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.
Sample Questions
Exactly one truth-teller puzzles unlock when you start with a meta-line (“X is lying”) and cascade: truth → fact, everyone else → negate.
One-truth-teller animal accusations recur on Selective mocks — the assume-and-cascade method is the same every time with four characters.
You must identify who tells the truth and who took the trophy so that exactly one statement is true and the thief is forced by the liars’ false claims.
Four animals each make one accusation or denial. Only one tells the truth. You find who took the trophy (or similar).
Best approach: Try the speaker who comments on another’s honesty first (e.g. Tiger: “Rabbit is lying”). If that cascade gives exactly one truth-teller and one thief, stop. Otherwise test the next character.
Question
Only one of these animals tells the truth:
- Fox: "Rabbit took the trophy."
- Rabbit: "Tiger took it."
- Owl: "I didn't take it."
- Tiger: "Rabbit is lying."
Who took the trophy?
- Afox
- Brabbit
- Cowl
- Dtiger
Decided on your answer? Check how you went below.
Truth-table puzzles reward one habit: assume each person won, mark every statement true or false, and drop anyone with two falses in their pair.
“At most one false per person” grids appear on Selective TS in the harder band — fast elimination once you test winners systematically instead of guessing.
The examiner checks whether you can test each candidate winner, count falses per row, and find the only scenario where nobody breaks the one-false rule.
Three people each make two statements about who won. Exactly one winner exists. No person may have more than one false statement in their pair.
Best approach: Test Finn, then Grace, then Hana as winner. For each trial, tick ✓/✗ on all six statements. Two ✗ in one row → reject that winner immediately. The survivor is the answer.
Question
Three students — Finn, Grace, and Hana — each entered the school art competition. The judge confirms that exactly one of them won first prize. Each student makes two statements about who won. Some statements are true and some are false. However, no more than one statement in each student's pair is false.
| Finn | Grace | Hana |
|---|---|---|
| Grace won first prize. | Finn won first prize. | Grace won first prize. |
| I did not win first prize. | Hana won first prize. | Finn did not win first prize. |
Based on the given information, which one of the following statements must be true?
- AFinn won first prize.
- BGrace won first prize.
- CHana won first prize.
- DNone of them won first prize.
Decided on your answer? Check how you went below.
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