Question 351532
1) Adam says Bob lies
2) Bob says Charlie lies
3) Charlie says Adam and Bob both lie
 
a) suppose Adam tells the truth, then Bob lies, 
  if Bob lies, then (2) Charlie tells the truth
 
b) if Adam tells the truth, from (a) we got Charlie tells the truth, 
 then from (3) Adam should lie which contradict the hypothesis
 
c) if Adam tells the truth, we got a contradiction, hence Adam lies
 
 if Adam lies then Bob tells the truth,
 if Bob tells the truth, then Charlie lies, 
 if Charlie lies then either Adam or Bob should tell the truth
  this is not contradicting, since Adam lies, but Bob tells the truth, 
 
hence Adam lies, Bob tells the truth and Charlie lies.