Truth-and-lie puzzles become manageable when you treat them as consistency problems. The rules about who tells the truth and how many statements are true are part of the problem, not optional background.
An original two-person puzzle
Each of two people is either a truth-teller, who always tells the truth, or a liar, who always lies. A says, B is a liar. B says, We are both liars. Who is which?
Assume B is a truth-teller. Then B's statement would be true, making B a liar. That contradicts the assumption. Therefore B must be a liar.
Because B's statement is false, they are not both liars. With B already identified as a liar, A must be a truth-teller. A's statement that B is a liar is then true, so the complete assignment is consistent.
Check every statement at the end
Do not stop after finding one plausible identity. Substitute the proposed roles into all statements and verify that each truth-teller speaks truth and each liar speaks falsely.
This final pass catches an assignment that solves one sentence while breaking another.
Different puzzle rules require different checks
Some questions say exactly one statement is true. Others say one person always lies. These are not equivalent rules. A person may make multiple statements, and a statement may describe several people.
Mark the unit being counted: people, statements or propositions. Confusing them can lead to an apparently neat but invalid solution.
Use a small case table
With two binary roles, there are four assignments to test. You can eliminate each inconsistent assignment rather than relying on intuition. For larger puzzles, begin with the statement that imposes the strongest restriction.
The method is simple: assume a case, derive what it requires and reject it if it contradicts a clue. A consistent surviving case is a candidate solution; check whether other cases survive before calling it unique.