A medium question on logic puzzles for P3–P4, with a step-by-step solution, diagrams and the answer. The Hua Xia Cup's P4 qualifying round and finals have true-or-false statements and match-scoring questions. A favourite thinking workout, too.
The question
The 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?
Show the hints (2)
💡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?
Worked solution
Have a go first, then read the solution step by step.
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".
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