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Clue riddles

Logic and puzzles · level 1, lesson 6 of 6

A question to start

Here is a riddle.

I am round. I am red. I am a fruit. What am I?

And here are six things it could be.

ball apple banana orange strawberry fire truck

You probably know the answer already. But here is the real question: how do you know? What did each clue do in your head? And would the riddle still work if the clues came in a different order?

The idea

A clue rules things out

A clue is a small piece of true information. In a riddle, one clue is usually not enough to tell you the answer. But each clue does something very useful: it tells you what the answer cannot be.

Watch the six things as the clues come in, one by one. Each time, we cross out everything that does not fit.

Clue 1: I am round. ball apple banana orange strawberry fire truck Clue 2: I am red. ball apple banana orange strawberry fire truck Clue 3: I am a fruit. ball apple banana orange strawberry fire truck
  1. "I am round." The banana is long, not round. Cross it out. The strawberry is pointy at one end, more like a heart. Cross it out. The fire truck is a box shape with wheels. Cross it out. Left: ball, apple, orange.
  2. "I am red." The orange is orange! Cross it out. Left: ball, apple.
  3. "I am a fruit." A ball is a toy, not a fruit. Cross it out. Left: apple.

Only one thing is left. So it must be the answer. That is how riddles work, and that is how detectives work too: rule out everything that cannot be true, and see what is left.

Each clue is a sorting rule

Do you see where you have met this before? Each clue is a sorting rule, like in the first lesson. "I am round" sorts the things into round ones (keep them) and not round ones (cross them out).

A riddle with three clues is like sorting three times in a row. Each time, you keep only the yes group.

The order of the clues does not matter

Let us read the same clues in a different order: "I am a fruit. I am red. I am round."

  1. "I am a fruit." Cross out the ball and the fire truck. Left: apple, banana, orange, strawberry.
  2. "I am red." Cross out the banana (yellow) and the orange. Left: apple, strawberry.
  3. "I am round." Cross out the strawberry. Left: apple.

Same answer! Why? Because the answer has to fit every clue. The apple fits all three, and every other thing breaks at least one. It does not matter in what order you check: something that breaks a clue will be crossed out whenever that clue comes.

But notice: in the second order, more things were left after the first clue. Some clues cross out a lot at once, and some only a little. A clever riddle solver sometimes looks for the clue that crosses out the most first.

Not enough clues

What if the riddle were only: "I am round. I am a fruit."?

  • "I am round": ball, apple, orange are left.
  • "I am a fruit": apple, orange are left.

Two things are left. We cannot tell which one is the answer! The riddle needs one more clue. A good riddle has enough clues to leave exactly one answer.

Too many clues, or wrong ones

What if the riddle were: "I am round. I am red. I am a fruit. I am yellow."?

After the first three clues only the apple is left. Then "I am yellow" crosses out the apple. Nothing is left! That means the clues do not fit together. Something is wrong: maybe someone made a mistake. When nothing is left, do not guess. Say: "these clues cannot all be true."

Number riddles

Riddles work with numbers too. Here is one.

I am a number from 1 to 10. I am more than 5. You cannot share me into pairs. I am not 9. What am I?

Write the numbers 1 to 10 and cross them out, clue by clue.

More than 5 1 2 3 4 5 6 7 8 9 10 Cannot share into pairs 1 2 3 4 5 6 7 8 9 10 Not 9 1 2 3 4 5 6 7 8 9 10
  1. "More than 5": cross out 1, 2, 3, 4, 5. (5 is not more than 5!) Left: 6, 7, 8, 9, 10.
  2. "You cannot share me into pairs": 6 is 3 pairs, 8 is 4 pairs, 10 is 5 pairs. Cross them out. Left: 7, 9.
  3. "I am not 9": cross out 9. Left: 7.

The answer is 7. Check it against every clue: 7 is from 1 to 10 ✓, more than 5 ✓, three pairs and one left over so it cannot be shared into pairs ✓, and it is not 9 ✓.

Checking is part of solving

When you have an answer, go back and check it against every clue. It only takes a moment, and it catches mistakes. If one clue does not fit, the answer is wrong, even if all the others fit.

Worked examples

Example 1. A shape riddle. I have corners. I have 4 sides. My sides are not all the same length. Which shape am I: circle, triangle, square, or rectangle?

  1. "I have corners": cross out the circle. Left: triangle, square, rectangle.
  2. "I have 4 sides": cross out the triangle (3 sides). Left: square, rectangle.
  3. "My sides are not all the same length": a square's 4 sides are all the same length. Cross it out. Left: rectangle.

Check: a rectangle has 4 corners ✓, 4 sides ✓, two long sides and two short sides ✓.

Example 2. A planet riddle. I am a planet. I look red. I have two small moons. What am I?

  1. "I am a planet": Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
  2. "I look red": only one planet looks red in the night sky, and it is called the red planet: Mars.
  3. "I have two small moons": Mars has two small moons, called Phobos and Deimos. ✓

The answer is Mars. The last clue was not needed to find it, but it is a good check.

Example 3. Not enough clues. I am an animal. I have four legs. I live on a farm. What am I?

  1. Animals with four legs that live on a farm: cow, horse, pig, sheep, goat, dog...
  2. Lots are left. We need more clues!

Add a clue: "I say moo." Now only the cow is left. One good clue can finish a riddle.

Example 4. Making your own riddle. Let us make a riddle for the number 4, using the numbers 1 to 10.

  1. Pick a first clue that 4 fits: "I am less than 6." Left: 1, 2, 3, 4, 5.
  2. Another clue that 4 fits: "You can share me into pairs." Left: 2, 4.
  3. One more clue to get rid of 2: "I am more than 3." Left: 4.

Riddle: "I am a number from 1 to 10. I am less than 6. You can share me into pairs. I am more than 3. What am I?" Test it on someone!

Try it

  1. I have four legs. I say "moo". I give milk. What am I?
  2. I am a number from 1 to 10. I am less than 4. I am not 1. I am not 2. What am I?
  3. I am a number from 1 to 10. You can share me into pairs. I am more than 6. I am less than 10. What am I?
  4. I have no corners. I am flat. What shape am I: circle, square, ball, or triangle?
  5. Ella's riddle: "I am a fruit. I am yellow." Is that enough clues? Add one more to make the answer a banana.
  6. Sam's riddle about the numbers 1 to 10: "I am more than 8. I am less than 5." What is wrong?
  7. I am a number from 1 to 20. When you count by tens, you say me. I am not 20. What am I?
  8. Make a riddle with three clues for your favourite animal. Try it on someone.
Answers
  1. A cow. ("Four legs" leaves lots of animals. "Moo" leaves only the cow. "Gives milk" is a check.)
  2. 3. "Less than 4": 1, 2, 3. Cross out 1 and 2. Left: 3.
  3. 8. "Share into pairs": 2, 4, 6, 8, 10. "More than 6": 8, 10. "Less than 10": 8.
  4. A circle. The square and the triangle have corners. A ball has no corners, but it is not flat: it is solid. Left: circle.
  5. Not enough: a lemon is also a yellow fruit. Add: "I am long and curved." Now only the banana is left.
  6. A number more than 8 (9 or 10) is never less than 5. After both clues nothing is left. The clues cannot both be true, so there is no answer. Sam made a mistake.
  7. 10. Counting by tens: 10, 20. Not 20. Left: 10.
  8. For example, for a giraffe: "I have four legs. I am very, very tall. I have a long neck." Check that only one animal fits all the clues.

Common mistake

Stopping too soon. After "I am round. I am red." some people shout "apple!" But the ball is still left! Do not stop until every clue is used and only one thing is left. Then check your answer against every clue.

Guessing when nothing fits. If every thing has been crossed out, the answer is not "the closest one". The answer is "these clues do not fit together".

Where it leads