r6c9
  197. 190: (0) Naked single: 4 in r6c2
  198. 191: (0) Naked single: 5 in r7c4
  199. 192: (0) Naked single: 5 in r5c9
  200. 193: (0) Naked single: 4 in r7c9
  201. 194: (0) Naked single: 7 in r8c9
  202. 195: (0) Naked single: 8 in r9c9
  203. 196: (0) Naked single: 5 in r6c1
  204. 197: (0) Naked single: 2 in r9c1
  205. 198: (0) Naked single: 7 in r7c1
  206. 199: (1) Hidden single: 9 in r1c1
  207. 200: (1) Hidden single: 8 in r3c6
  208. 201: (1) Hidden single: 5 in r8c2
  209. 202: (0) Naked single: 8 in r4c2
  210. 203: (0) Naked single: 7 in r5c2
  211. 204: (0) Naked single: 4 in r8c3
  212. 205: (1) Hidden single: 5 in r2c3
  213. 206: (1) Hidden single: 8 in r2c1
  214. 207: (0) Naked single: 1 in r1c2
  215. 208: (0) Naked single: 8 in r2c1
  216. 209: (1) Hidden single: 2 in r7c2
  217. 210: (0) Naked single: 3 in r7c6
  218. 211: (0) Naked single: 2 in r8c6
  219. 212: (0) Naked single: 6 in r7c5
  220. 213: (0) Naked single: 2 in r6c5
  221. 214: (0) Naked single: 7 in r6c6
  222. 215: (0) Naked single: 9 in r4c6
  223. 216: (0) Naked single: 9 in r3c8
  224. 217: (0) Naked single: 9 in r2c2
  225. 218: (0) Naked single: 3 in r3c2
  226. 219: (0) Naked single: 3 in r2c5
  227. 220: (0) Naked single: 2 in r2c7
  228. 221: (0) Naked single: 3 in r1c9
  229. 222: (0) Naked single: 7 in r1c3
  230. 223: (0) Naked single: 5 in r1c5
  231. 224: (0) Naked single: 1 in r9c5
  232. 225: (0) Naked single: 1 in r3c4
  233. 226: (0) Naked single: 6 in r3c3
  234. 227: (0) Naked single: 4 in r3c1
  235. 228: (0) Naked single: 6 in r4c1
  236. 229: (0) Naked single: 8 in r5c3
  237. 230: (0) Naked single: 1 in r6c3
  238. 231: (0) Naked single: 8 in r6c4
  239. 232: (0) Naked single: 3 in r8c4
  240. 233: (0) Naked single: 6 in r9c2
  241. 234: (0) Naked single: 3 in r9c3
  242. 235: (0) Naked single: 9 in r9c4
  243. 236: (0) Naked single: 8 in r8c5
  244. 237: (0) Naked single: 8 in r7c7
  245. 238: (0) Naked single: 4 in r1c7
  246. 239: (0) Naked single: 4 in r2c4
  247. 240: (0) Naked single: 1 in r2c6
  248. 241: (0) Naked single: 7 in r2c8
  249. 242: (0) Naked single: 7 in r9c7
  250. 243: (0) Naked single: 5 in r3c7
  251. 244: (0) Naked single: 3 in r4c7
  252. 245: (0) Naked single: 4 in r9c8
  253. 246: (0) Naked single: 6 in r2c9
  254. 247: (0) Naked single: 7 in r4c4
  255. 248: (0) Naked single: 4 in r4c5
  256. 249: (0) Naked single: 9 in r5c5
  257. 250: (0) Naked single: 4 in r5c6
  258. 251: (0) Naked single: 8 in r1c8
  259. 252: (0) Naked single: 9 in r8c7
  260. 253: (0) Naked single: 6 in r5c4
  261. 254: (0) Naked single: 2 in r1c4
  262. 255: (0) Naked single: 2 in r4c3
  263. 256: (0) Naked single: 2 in r3c9
  264. 257: (0) Naked single: 1 in r4c9
  265. 258: (0) Naked single: 7 in r3c5
  266. 259: (0) Naked single: 5 in r9c6
  267. 260: (0) Naked single: 6 in r1c6
  268. 261: (0) Naked single: 5 in r4c8
  269. 262: (0) Naked single: 9 in r7c3
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