# Logic Question!

Homework Helper
My friend asked me this and I couldn't crack it, wasnt ever good at logic anyway:

Statement A: Both fathers always tell the truth or both fathers always lies.
Statement B: One son always tells the truth and the other son always lie.
Statement C: Statement A and Statement B are not both lies.

Of the statements above and the men who made them:

- Samuel made one of the statements, his father made another of the statements, and Samuel's son made the remaining statement.

- Each father and son mentioned in the statements refer to one of the three men.

- Each man either always tells the truth or always lies

Which statement was made by Samuel?

Alfi
This sentence is false.

It was a fun puzzle.

1) If statement B is true, there is a lie somewhere (one of the sons lies).
2) If statement A is false, there is a truth somewhere (one of the fathers says the truth).
3) From 1 and 2 it follows that A,B,C cannot be all true (because B true would force a lie somewhere), nor all false (because A false would force a truth somewhere).
4) C must be true: its falsehood would imply that all three A,B,C are false, which is forbidden by 3.
5) Thus one of A,B is true and the other false (to avoid all three being true, forbidden by 3).
6) A true and B false would mean that either all three men say the truth, or all lie; both are forbidden by 3. Thus A is false and B is true.
7) From 4 and 6, there are in total 2 true statements and 1 false.
8) From 6, the fathers have opposite 'signs', and so do the sons. If Samuel says the truth, the other two would lie and viceversa. From 7, Samuel must be lying.
9) Since A is the only false statement, Samuel must be saying statement A.

It was a fun puzzle.

1) If statement B is true, there is a lie somewhere (one of the sons lies).
2) If statement A is false, there is a truth somewhere (one of the fathers says the truth).
3) From 1 and 2 it follows that A,B,C cannot be all true (because B true would force a lie somewhere), nor all false (because A false would force a truth somewhere).
4) C must be true: its falsehood would imply that all three A,B,C are false, which is forbidden by 3.
5) Thus one of A,B is true and the other false (to avoid all three being true, forbidden by 3).
6) A true and B false would mean that either all three men say the truth, or all lie; both are forbidden by 3. Thus A is false and B is true.
7) From 4 and 6, there are in total 2 true statements and 1 false.
8) From 6, the fathers have opposite 'signs', and so do the sons. If Samuel says the truth, the other two would lie and viceversa. From 7, Samuel must be lying.
9) Since A is the only false statement, Samuel must be saying statement A.

I arrived at the same conclusion. Samuel = liar.

It's a nicely crafted puzzle.

Homework Helper
Thanks for that Dodo, it was bugging me =] Nice work!