96 Constraints C1..C96 #### 6,6,6 = 6*36 all possible ways
6,1,1 = 6*1 ways to violate C1
= 6*35 ways to not violate C1 (via subtraction)
#### B1 = 6 * 6**(64-3) #### 6,6,6 = 6*36 = T3 = all possible ways to fill first 3 locations 6,1,1 = 6*1 = B1,3 = ways to violate C1 (after filling 3 locations) 6,5,1 = 6*5 = B2,3 = ways to not violate C1 but might violate C2 = 6*30 = B0,3 = ways to not violate C1 nor C2 (via subtraction) #### 6,6,6,6 = T4 = all possible ways to fill first 4 locations 6,1,1,6 = B1,4 = ways to violate C1 (after 4 locations) 6,5,1,1 = B2,4 = ways to violate C2 (but not C1) B3,4 = ways to maybe violate C3, never C1..C2 6,5,5,1 + A,B,C,C (maybe C = A) 6,1,5,1 + A,A,B,B B0,4 = T4 - B(1..3),4 Let's enumerate these so we can check our work: 6,1,5,5 + A,A,B,C (maybe C = A) 6,5,1,5 + A,B,B,C 6,5,5,5 + A,B,C,D #### B2 = 6*5*1*1 * 6**(64-4) #### 6,6,6,6,6 = T5 = all possible ways to fill first 5 locations 6,1,1,6,6 = B1,5 = ways to violate C1 6,5,1,1,6 = B2,5 = ways to violate C2 (but not C1) B3,5 = ways to violate C3 (not C1 nor C2) 6,5,5,1,1 + A,B,C,C,C (maybe C = A) 6,1,5,1,1 + A,A,B,B,B B4,5 = ways to maybe violate only C4 6,1,5,5,1 + A,A,B,C,C (maybe A=C) 6,5,1,5,1 + A,B,B,C,C (maybe A=C) 6,5,5,5,1 + A,B,C,D,D (maybe A=C, A=D, or B=D) B0,5 = T5 - B(1..4),5 6,5,5,1,5 + A,B,C,C,D (A!=B && B!=C && C!=D) 6,1,5,1,5 + A,A,B,B,C 6,1,5,5,5 + A,A,B,C,D 6,5,1,5,5 + A,B,B,C,D 6,5,5,5,5 + A,B,C,D,E #### B3 = ( 6*5*5 + 6*5 ) * 6**(64-5) #### 6,6,6,6,6,6 = T6 = all possible ways to fill first 5 locations 6,1,1,6,6,6 = B1,6 = ways to violate C1 6,5,1,1,6,6 = B2,6 = ways to violate C2 (but not C1) B3,6 = ways to violate C3 first 6,5,5,1,1,6 + A,B,C,C,C 6,1,5,1,1,6 + A,A,B,B,B B4,6 = ways to violate C4 first 6,1,5,5,1,1 + A,A,B,C,C,C 6,5,1,5,1,1 + A,B,B,C,C,C 6,5,5,5,1,1 + A,B,C,D,D,D B5,6 = ways to maybe violate only C5 6,5,5,1,5,1 + A,B,C,C,D,D 6,1,5,1,5,1 + A,A,B,B,C,C 6,1,5,5,5,1 + A,A,B,C,D,D 6,5,1,5,5,1 + A,B,B,C,D,D 6,5,5,5,5,1 + A,B,C,D,E,E B0,6 = T6 - B(1..5),6 6,1,5,5,1,5 + A,A,B,C,C,D 6,5,1,5,1,5 + A,B,B,C,C,D 6,5,5,5,1,5 + A,B,C,D,D,E 6,5,5,1,5,5 + A,B,C,C,D,E 6,1,5,1,5,5 + A,A,B,B,C,D 6,1,5,5,5,5 + A,A,B,C,D,E 6,5,1,5,5,5 + A,B,B,C,D,E 6,5,5,5,5,5 + A,B,C,D,E,F #### B4 = ( 6*5*5*5 + 2*6*5*5 ) * 6**(64-6) #### 6,6,6,6,6,6,6 = T7 = all possible ways to fill first 5 locations 6,1,1,6,6,6,6 = B1,7 = ways to violate C1 ... B5,7 = ways to violate C5 first 6,5,5,1,5,1,1 + A,B,C,C,D,D,D 6,1,5,1,5,1,1 + A,A,B,B,C,C,C 6,1,5,5,5,1,1 + A,A,B,C,D,D,D 6,5,1,5,5,1,1 + A,B,B,C,D,D,D 6,5,5,5,5,1,1 + A,B,C,D,E,E,E B6,7 = ways to maybe violate C6 first 6,1,5,5,1,5,1 + A,A,B,C,C,D,D 6,5,1,5,1,5,1 + A,B,B,C,C,D,D 6,5,5,5,1,5,1 + A,B,C,D,D,E,E 6,5,5,1,5,5,1 + A,B,C,C,D,E,E 6,1,5,1,5,5,1 + A,A,B,B,C,D,D 6,1,5,5,5,5,1 + A,A,B,C,D,E,E 6,5,1,5,5,5,1 + A,B,B,C,D,E,E 6,5,5,5,5,5,1 + A,B,C,D,E,F,F B0,7 6,5,5,1,5,1,5 + A,B,C,C,D,D,E 6,1,5,1,5,1,5 + A,A,B,B,C,C,D 6,1,5,5,5,1,5 + A,A,B,C,D,D,E 6,5,1,5,5,1,5 + A,B,B,C,D,D,E 6,5,5,5,5,1,5 + A,B,C,D,E,E,F 6,1,5,5,1,5,5 + A,A,B,C,C,D,E 6,5,1,5,1,5,5 + A,B,B,C,C,D,E 6,5,5,5,1,5,5 + A,B,C,D,D,E,F 6,5,5,1,5,5,5 + A,B,C,C,D,E,F 6,1,5,1,5,5,5 + A,A,B,B,C,D,E 6,1,5,5,5,5,5 + A,A,B,C,D,E,F 6,5,1,5,5,5,5 + A,B,B,C,D,E,F 6,5,5,5,5,5,5 + A,B,C,D,E,F,G #### B5 = ( 6*5*5 + 3*6*5*5*5 + 6*5**4 ) * 6**(64-7) #### 6,6,6,6,6,6,6,6 = T8 = all possible ways to fill first 5 locations 6,1,1,6,6,6,6,6 = B1,8 = ways to violate C1 ... B6,8 = ways to violate C6 first 6,1,5,5,1,5,1,1 + A,A,B,C,C,D,D,D 6,5,1,5,1,5,1,1 + A,B,B,C,C,D,D,D 6,5,5,5,1,5,1,1 + A,B,C,D,D,E,E,E 6,5,5,1,5,5,1,1 + A,B,C,C,D,E,E,E 6,1,5,1,5,5,1,1 + A,A,B,B,C,D,D,D 6,1,5,5,5,5,1,1 + A,A,B,C,D,E,E,E 6,5,1,5,5,5,1,1 + A,B,B,C,D,E,E,E 6,5,5,5,5,5,1,1 + A,B,C,D,E,F,F,F B0,8 = ways to not violate constraints in a row 6,1,5,5,1,5,1,5 + A,A,B,C,C,D,D,E 6,5,1,5,1,5,1,5 + A,B,B,C,C,D,D,E 6,5,5,5,1,5,1,5 + A,B,C,D,D,E,E,F 6,5,5,1,5,5,1,5 + A,B,C,C,D,E,E,F 6,1,5,1,5,5,1,5 + A,A,B,B,C,D,D,E 6,1,5,5,5,5,1,5 + A,A,B,C,D,E,E,F 6,5,1,5,5,5,1,5 + A,B,B,C,D,E,E,F 6,5,5,5,5,5,1,5 + A,B,C,D,E,F,F,G 6,5,5,1,5,1,5,6 + A,B,C,C,D,D,E,* 6,1,5,1,5,1,5,6 + A,A,B,B,C,C,D,* 6,1,5,5,5,1,5,6 + A,A,B,C,D,D,E,* 6,5,1,5,5,1,5,6 + A,B,B,C,D,D,E,* 6,5,5,5,5,1,5,6 + A,B,C,D,E,E,F,* 6,1,5,5,1,5,5,6 + A,A,B,C,C,D,E,* 6,5,1,5,1,5,5,6 + A,B,B,C,C,D,E,* 6,5,5,5,1,5,5,6 + A,B,C,D,D,E,F,* 6,5,5,1,5,5,5,6 + A,B,C,C,D,E,F,* 6,1,5,1,5,5,5,6 + A,A,B,B,C,D,E,* 6,1,5,5,5,5,5,6 + A,A,B,C,D,E,F,* 6,5,1,5,5,5,5,6 + A,B,B,C,D,E,F,* 6,5,5,5,5,5,5,6 + A,B,C,D,E,F,G,* #### B6 = ( 3 + 4*5 + 5**2 ) 5**3 * 6**(64-7) #### B1 = 6**(64-2) B2 = 5*6**(64-3) B3 = ( 5 + 1 ) * 5 * 6**(64-4) B4 = ( 5 + 2 ) * 5**2 * 6**(64-5) B5 = ( 1 + 3*5 + 5**2 ) * 5**2 * 6**(64-6) B6 = ( 3 + 4*5 + 5**2 ) * 5**3 * 6**(64-7) #### 1.75945240730481e48 1.46621033942068e48 1.46621033942068e48 1.42548227443677e48 1.39154222028351e48 1.35760216613026e48 #### B0 < 6.33402866629733e49 B0 < 6.15808342556685e49 B0 < 6.01146239162478e49 B0 < 5.86484135768271e49 B0 < 5.72229313023903e49 B0 < 5.58313890821068e49 B0 < 5.44737869159766e49 #### 1444500 ** 8 or 1.8955723685859e49 #### 6,1,5,5,1,5,1,5 + |,<,],],<,],<,] 6,5,1,5,1,5,1,5 + |,],<,],<,],<,] 6,5,5,5,1,5,1,5 + |,],],],<,],<,] 6,5,5,1,5,5,1,5 + |,],],<,],],<,] 6,1,5,1,5,5,1,5 + |,<,],<,],],<,] 6,1,5,5,5,5,1,5 + |,<,],],],],<,] 6,5,1,5,5,5,1,5 + |,],<,],],],<,] 6,5,5,5,5,5,1,5 + |,],],],],],],] 6,5,5,1,5,1,5,6 + |,],],<,],<,],| 6,1,5,1,5,1,5,6 + |,<,],<,],<,],| 6,1,5,5,5,1,5,6 + |,<,],],],<,],| 6,5,1,5,5,1,5,6 + |,],<,],],<,],| 6,5,5,5,5,1,5,6 + |,],],],],<,],| 6,1,5,5,1,5,5,6 + |,<,],],<,],],| 6,5,1,5,1,5,5,6 + |,],<,],<,],],| 6,5,5,5,1,5,5,6 + |,],],],<,],],| 6,5,5,1,5,5,5,6 + |,],],<,],],],| 6,1,5,1,5,5,5,6 + |,<,],<,],],],| 6,1,5,5,5,5,5,6 + |,<,],],],],],| 6,5,1,5,5,5,5,6 + |,],<,],],],],| 6,5,5,5,5,5,5,6 + |,],],],],],],| #### 5**6: (not counting the two end values) 6,5,5,5,5,5,5,6 + |,],],],],],],| 5**5: 6,1,5,5,5,5,5,6 + |,<,],],],],],| 6,5,1,5,5,5,5,6 + |,],<,],],],],| 6,5,5,1,5,5,5,6 + |,],],<,],],],| 6,5,5,5,1,5,5,6 + |,],],],<,],],| 6,5,5,5,5,1,5,6 + |,],],],],<,],| 6,5,5,5,5,5,1,5 + |,],],],],],],] 5**4: 6,1,5,1,5,5,5,6 + |,<,],<,],],],| 6,1,5,5,1,5,5,6 + |,<,],],<,],],| 6,1,5,5,5,1,5,6 + |,<,],],],<,],| 6,1,5,5,5,5,1,5 + |,<,],],],],<,] 6,5,1,5,1,5,5,6 + |,],<,],<,],],| 6,5,1,5,5,1,5,6 + |,],<,],],<,],| 6,5,1,5,5,5,1,5 + |,],<,],],],<,] 6,5,5,1,5,1,5,6 + |,],],<,],<,],| 6,5,5,1,5,5,1,5 + |,],],<,],],<,] 6,5,5,5,1,5,1,5 + |,],],],<,],<,] 5**3: 6,1,5,1,5,1,5,6 + |,<,],<,],<,],| 6,1,5,1,5,5,1,5 + |,<,],<,],],<,] 6,1,5,5,1,5,1,5 + |,<,],],<,],<,] 6,5,1,5,1,5,1,5 + |,],<,],<,],<,] #### 6,5,5,5,5,5,5,6;1 + |,],],],],],],|;|^ 6,1,5,5,5,5,5,6;1 + |,<,],],],],],|;|^ 6,5,1,5,5,5,5,6;1 + |,],<,],],],],|;|^ 6,5,5,1,5,5,5,6;1 + |,],],<,],],],|;|^ 6,5,5,5,1,5,5,6;1 + |,],],],<,],],|;|^ 6,5,5,5,5,1,5,6;1 + |,],],],],<,],|;|^ 6,5,5,5,5,5,1,5;1 + |,],],],],],],];|^ 6,1,5,1,5,5,5,6;1 + |,<,],<,],],],|;|^ 6,1,5,5,1,5,5,6;1 + |,<,],],<,],],|;|^ 6,1,5,5,5,1,5,6;1 + |,<,],],],<,],|;|^ 6,1,5,5,5,5,1,5;1 + |,<,],],],],<,];|^ 6,5,1,5,1,5,5,6;1 + |,],<,],<,],],|;|^ 6,5,1,5,5,1,5,6;1 + |,],<,],],<,],|;|^ 6,5,1,5,5,5,1,5;1 + |,],<,],],],<,];|^ 6,5,5,1,5,1,5,6;1 + |,],],<,],<,],|;|^ 6,5,5,1,5,5,1,5;1 + |,],],<,],],<,];|^ 6,5,5,5,1,5,1,5;1 + |,],],],<,],<,];|^ 6,1,5,1,5,1,5,6;1 + |,<,],<,],<,],|;|^ 6,1,5,1,5,5,1,5;1 + |,<,],<,],],<,];|^ 6,1,5,5,1,5,1,5;1 + |,<,],],<,],<,];|^ 6,5,1,5,1,5,1,5;1 + |,],<,],<,],<,];|^ 6,5,5,5,5,5,5,6;5 + |,],],],],],],|;|u 6,1,5,5,5,5,5,6;5 + |,<,],],],],],|;|u 6,5,1,5,5,5,5,6;5 + |,],<,],],],],|;|u 6,5,5,1,5,5,5,6;5 + |,],],<,],],],|;|u 6,5,5,5,1,5,5,6;5 + |,],],],<,],],|;|u 6,5,5,5,5,1,5,6;5 + |,],],],],<,],|;|u 6,5,5,5,5,5,1,5;5 + |,],],],],],],];|u 6,1,5,1,5,5,5,6;5 + |,<,],<,],],],|;|u 6,1,5,5,1,5,5,6;5 + |,<,],],<,],],|;|u 6,1,5,5,5,1,5,6;5 + |,<,],],],<,],|;|u 6,1,5,5,5,5,1,5;5 + |,<,],],],],<,];|u 6,5,1,5,1,5,5,6;5 + |,],<,],<,],],|;|u 6,5,1,5,5,1,5,6;5 + |,],<,],],<,],|;|u 6,5,1,5,5,5,1,5;5 + |,],<,],],],<,];|u 6,5,5,1,5,1,5,6;5 + |,],],<,],<,],|;|u 6,5,5,1,5,5,1,5;5 + |,],],<,],],<,];|u 6,5,5,5,1,5,1,5;5 + |,],],],<,],<,];|u 6,1,5,1,5,1,5,6;5 + |,<,],<,],<,],|;|u 6,1,5,1,5,5,1,5;5 + |,<,],<,],],<,];|u 6,1,5,5,1,5,1,5;5 + |,<,],],<,],<,];|u 6,5,1,5,1,5,1,5;5 + |,],<,],<,],<,];|u #### Might violate VC1: 6,5,1,5,1,5,1,5;1,... + |,],<,],<,],<,];|^,] ,<,],<,],<,] Can't violate VC1, but maybe VC2: 6,5,1,5,1,5,1,5;5,?,... + |,],<,],<,],<,];|u,]^,<,],<,],<,] #### A B ... C D ... 6,5,...;5,4,... vs A B ... B C ... 6,5,...;1,5,...