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The solver is run like this (be patient, it takes several hours to run):

python puzzle.py

Eventually it will output something like this:

2021-11-18 05:46:05,017 - Found 4 solutions
[(True, [103481868288, 1077960768, 2207730630656, 216455360897089536, 2282603319132160, 412856877056, 459009, 2019301482922246144, 530480, 2337403390977376256, 1550, 551911719040, 13871297958533660672]), (True, [103481868288, 145806245549309952, 963150610432, 2155905216, 540545024, 13211420065792, 9259647124478361600, 24632, 871464120082235392, 265732, 8097472130012151808, 72340172838010880, 196867]), (True, [103481868288, 4224323673915392, 538632, 33008, 139052711936, 4534403132817408, 263175, 551915896832, 1112497192960, 18260963992010752, 16974592, 2233785415175766016, 16185937060769562624]), (True, [103481868288, 4255744, 1160820396140789760, 1081145385545629696, 13219976445952, 540542976, 16149943448122687488, 566252800049152, 415546474496, 34013696, 54254851516792832, 248, 1287])]
2021-11-18 05:46:05,019 - Solution#1/4:
    Move¤1:
     ABCDEFGH
    1        
    2        
    3        
    4   WB   
    5   BW   
    6        
    7        
    8        

    Move¤2:
     ABCDEFGH
    1      W 
    2     WB 
    3      W 
    4      B 
    5        
    6        
    7        
    8        

    Move¤3:
     ABCDEFGH
    1        
    2        
    3        
    4BWB     
    5 B      
    6 W      
    7        
    8        

    Move¤4:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5W       
    6B       
    7W       
    8BW      

    Move¤5:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5  W     
    6  BWB   
    7   B    
    8        

    Move¤6:
     ABCDEFGH
    1        
    2        
    3    WB  
    4     W  
    5     BW 
    6        
    7        
    8        

    Move¤7:
     ABCDEFGH
    1W       
    2B       
    3WBW     
    4        
    5        
    6        
    7        
    8        

    Move¤8:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6        
    7 BW     
    8  BWB   

    Move¤9:
     ABCDEFGH
    1    WB  
    2   WB   
    3   B    
    4        
    5        
    6        
    7        
    8        

    Move¤10:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6     W  
    7    WBW 
    8     W  

    Move¤11:
     ABCDEFGH
    1 BWB    
    2 WB     
    3        
    4        
    5        
    6        
    7        
    8        

    Move¤12:
     ABCDEFGH
    1       B
    2       W
    3       B
    4       W
    5       B
    6        
    7        
    8        

    Move¤13:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6      BW
    7       B
    8      BW


2021-11-18 05:46:05,021 - Solution#2/4:
    Move¤1:
     ABCDEFGH
    1        
    2        
    3        
    4   WB   
    5   BW   
    6        
    7        
    8        

    Move¤2:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5 B      
    6 W      
    7 BW     
    8 W      

    Move¤3:
     ABCDEFGH
    1        
    2        
    3      W 
    4      B 
    5     BWB
    6        
    7        
    8        

    Move¤4:
     ABCDEFGH
    1      WB
    2       W
    3       B
    4       W
    5        
    6        
    7        
    8        

    Move¤5:
     ABCDEFGH
    1        
    2    B   
    3   BWB  
    4     W  
    5        
    6        
    7        
    8        

    Move¤6:
     ABCDEFGH
    1        
    2        
    3        
    4 WB     
    5  W     
    6  BW    
    7        
    8        

    Move¤7:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6     WBW
    7       B
    8       W

    Move¤8:
     ABCDEFGH
    1   BWB  
    2     WB 
    3        
    4        
    5        
    6        
    7        
    8        

    Move¤9:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6    B   
    7   BW   
    8  BW    

    Move¤10:
     ABCDEFGH
    1  W     
    2 WBW    
    3  W     
    4        
    5        
    6        
    7        
    8        

    Move¤11:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6        
    7     BW 
    8    BWB 

    Move¤12:
     ABCDEFGH
    1        
    2        
    3        
    4B       
    5W       
    6B       
    7W       
    8B       

    Move¤13:
     ABCDEFGH
    1WB      
    2B       
    3WB      
    4        
    5        
    6        
    7        
    8        


2021-11-18 05:46:05,023 - Solution#3/4:
    Move¤1:
     ABCDEFGH
    1        
    2        
    3        
    4   WB   
    5   BW   
    6        
    7        
    8        

    Move¤2:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6 W      
    7WBWB    
    8        

    Move¤3:
     ABCDEFGH
    1   B    
    2   WBW  
    3   B    
    4        
    5        
    6        
    7        
    8        

    Move¤4:
     ABCDEFGH
    1    WBWB
    2       W
    3        
    4        
    5        
    6        
    7        
    8        

    Move¤5:
     ABCDEFGH
    1        
    2        
    3    WB  
    4     WB 
    5     B  
    6        
    7        
    8        

    Move¤6:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5  W     
    6  BWB   
    7    W   
    8        

    Move¤7:
     ABCDEFGH
    1WBW     
    2  B     
    3  W     
    4        
    5        
    6        
    7        
    8        

    Move¤8:
     ABCDEFGH
    1        
    2      B 
    3      WB
    4       W
    5       B
    6        
    7        
    8        

    Move¤9:
     ABCDEFGH
    1        
    2        
    3        
    4 WB     
    5WB      
    6B       
    7        
    8        

    Move¤10:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5      W 
    6     WBW
    7      W 
    8        

    Move¤11:
     ABCDEFGH
    1        
    2BW      
    3WB      
    4B       
    5        
    6        
    7        
    8        

    Move¤12:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6        
    7        
    8BWBWB   

    Move¤13:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6        
    7     B B
    8     WBW


2021-11-18 05:46:05,025 - Solution#4/4:
    Move¤1:
     ABCDEFGH
    1        
    2        
    3        
    4   WB   
    5   BW   
    6        
    7        
    8        

    Move¤2:
     ABCDEFGH
    1        
    2    BWBW
    3      W 
    4        
    5        
    6        
    7        
    8        

    Move¤3:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6    B   
    7  WBW   
    8    B   

    Move¤4:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6        
    7W       
    8BWBW    

    Move¤5:
     ABCDEFGH
    1        
    2        
    3        
    4  B     
    5 BW     
    6  BW    
    7        
    8        

    Move¤6:
     ABCDEFGH
    1        
    2   W    
    3   BWB  
    4     W  
    5        
    6        
    7        
    8        

    Move¤7:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5        
    6     W  
    7     B  
    8     WBW

    Move¤8:
     ABCDEFGH
    1        
    2        
    3        
    4B       
    5W       
    6BW      
    7 B      
    8        

    Move¤9:
     ABCDEFGH
    1        
    2        
    3       B
    4      BW
    5     BW 
    6        
    7        
    8        

    Move¤10:
     ABCDEFGH
    1        
    2 W      
    3WBW     
    4 W      
    5        
    6        
    7        
    8        

    Move¤11:
     ABCDEFGH
    1        
    2        
    3        
    4        
    5       B
    6      BW
    7      WB
    8        

    Move¤12:
     ABCDEFGH
    1   BWBWB
    2        
    3        
    4        
    5        
    6        
    7        
    8        

    Move¤13:
     ABCDEFGH
    1WBW     
    2B B     
    3        
    4        
    5        
    6        
    7        
    8        

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