[Retros] =N double checkmates (Summary)

[Mario Richter]

Dear Hiro,

some of the games you gave are not the shortest possbile ones:

axb1N++# (old: 22 plies, new: 16 plies):
 1. Pc2-c4   Pd7-d5   2. Qd1-b3   Pd5xc4    3. Qb3-b4   Qd8-d4    
 4. Pb2-b3   Pc4xb3   5. Ke1-d1   Pb3xa2    6. Kd1-c2   Qd4xa1    
 7. Kc2-b3   Bc8-e6   8. Kb3-a3   Pa2xb1=N#

bxc8N++# (old: 19 plies, new: 15 plies):
 1. Pc2-c4   Pd7-d5   2. Pc4xd5   Nb8-c6    3. Pd5xc6   Pa7-a6    
 4. Pc6xb7   Ke8-d7   5. Pd2-d3   Kd7-c6    6. Qd1-c2   Kc6-b6    
 7. Qc2xc7   Kb6-a7   8. Pb7xc8=N 
  
dxc8N++# (old: 14 plies, new: 13 plies):
 1. Pc2-c4   Pe7-e6   2. Pc4-c5   Ke8-e7    3. Pc5-c6   Qd8-e8    
 4. Pc6xd7   Nb8-c6   5. Qd1-c2   Nc6-d8    6. Qc2xc7   Ng8-f6    
 7. Pd7xc8=N 

cxd8N++# (old: 17 plies. new: 15 plies)
 1. Pf2-f4   Pe7-e5   2. Pf4xe5   Bf8-d6    3. Pe5xd6   Pb7-b6    
 4. Pd6xc7   Ke8-e7   5. Pe2-e4   Ke7-d6    6. Qd1-g4   Kd6-c6    
 7. Qg4xd7   Kc6-b7   8. Pc7xd8=N 


regards,

  mario