EDIT:: I can't seem to figure out how to correctly implement a spoiler for some reason >! doesn't work for the entire text, so DONT read this if you dont want the solution. If anyone could comment on how to make a spoiler for the entire text then I'll change the post.
If one sheriff outright states that one suspect is not on his list then the problem resembles the original problem with eight. In the special case that the first sheriff eliminates a suspect who is on the list of the second sheriff, then the second sheriff (knowing that one of his suspects is innocent) replaces the removed suspect with a random other suspect.
Lets say S1 has list {a,b} and S2 has list {a,c}.S1 says: I know with certainty that d is not guilty. My list is one of the following: {a,b},{c,e},{f,g}.
S2 says: My list is one of the following: {a,c},{b,f},{e,g}
S1 now knows that S2 has either {a,c} or {b,f}
S1 says##Solution: The criminal is either in the set {a,f} or {b,g}
As criminal c is now excluded, S2 knows that the criminal is a so he says: the criminal is in the set {a,g}
S1 now knows that the criminal is a.
If one sheriff outright states that one suspect is not on his list then the problem resembles the original problem with eight. In the special case that the first sheriff eliminates a suspect who is on the list of the second sheriff, then the second sheriff (knowing that one of his suspects is innocent) replaces the removed suspect with a random other suspect.
Lets say S1 has list {a,b} and S2 has list {a,c}.S1 says: I know with certainty that d is not guilty. My list is one of the following: {a,b},{c,e},{f,g}.
S2 says: My list is one of the following: {a,c},{b,f},{e,g}
S1 now knows that S2 has either {a,c} or {b,f}
S1 says: The criminal is either in the set {a,f} or {b,g}
As criminal c is now excluded, S2 knows that the criminal is a so he says: the criminal is in the set {a,g}
S1 now knows that the criminal is a.
