Imagine two robots. One always tells the truth. The other always lies, every single time. You don't know which is which, and they look exactly alike. Can you work it out just from what they say?
Truth-teller and liar puzzles are a favourite with older children because they feel like a trick, yet they can be solved with careful reasoning. They practise a powerful thinking skill: "Suppose this were true. What would follow? Does it lead to a contradiction?"
The rules
- A truth-teller only ever says true things.
- A liar only ever says false things. Not some of the time: every statement is false.
- Nobody is in between, unless the puzzle says so.
Make sure your child is comfortable with "false". If a liar says "The sky is green", that's a lie. If a liar says "I always tell the truth", that's also a lie, which is exactly what we'd expect.
The method: try each possibility
The secret is not to guess, but to test. For each character, ask:
| Suppose... | Then their statement is... | Does everything fit? |
|---|---|---|
| ...they tell the truth | True | Check against the other facts |
| ...they lie | False | Check against the other facts |
If one possibility leads to something impossible (a contradiction), it can't be right. Whatever is left must be the answer. Writing it down helps a lot, especially at first.
Puzzle 1: the boastful robot
There are two robots, Green and Yellow. One always tells the truth and one always lies.
Green says: "We are both liars."
Who tells the truth?
Puzzle 2: same or different?
Now each robot could be either kind. Maybe both tell the truth, maybe both lie, maybe one of each.
Red says: "Blue and I are the same kind." Blue says: "Red and I are different kinds."
What kind is each robot?
Puzzle 3: the two doors
You stand in front of two doors. One leads to the treasure, the other to an empty room. Each door has a guard. One guard always tells the truth and the other always lies, but you don't know which is which. You may ask one guard one question.
What question finds the treasure for sure?
Answers
- Puzzle 1: Yellow tells the truth. Suppose Green tells the truth: then "we are both liars" would be true, so Green would be a liar. That's a contradiction. So Green lies, and "we are both liars" is false, which means Yellow is not a liar.
- Puzzle 2: Red lies and Blue tells the truth. The two statements say opposite things, so exactly one is true. If Red told the truth, they'd be the same kind, so Blue would tell the truth too, but then both statements would be true, which is impossible. So Red lies, they are different kinds, and Blue's statement is true.
- Puzzle 3: Ask either guard: "Which door would the other guard say leads to the treasure?" Then choose the other door. If you ask the truth-teller, they truthfully report the liar's wrong answer. If you ask the liar, they lie about the truth-teller's right answer. Either way, you hear the wrong door.
Puzzle 3 is hard for adults too. Draw both cases on paper and act it out with two toys.
Tips and inventing your own
- Act it out. Give toys or family members roles and let them say the lines.
- Use the table. Write "if true" and "if false" for each character and cross out the case that breaks.
- Start from the answer. To invent a puzzle, decide who lies first, then write a statement that only works one way.
- Test it. Check that only one answer fits. If two answers work, change a statement.
Ages are rough guides: many children enjoy puzzle 1 from about 9, puzzle 2 from about 10, and puzzle 3 from about 11 or 12, but every child is different.
In short
- A truth-teller always says true things; a liar always says false things.
- Test each possibility and look for a contradiction instead of guessing.
- Start with one-step puzzles and build up to the two doors.
- Act puzzles out, use a simple table, and invent your own.
Read more: Logic grid puzzles for older children: who has which pet?