A hard question on logic puzzles for P4–P5, 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 5 pupils who were in the room; one of them broke it.
Their numbers:
Ka-yan 1, Ching 2, Ho-yin 3, Kit 4 and May 5.
Here is what they say.
Ka-yan:
"It wasn't Ho-yin."
Ching:
"It was May or Ka-yan."
Ho-yin:
"It was Ka-yan or Ching."
Kit:
"It wasn't Ching."
May:
"It was Ching."
Exactly one of the five is telling the truth; the other four are lying.
Put the number of the pupil telling the truth in the tens place and the number of the pupil who broke the vase in the units place. What two-digit number do you get?
Show the hints (3)
💡Hint 1: Among the five, are there two statements that must be one true and one false?
💡Hint 2: Look at May and Kit: one is true and one false. With only one truth-teller, what about the other three?
💡Hint 3: The other three are all lying. Turn each of their statements round to find out who did it; then see which of May and Kit told the truth.
Worked solution
Have a go first, then read the solution step by step.
1.May says "It was Ching" and Kit says "It wasn't Ching": exactly one of these is true.
2.The one truth-teller is May or Kit, so Ka-yan, Ching and Ho-yin are all lying.
3.Turn their words round: Ka-yan's "It wasn't Ho-yin" is false, so it was Ho-yin; Ching's "It was May or Ka-yan" is false, so neither May nor Ka-yan; Ho-yin's "It was Ka-yan or Ching" is false, so neither Ka-yan nor Ching.
4.All three must hold, so it can only be Ho-yin (number 3).
5.If it was Ho-yin, then of May and Kit, the one telling the truth is Kit (number 4).
6.Tens 4, units 3: the answer is 43.
⚠️Common mistake: turning a lie round wrongly. If "it was A or B" is false, then it was neither A nor B — not just "one of them didn't".
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