Unit 15
Truth and Lie Logic
About this unit
Determine who is telling the truth and who is lying by testing each possibility against all statements simultaneously. These puzzles require you to systematically assume each person is the guilty one (or the truth-teller), check for consistency, and find the unique scenario where all constraints are satisfied.
What types of questions will you face?
- 1One guilty party, one truth-teller among 3-4 people — find who broke the rule and who told the truth
- 2Exactly one truth-teller among N animals/people making accusations — find the truth-teller and the culprit
- 3Two-statement per person format: "no more than one false statement per person" — use this to find who won
- 4House/room hiding puzzle: two statements per door, with at most one false per door — find which room
- 54-person contradiction puzzles where exactly one person's statements are all true
Skills you will build
- Systematic case testing: assume each person is the culprit, then check if all statements are consistent
- Using the "exactly one truth-teller" constraint as a filter
- Tracking which statements must be true or false under each assumption
- Verifying that a proposed solution is internally consistent before accepting it
- Working efficiently through cases to avoid repetitive testing
By the end of this unit, you will be able to
- Solve any truth-and-lie puzzle by systematic case testing
- Identify the unique consistent scenario when only one person can be telling the truth
- Handle two-statement per person puzzles using the "at most one false" constraint
- Verify proposed solutions rigorously before committing to an answer
Difficulty profile
Difficult (avg 3.91). Simple 3-person single-statement puzzles are Medium; two-statement "at most one false per person" puzzles with 3 people and 6 statements to check are Difficult to Very Difficult.
Exam tip: Truth and Lie Logic
Use the "assume and check" method: suppose Person A is the culprit/truth-teller, then check every other statement for consistency. If a contradiction appears, discard that assumption. Only one scenario will be fully consistent — that's your answer.
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