variant of hardest

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_,a18s2s2s1a15a12m21d2s1s2d3s1s2a14d2s1a11a8s2a13m6a7m504m40a9d3m144m6s1m1344s3s1s1m162a6

Time taken: 68240048 ms

Max difficulty: 5.2; total difficulty: 799.5

0: Filled in initial combinations & candidates
1: (1.5) Pointing candidates: all combinations for cage 33 contain 3r9,6r9,9r9; eliminations in r9c1, r9c7, r9c8, r9c9
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
3: (4) Cage comparison: cages 20, 12 interact such that cage 12 has incongruous combinations; reduced from 14 to 12 combinations
4: (4) Cage comparison: cages 20, 28 interact such that cage 28 has incongruous combinations; reduced from 16 to 14 combinations
5: (4) Cage comparison: cages 27, 11 interact such that cage 11 has incongruous combinations; reduced from 16 to 14 combinations
6: (4) Cage comparison: cages 34, 29 interact such that cage 29 has incongruous combinations; reduced from 108 to 96 combinations
7: (4) Cage comparison: cages 25, 24 interact such that cage 24 has incongruous combinations; reduced from 8 to 6 combinations
8: (4.2) Cage comparison: cages 20, 12, 28 interact such that cage 28 has incongruous combinations; reduced from 14 to 12 combinations
9: (4.2) Cage comparison: cages 17, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 45 to 43 combinations
10: (4.2) Cage comparison: cages 19, 21, 18 interact such that cage 18 has incongruous combinations; reduced from 14 to 12 combinations
11: (4.4) Cage comparison: cages 20, 17, 21, 18 interact such that cage 18 has incongruous combinations; reduced from 12 to 10 combinations
12: (4.2) Cage comparison: cages 18, 19, 21 interact such that cage 19 has incongruous combinations; reduced from 6 to 4 combinations
13: (4.4) Cage comparison: cages 17, 19, 21, 18 interact such that cage 17 has incongruous combinations; reduced from 6 to 5 combinations
14: (4.4) Cage comparison: cages 17, 31, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 43 to 42 combinations
15: (4.4) Cage comparison: cages 19, 21, 18, 15 interact such that cage 15 has incongruous combinations; reduced from 16 to 14 combinations
16: (4.4) Cage comparison: cages 20, 17, 24, 23 interact such that cage 23 has incongruous combinations; reduced from 12 to 10 combinations
17: (4.6) Cage comparison: cages 13, 21, 25, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 96 to 92 combinations
18: (4.6) Cage comparison: cages 13, 21, 25, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 48 to 47 combinations
19: (4.6) Cage comparison: cages 13, 25, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 47 to 46 combinations
20: (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
21: (4.6) Cage comparison: cages 20, 17, 24, 25, 22 interact such that cage 22 has incongruous combinations; reduced from 80 to 77 combinations
22: (4.6) Cage comparison: cages 20, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 77 to 69 combinations
23: (4.6) Cage comparison: cages 20, 24, 25, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 69 to 62 combinations
24: (4.6) Cage comparison: cages 17, 24, 25, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 62 to 56 combinations
25: (4.6) Cage comparison: cages 17, 31, 9, 0, 22 interact such that cage 0 has incongruous combinations; reduced from 42 to 40 combinations
26: (4.6) Cage comparison: cages 10, 33, 18, 23, 1 interact such that cage 18 has incongruous combinations; reduced from 10 to 9 combinations
27: (4.6) Cage comparison: cages 21, 25, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 92 to 88 combinations
28: (4.6) Cage comparison: cages 13, 21, 25, 8, 29 interact such that cage 8 has incongruous combinations; reduced from 16 to 15 combinations
29: (4.6) Cage comparison: cages 13, 21, 25, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 46 to 44 combinations
30: (4.6) Cage comparison: cages 13, 25, 14, 30, 29 interact such that cage 29 has incongruous combinations; reduced from 88 to 80 combinations
31: (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
32: (4.8) Cage comparison: cages 13, 20, 25, 24, 23, 29 interact such that cage 29 has incongruous combinations; reduced from 80 to 72 combinations
33: (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
34: (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
35: (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
36: (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
37: (4.8) Cage comparison: cages 19, 27, 34, 24, 11, 3 interact such that cage 3 has incongruous combinations; reduced from 16 to 15 combinations
38: (4.8) Cage comparison: cages 20, 25, 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 56 to 49 combinations
39: (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
40: (4.2) Cage comparison: cages 18, 19, 15 interact such that cage 15 has incongruous combinations; reduced from 14 to 13 combinations
41: (4.6) Cage comparison: cages 18, 10, 33, 1, 22 interact such that cage 22 has incongruous combinations; reduced from 49 to 46 combinations
42: (4.8) Cage comparison: cages 17, 5, 31, 9, 0, 22 interact such that cage 0 has incongruous combinations; reduced from 40 to 38 combinations
43: (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
44: (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
45: (5) Cage comparison: cages 13, 25, 17, 21, 24, 23, 29 interact such that cage 21 has incongruous combinations; reduced from 6 to 5 combinations
46: (5) Cage comparison: cages 13, 25, 21, 14, 30, 8, 29 interact such that cages 21, 29 have incongruous combinations; reduced from 5, 72 to 4, 54 combinations respectively
47: (5) Cage comparison: cages 13, 25, 21, 14, 30, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 35 to 34 combinations
48: (5) Cage comparison: cages 13, 21, 14, 30, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 34 to 33 combinations
49: (5) Cage comparison: cages 19, 27, 34, 6, 24, 11, 3 interact such that cage 3 has incongruous combinations; reduced from 15 to 14 combinations
50: (5) Cage comparison: cages 20, 25, 17, 21, 24, 18, 23 interact such that cage 18 has incongruous combinations; reduced from 7 to 6 combinations
51: (5) Cage comparison: cages 27, 34, 31, 30, 26, 32, 29 interact such that cage 29 has incongruous combinations; reduced from 54 to 52 combinations
52: (5) Cage comparison: cages 34, 31, 28, 30, 26, 32, 29 interact such that cage 29 has incongruous combinations; reduced from 52 to 50 combinations
53: (5) Cage comparison: cages 17, 5, 6, 31, 9, 0, 22 interact such that cage 0 has incongruous combinations; reduced from 38 to 37 combinations
54: (5) Cage comparison: cages 17, 5, 33, 31, 9, 0, 22 interact such that cages 0, 22 have incongruous combinations; reduced from 37, 46 to 33, 44 combinations respectively
55: (5) Cage comparison: cages 5, 6, 7, 1, 2, 8, 0 interact such that cage 0 has incongruous combinations; reduced from 33 to 32 combinations
56: (5.2) Cage comparison: cages 13, 20, 21, 25, 24, 23, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 33 to 32 combinations
57: (5.2) Cage comparison: cages 13, 20, 21, 25, 14, 30, 8, 29 interact such that cage 29 has incongruous combinations; reduced from 50 to 48 combinations
58: (5.2) Cage comparison: cages 13, 20, 21, 25, 14, 30, 4, 29 interact such that cages 4, 29 have incongruous combinations; reduced from 32, 48 to 31, 46 combinations respectively
59: (5.2) Cage comparison: cages 13, 20, 21, 25, 14, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 31 to 30 combinations
60: (5.2) Cage comparison: cages 13, 21, 25, 14, 30, 8, 4, 29 interact such that cages 8, 4, 29 have incongruous combinations; reduced from 14, 30, 46 to 12, 20, 37 combinations respectively
61: (5.2) Cage comparison: cages 20, 21, 25, 34, 17, 14, 31, 29 interact such that cage 29 has incongruous combinations; reduced from 37 to 36 combinations
62: (5.2) Cage comparison: cages 20, 21, 25, 14, 30, 8, 4, 29 interact such that cages 8, 4 have incongruous combinations; reduced from 12, 20 to 11, 19 combinations respectively
63: (4.8) Cage comparison: cages 4, 20, 7, 12, 28, 29 interact such that cage 29 has incongruous combinations; reduced from 36 to 34 combinations
64: (5) Cage comparison: cages 8, 29, 13, 21, 25, 14, 30 interact such that cage 8 has incongruous combinations; reduced from 11 to 10 combinations
65: (5) Cage comparison: cages 29, 27, 31, 28, 30, 26, 32 interact such that cage 26 has incongruous combinations; reduced from 14 to 13 combinations
66: (5.2) Cage comparison: cages 20, 21, 17, 18, 24, 23, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 44 to 43 combinations
67: (5.2) Cage comparison: cages 20, 21, 7, 14, 30, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 19 to 18 combinations
68: (5.2) Cage comparison: cages 20, 25, 27, 34, 6, 24, 7, 11 interact such that cage 24 has incongruous combinations; reduced from 6 to 5 combinations
69: (5.2) Cage comparison: cages 25, 17, 5, 31, 15, 9, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 43 to 42 combinations
70: (5.2) Cage comparison: cages 27, 34, 17, 31, 28, 9, 22, 29 interact such that cage 22 has incongruous combinations; reduced from 42 to 40 combinations
71: (5.2) Cage comparison: cages 27, 34, 31, 28, 30, 26, 32, 29 interact such that cages 26, 32, 29 have incongruous combinations; reduced from 13, 16, 34 to 9, 14, 27 combinations respectively
72: (5) Cage comparison: cages 29, 13, 20, 21, 25, 8, 4 interact such that cage 8 has incongruous combinations; reduced from 10 to 9 combinations
73: (5.2) Cage comparison: cages 27, 17, 5, 31, 9, 0, 22, 29 interact such that cage 22 has incongruous combinations; reduced from 40 to 39 combinations
74: (5.2) Cage comparison: cages 27, 5, 28, 30, 26, 32, 22, 29 interact such that cage 22 has incongruous combinations; reduced from 39 to 38 combinations
75: (5.2) Cage comparison: cages 27, 23, 28, 30, 26, 32, 22, 29 interact such that cage 22 has incongruous combinations; reduced from 38 to 36 combinations
76: (5.2) Cage comparison: cages 27, 31, 28, 30, 26, 32, 22, 29 interact such that cages 31, 30, 22, 29 have incongruous combinations; reduced from 10, 12, 36, 27 to 9, 11, 26, 25 combinations respectively
77: (4.4) Cage comparison: cages 31, 17, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 32 to 28 combinations
78: (4.8) Cage comparison: cages 29, 22, 13, 25, 24, 23 interact such that cage 29 has incongruous combinations; reduced from 25 to 23 combinations
79: (4.6) Cage comparison: cages 29, 34, 17, 31, 22 interact such that cage 22 has incongruous combinations; reduced from 26 to 24 combinations
80: (5.2) Cage comparison: cages 17, 5, 24, 23, 31, 9, 0, 22 interact such that cage 22 has incongruous combinations; reduced from 24 to 23 combinations
81: (5) Cage comparison: cages 22, 13, 25, 14, 26, 30, 29 interact such that cage 30 has incongruous combinations; reduced from 11 to 10 combinations
82: (5) Cage comparison: cages 30, 21, 25, 14, 8, 4, 29 interact such that cage 29 has incongruous combinations; reduced from 23 to 22 combinations
83: (5.2) Cage comparison: cages 5, 6, 1, 2, 3, 8, 0, 4 interact such that cage 0 has incongruous combinations; reduced from 28 to 26 combinations
84: (5.2) Cage comparison: cages 13, 21, 25, 14, 30, 8, 4, 29 interact such that cages 8, 4, 29 have incongruous combinations; reduced from 9, 18, 22 to 8, 17, 21 combinations respectively
85: (5) Cage comparison: cages 29, 25, 27, 34, 14, 31, 30 interact such that cage 30 has incongruous combinations; reduced from 10 to 9 combinations
86: (5) Cage comparison: cages 30, 4, 29, 13, 21, 25, 14 interact such that cage 4 has incongruous combinations; reduced from 17 to 16 combinations
87: (5.2) Cage comparison: cages 13, 21, 25, 14, 30, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 16 to 14 combinations
88: (5) Cage comparison: cages 4, 13, 20, 21, 12, 28, 29 interact such that cage 12 has incongruous combinations; reduced from 12 to 10 combinations
89: (5.2) Cage comparison: cages 13, 25, 34, 24, 23, 26, 22, 29 interact such that cage 34 has incongruous combinations; reduced from 4 to 3 combinations
90: (5) Cage comparison: cages 34, 19, 27, 24, 7, 3, 11 interact such that cage 7 has incongruous combinations; reduced from 8 to 7 combinations
91: (4.8) Cage comparison: cages 7, 13, 20, 8, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 14 to 13 combinations
92: (4.6) Cage comparison: cages 4, 21, 25, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 21 to 18 combinations
93: (4.8) Cage comparison: cages 4, 29, 34, 31, 3, 0 interact such that cage 0 has incongruous combinations; reduced from 26 to 25 combinations
94: (5) Cage comparison: cages 34, 29, 0, 17, 31, 9, 22 interact such that cage 0 has incongruous combinations; reduced from 25 to 23 combinations
95: (5) Cage comparison: cages 34, 29, 24, 23, 26, 31, 22 interact such that cage 31 has incongruous combinations; reduced from 9 to 8 combinations
96: (5) Cage comparison: cages 34, 31, 4, 29, 0, 21, 17 interact such that cage 0 has incongruous combinations; reduced from 23 to 22 combinations
97: (5) Cage comparison: cages 7, 4, 29, 20, 27, 12, 28 interact such that cage 28 has incongruous combinations; reduced from 12 to 10 combinations
98: (5) Cage comparison: cages 31, 28, 29, 27, 26, 32, 22 interact such that cage 29 has incongruous combinations; reduced from 18 to 17 combinations
99: (5) Cage comparison: cages 4, 29, 13, 21, 25, 8, 30 interact such that cage 8 has incongruous combinations; reduced from 8 to 7 combinations
100: (5.2) Cage comparison: cages 20, 21, 14, 12, 28, 30, 26, 29 interact such that cage 29 has incongruous combinations; reduced from 17 to 16 combinations
101: (4.8) Cage comparison: cages 29, 20, 21, 14, 30, 4 interact such that cage 21 has incongruous combinations; reduced from 4 to 3 combinations
102: (4.2) Cage comparison: cages 21, 19, 18 interact such that cage 18 has incongruous combinations; reduced from 6 to 4 combinations
103: (4.2) Cage comparison: cages 21, 19, 15 interact such that cage 15 has incongruous combinations; reduced from 13 to 11 combinations
104: (4.2) Cage comparison: cages 18, 15, 19 interact such that cage 15 has incongruous combinations; reduced from 11 to 9 combinations
105: (4.8) Cage comparison: cages 21, 29, 13, 25, 17, 31 interact such that cage 17 has incongruous combinations; reduced from 5 to 4 combinations
106: (4.4) Cage comparison: cages 17, 20, 24, 23 interact such that cage 20 has incongruous combinations; reduced from 4 to 3 combinations
107: (4.4) Cage comparison: cages 17, 24, 23, 22 interact such that cage 22 has incongruous combinations; reduced from 23 to 20 combinations
108: (4.8) Cage comparison: cages 15, 29, 22, 27, 5, 32 interact such that cage 22 has incongruous combinations; reduced from 20 to 19 combinations
109: (5) Cage comparison: cages 20, 21, 17, 22, 31, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 22 to 20 combinations
110: (5) Cage comparison: cages 20, 21, 29, 25, 14, 30, 4 interact such that cage 25 has incongruous combinations; reduced from 4 to 3 combinations
111: (4.8) Cage comparison: cages 25, 21, 13, 8, 30, 29 interact such that cage 30 has incongruous combinations; reduced from 9 to 8 combinations
112: (4.6) Cage comparison: cages 30, 21, 14, 4, 29 interact such that cage 4 has incongruous combinations; reduced from 13 to 12 combinations
113: (4.8) Cage comparison: cages 25, 30, 4, 21, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 16 to 15 combinations
114: (5) Cage comparison: cages 20, 21, 25, 30, 4, 29, 12 interact such that cage 4 has incongruous combinations; reduced from 12 to 11 combinations
115: (5) Cage comparison: cages 20, 25, 17, 15, 22, 24, 23 interact such that cage 15 has incongruous combinations; reduced from 9 to 8 combinations
116: (4.8) Cage comparison: cages 15, 20, 21, 25, 5, 22 interact such that cage 22 has incongruous combinations; reduced from 19 to 18 combinations
117: (4.4) Cage comparison: cages 22, 24, 23, 26 interact such that cage 26 has incongruous combinations; reduced from 9 to 8 combinations
118: (4.6) Cage comparison: cages 22, 5, 33, 15, 0 interact such that cage 0 has incongruous combinations; reduced from 20 to 19 combinations
119: (4.8) Cage comparison: cages 22, 20, 25, 17, 24, 23 interact such that cage 20 has incongruous combinations; reduced from 3 to 2 combinations
120: (4.6) Cage comparison: cages 20, 25, 14, 30, 4 interact such that cage 4 has incongruous combinations; reduced from 11 to 10 combinations
121: (4.8) Cage comparison: cages 20, 4, 21, 14, 30, 29 interact such that cage 4 has incongruous combinations; reduced from 10 to 9 combinations
122: (4.8) Cage comparison: cages 4, 21, 25, 13, 14, 29 interact such that cage 29 has incongruous combinations; reduced from 15 to 14 combinations
123: (1.5) Pointing candidates: all combinations for cage 29 contain 8r9; eliminations in r9c1
124: (4.8) Cage comparison: cages 29, 22, 25, 14, 30, 28 interact such that cage 29 has incongruous combinations; reduced from 14 to 13 combinations
125: (4.4) Cage comparison: cages 29, 17, 31, 22 interact such that cage 22 has incongruous combinations; reduced from 18 to 17 combinations
126: (5) Cage comparison: cages 20, 25, 26, 29, 22, 27, 23 interact such that cage 23 has incongruous combinations; reduced from 8 to 7 combinations
127: (5) Cage comparison: cages 20, 25, 4, 29, 13, 12, 28 interact such that cage 29 has incongruous combinations; reduced from 13 to 12 combinations
128: (1.5) Claiming candidates: cage 34 must contain 1 in r9c5, r9c6: from 3 combinations to 2
129: (1.5) Pointing candidates: all combinations for cage 34 contain 5r9; eliminations in r9c1
130: (4.6) Cage comparison: cages 31, 29, 27, 28, 22 interact such that cage 28 has incongruous combinations; reduced from 10 to 9 combinations
131: (4.6) Cage comparison: cages 29, 20, 25, 13, 8 interact such that cage 8 has incongruous combinations; reduced from 7 to 6 combinations
132: (4.8) Cage comparison: cages 31, 29, 21, 17, 18, 19 interact such that cage 17 has incongruous combinations; reduced from 4 to 3 combinations
133: (4) Cage comparison: cages 17, 9 interact such that cage 9 has incongruous combinations; reduced from 14 to 10 combinations
134: (4.2) Cage comparison: cages 17, 9, 31 interact such that cage 9 has incongruous combinations; reduced from 10 to 8 combinations
135: (4.6) Cage comparison: cages 17, 9, 31, 22, 0 interact such that cage 31 has incongruous combinations; reduced from 6 to 5 combinations
136: (4.6) Cage comparison: cages 17, 21, 5, 15, 22 interact such that cage 22 has incongruous combinations; reduced from 17 to 15 combinations
137: (4.8) Cage comparison: cages 17, 31, 9, 29, 22, 0 interact such that cage 0 has incongruous combinations; reduced from 19 to 17 combinations
138: (4.8) Cage comparison: cages 17, 31, 9, 22, 0, 5 interact such that cage 22 has incongruous combinations; reduced from 15 to 13 combinations
139: (4.8) Cage comparison: cages 17, 31, 29, 0, 21, 4 interact such that cage 0 has incongruous combinations; reduced from 17 to 16 combinations
140: (4.8) Cage comparison: cages 17, 22, 21, 18, 19, 15 interact such that cage 22 has incongruous combinations; reduced from 13 to 11 combinations
141: (4.4) Cage comparison: cages 22, 31, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 16 to 14 combinations
142: (4.4) Cage comparison: cages 0, 17, 31, 9 interact such that cage 31 has incongruous combinations; reduced from 5 to 4 combinations
143: (4.8) Cage comparison: cages 17, 20, 21, 18, 19, 15 interact such that cage 15 has incongruous combinations; reduced from 8 to 6 combinations
144: (4.4) Cage comparison: cages 15, 5, 33, 22 interact such that cage 22 has incongruous combinations; reduced from 11 to 7 combinations
145: (4.4) Cage comparison: cages 22, 31, 9, 0 interact such that cage 0 has incongruous combinations; reduced from 14 to 12 combinations
146: (4.2) Cage comparison: cages 0, 4, 3 interact such that cage 3 has incongruous combinations; reduced from 14 to 13 combinations
147: (4.4) Cage comparison: cages 22, 0, 17, 9 interact such that cage 9 has incongruous combinations; reduced from 8 to 6 combinations
148: (4.6) Cage comparison: cages 15, 22, 5, 33, 32 interact such that cage 32 has incongruous combinations; reduced from 14 to 13 combinations
149: (4.6) Cage comparison: cages 22, 17, 21, 18, 19 interact such that cage 18 has incongruous combinations; reduced from 4 to 3 combinations
150: (4.4) Cage comparison: cages 18, 10, 33, 1 interact such that cage 1 has incongruous combinations; reduced from 14 to 12 combinations
151: (4.6) Cage comparison: cages 18, 22, 1, 10, 33 interact such that cage 1 has incongruous combinations; reduced from 12 to 10 combinations
152: (4.8) Cage comparison: cages 17, 18, 15, 22, 24, 23 interact such that cage 22 has incongruous combinations; reduced from 7 to 6 combinations
153: (4.6) Cage comparison: cages 22, 5, 15, 33, 0 interact such that cage 0 has incongruous combinations; reduced from 12 to 10 combinations
154: (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 22 reduced from 6 combinations to 5
155: (4.2) Cage comparison: cages 31, 9, 0 interact such that cage 31 has incongruous combinations; reduced from 4 to 3 combinations
156: (1.5) Claiming candidates: cage 29 must contain 4 in r9c7, r9c8, r9c9: from 12 combinations to 11
157: (4.2) Cage comparison: cages 0, 4, 3 interact such that cage 3 has incongruous combinations; reduced from 13 to 11 combinations
158: (4.4) Cage comparison: cages 31, 0, 29, 4 interact such that cage 4 has incongruous combinations; reduced from 9 to 8 combinations
159: (1.5) Claiming candidates: cage 29 must contain 1 in r7c8, r8c8, r9c8: from 11 combinations to 10
160: (1) Hidden single: 2 in r9c1
161: (1.5) Pointing candidates: all combinations for cage 29 contain 6c8; eliminations in r3c8, r4c8
162: (1.5) Pointing candidates: all combinations for cage 13 contain 5c8,9c8; eliminations in r2c8, r6c8
163: (4.2) Cage comparison: cages 31, 17, 0 interact such that cage 0 has incongruous combinations; reduced from 10 to 9 combinations
164: (4.2) Cage comparison: cages 29, 22, 32 interact such that cage 32 has incongruous combinations; reduced from 13 to 12 combinations
165: (4.4) Cage comparison: cages 31, 22, 29, 32 interact such that cage 32 has incongruous combinations; reduced from 12 to 10 combinations
166: (4.4) Cage comparison: cages 31, 22, 29, 27 interact such that cage 27 has incongruous combinations; reduced from 4 to 3 combinations
167: (4.2) Cage comparison: cages 27, 29, 32 interact such that cage 32 has incongruous combinations; reduced from 10 to 9 combinations
168: (4.4) Cage comparison: cages 31, 27, 32, 29 interact such that cage 32 has incongruous combinations; reduced from 9 to 8 combinations
169: (4.4) Cage comparison: cages 27, 22, 29, 26 interact such that cage 26 has incongruous combinations; reduced from 8 to 6 combinations
170: (4.6) Cage comparison: cages 25, 8, 0, 17, 21 interact such that cage 0 has incongruous combinations; reduced from 9 to 8 combinations
171: (4.6) Cage comparison: cages 25, 8, 21, 5, 15 interact such that cage 5 has incongruous combinations; reduced from 6 to 5 combinations
172: (4.2) Cage comparison: cages 5, 22, 0 interact such that cage 0 has incongruous combinations; reduced from 8 to 7 combinations
173: (3) Region parity: Col 1 must sum to Odd number; cage 22's cells within this region must sum to Odd number; reduced from 5 combinations to 4
174: (1) Hidden single: 9 in r6c9
175: (0) Naked single: 3 in r6c8
176: (0) Naked single: 1 in r5c7
177: (0) Naked single: 6 in r6c7
178: (0) Naked single: 9 in r6c9
179: (1) Hidden single: 2 in r5c8
180: (0) Naked single: 5 in r5c9
181: (1.5) Claiming candidates: cage 18 must contain 8 in r5c3, r5c4: from 3 combinations to 2
182: (1.5) Pointing candidates: all combinations for cage 8 contain 7r2; eliminations in r2c3, r2c4, r2c5
183: (1.5) Pointing candidates: all combinations for cage 6 contain 7r3; eliminations in r3c2, r3c6, r3c7
184: (1.5) Pointing candidates: all combinations for cage 18 contain 6r5; eliminations in r5c2
185: (1.5) Pointing candidates: all combinations for cage 22 contain 9r7; eliminations in r7c7
186: (1.5) Pointing candidates: all combinations for cage 30 contain 4c9; eliminations in r3c9, r4c9, r9c9
187: (3.2) Region parity: Rows 3, 4 must sum to Even number; cage 5's cells within this region must sum to Odd number; reduced from 4 combinations to 2
188: (1.5) Pointing candidates: all combinations for cage 5 contain 3c2,9c2; eliminations in r5c2, r8c2, r9c2, r1c2
189: (0) Naked single: 7 in r5c2
190: (0) Naked single: 3 in r5c1
191: (0) Naked single: 1 in r8c1
192: (0) Naked single: 1 in r7c8
193: (0) Naked single: 4 in r6c2
194: (0) Naked single: 5 in r7c4
195: (0) Naked single: 2 in r7c2
196: (0) Naked single: 3 in r7c6
197: (0) Naked single: 2 in r8c6
198: (0) Naked single: 6 in r8c8
199: (0) Naked single: 5 in r8c2
200: (0) Naked single: 1 in r1c2
201: (0) Naked single: 4 in r8c3
202: (0) Naked single: 6 in r7c5
203: (0) Naked single: 4 in r7c9
204: (0) Naked single: 7 in r8c9
205: (0) Naked single: 7 in r2c8
206: (0) Naked single: 7 in r9c7
207: (0) Naked single: 8 in r7c7
208: (0) Naked single: 9 in r8c7
209: (0) Naked single: 8 in r1c8
210: (0) Naked single: 9 in r1c1
211: (0) Naked single: 7 in r7c1
212: (0) Naked single: 9 in r7c3
213: (0) Naked single: 6 in r9c2
214: (0) Naked single: 8 in r4c2
215: (0) Naked single: 3 in r9c3
216: (0) Naked single: 7 in r1c3
217: (0) Naked single: 5 in r2c3
218: (0) Naked single: 9 in r9c4
219: (0) Naked single: 8 in r2c1
220: (0) Naked single: 6 in r2c9
221: (0) Naked single: 2 in r2c7
222: (0) Naked single: 4 in r9c8
223: (0) Naked single: 8 in r9c9
224: (0) Naked single: 5 in r6c1
225: (1) Hidden single: 9 in r2c2
226: (0) Naked single: 3 in r3c2
227: (0) Naked single: 3 in r2c5
228: (0) Naked single: 3 in r8c4
229: (0) Naked single: 4 in r2c4
230: (0) Naked single: 1 in r2c6
231: (0) Naked single: 1 in r9c5
232: (0) Naked single: 1 in r3c4
233: (0) Naked single: 2 in r3c9
234: (0) Naked single: 6 in r3c3
235: (0) Naked single: 4 in r3c1
236: (0) Naked single: 6 in r4c1
237: (0) Naked single: 8 in r5c3
238: (0) Naked single: 1 in r6c3
239: (0) Naked single: 8 in r6c4
240: (0) Naked single: 2 in r6c5
241: (0) Naked single: 7 in r6c6
242: (0) Naked single: 6 in r5c4
243: (0) Naked single: 2 in r1c4
244: (0) Naked single: 7 in r4c4
245: (0) Naked single: 4 in r4c5
246: (0) Naked single: 8 in r3c6
247: (0) Naked single: 9 in r4c6
248: (0) Naked single: 9 in r3c8
249: (0) Naked single: 5 in r4c8
250: (0) Naked single: 5 in r3c7
251: (0) Naked single: 4 in r1c7
252: (0) Naked single: 5 in r1c5
253: (0) Naked single: 6 in r1c6
254: (0) Naked single: 3 in r1c9
255: (0) Naked single: 3 in r4c7
256: (0) Naked single: 9 in r5c5
257: (0) Naked single: 4 in r5c6
258: (0) Naked single: 2 in r4c3
259: (0) Naked single: 1 in r4c9
260: (0) Naked single: 7 in r3c5
261: (0) Naked single: 5 in r9c6
262: (0) Naked single: 8 in r8c5