All Humans have the same gender This was actually a homework assignment in a math lecture in Germany. We prove with mathematical induction that all humans have the same gender. So consider a room with $n$ people. For $n=1$ the statement is obviously true. Now the inductive step: If there are $n+1$ people in the room we ask one arbitrary person to leave the room. So now only $n$ people are left in the room. By the induction hypothesis all these people have the same gender. The person outside now comes back and another person has to leave the room. So again there are $n$ people in the room and all having the same gender. Hence the $n+1$ people all have the same gender. So were is the flaw :-)

Consider the possibilities when you started off with two people ... they are ever in the room together when the decisive judgment is made.