Skip to main content

Challenge 464: A line of lies

You might have noticed I'm a fan of logic puzzles - no apologies for another one!

In each part of this question, there are 20 people standing in a line. Each person is either a Falsifier (who always lies) or a Truthicator (who always tells the truth).

For each part, you should find all possible values of X, where X is the number of Truthicators minus the number of Falsifiers.

Each part is completely separate, so ignore all previous statements.

(1) Everyone in the line says "the person two in front of me is a Falsifier."

(2) Everyone in the line says "exactly one person adjacent to me is a Falsifier."

(3) Everyone in the line says "there are more Falsifiers in front of me than behind me."

(4) Everyone in the line says "there are more Falsifiers in front of me than Truthicators behind me."