Olympiad topic · P2–P6
Logic puzzles
The Hua Xia Cup's P4 qualifying round and finals have true-or-false statements and match-scoring questions. A favourite thinking workout, too.
Try one
★★ MediumThe vase on the classroom windowsill has been broken.
The teacher asks the 4 pupils who were in the room; one of them broke it.
Their class numbers:
Ka-yan 24, Ching 14, Ho-yin 22 and Kit 2.
Here is what they say.
Ka-yan:
"It was Ching."
Ching:
"It was Ho-yin or Ka-yan."
Ho-yin:
"It wasn't Ching."
Kit:
"It was Ka-yan or Ching."
Exactly one of the four is lying.
What is the class number of the pupil who broke the vase?
- Hint 1: Among the four, are there two statements where, if one is true, the other must be false?
- Hint 2: Ka-yan and Ho-yin can't both be right or both be wrong, so the liar is one of them. What does that say about the other two?
- 1.Ka-yan says "It was Ching" and Ho-yin says "It wasn't Ching". These can't both be true or both be false, so the liar is Ka-yan or Ho-yin.
- 2.Only one person lies, so Ching and Kit are both telling the truth.
- 3.Ching says "It was Ho-yin or Ka-yan" and Kit says "It was Ka-yan or Ching". With both true, it can only be Ka-yan.
- 4.Check: if it was Ka-yan, only Ka-yan said something false and the other three told the truth, as required. Ka-yan's class number is 24.
- ⚠️Common mistake: believing whoever says "it wasn't me" from the start. Anyone might be lying; it has to follow from "exactly one is lying".
Answer: 24
Four levels, step by step
- ★EasyFree2 question types · unlimited questionsOrdering, places.
- ★★MediumFree3 question types · unlimited questionsExactly one liar, match points.
- ★★★HardFree4 question types · unlimited questionsExactly one truth-teller, each half right.
- ★★★★Expert (competition level)VIP2 question types · unlimited questionsNumber clues with one wrong, three kinds of speaker.
Logic puzzles: what it is and how to solve it
From a few statements or conditions, work out who is who, who's telling the truth, or the order of finishing.
For example: A race of three: Lok is slower than Mei, Kit faster than Mei. Who's third? Fastest to slowest: Kit, Mei, Lok — so Lok.
The key idea: Keep a table of yes and no; with truth and lies, suppose one statement is true and see whether it leads to a contradiction. Every step needs a reason — no guessing.
Practise this topic free →Easy to Hard (★ to ★★★) all free, unlimited questions, no download