Statement A: Both fathers always tell the truth or both fathers always lie.
Statement B: One son always tells the truth and one son always lies.
Statement C: Statement A and Statement B are not both lies.
Here are a few facts given related to the statements above and the men who made them:
(i) Albert made one of the statements, his father made another of the statements, and his son made the remaining statement.
(ii) Each father and son mentioned in the statements refers to one of the three men.
(iii) Each man either always tells the truth or always lies.
Which statement – A, B or C – was made by Albert?
(In reply to
Puzzle Answer by K Sengupta)
Assume that the Statement C is false.
Then, both Statement A and Statement B must be false.
Since all three statements are false, it follows that both fathers are liars and Statement A is true. This is a contradiction.
Accordingly, Statement C must be true. Since both the Statements A and B cannot be false, we must have these cases:
CASE 1: A true, B true, C true
CASE 2: A true, B false, C true
CASE 3: A false, B true, C true
Assume that Case 1 holds. Then Statement B is true so that one son is a liar who made a true statement. This leads to a contradiction .
Case 2: If Statement A is true, then either both Albert and his father are liars or both are truth tellers. Since there is only one false statement, it follows that both the father are truth tellers and Albert's son is a liar. Thus, it follows that Statement B is true. This leads to a contradiction.
Case 3: If Statement B is true, then Albert and his son has opposite veracity. Since A is false it follows that Albert and his father also possess opposite veracity. Since there are two true statements and one false statement, it follows that Albert is the liar and he made the false statement. Consequently, Statement A was made by Albert.
Explanation to Puzzle Answer
