An expert question on logic puzzles for P5–P6, 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
A logic game: three pupils each draw a role card — Honest, Liar or Fox, one each.
Whoever has Honest says only true things; whoever has Liar says only false things; whoever has Fox, saying two things, always says one true and one false (in either order).
Their class numbers:
Yan 7, Sze-ki 6 and Lok 3.
Each says two things.
Yan:
"Lok has the Liar card;
I don't have the Fox card."
Sze-ki:
"I don't have the Fox card;
Yan doesn't have the Honest card."
Lok:
"Sze-ki has the Fox card;
Yan doesn't have the Fox card."
Write the class numbers of the Honest, Liar and Fox card holders, in that order, as a three-digit number. What is it?
Show the hints (3)
💡Hint 1: There are only 6 ways to share the cards. You can try them one by one, but each time check both statements of all three.
💡Hint 2: Start by supposing Yan has Honest: both of Yan's statements must be true. Who is the Liar and who the Fox? Try both ways.
💡Hint 3: Sze-ki has the Honest card. Now tell the other two apart.
Worked solution
Have a go first, then read the solution step by step.
1.There are 6 ways to share the cards; check each:
2.If Yan is Honest, Sze-ki the Liar and Lok the Fox: Yan's "Lok has the Liar card" is false, yet Yan only tells the truth — no.
3.If Yan is Honest, Lok the Liar and Sze-ki the Fox: Lok's "Sze-ki has the Fox card" is true, yet Lok only lies — no.
4.If Sze-ki is Honest, Yan the Liar and Lok the Fox: Yan's "I don't have the Fox card" is true, yet Yan only lies — no.
5.If Sze-ki is Honest, Lok the Liar and Yan the Fox: Sze-ki has two truths, Lok two lies, Yan one of each — everything fits.
6.If Lok is Honest, Yan the Liar and Sze-ki the Fox: Yan's "I don't have the Fox card" is true, yet Yan only lies — no.
7.If Lok is Honest, Sze-ki the Liar and Yan the Fox: Lok's "Sze-ki has the Fox card" is false, yet Lok only tells the truth — no.
8.Only one way works: Honest Sze-ki (6), Liar Lok (3), Fox Yan (7). The number is 637.
⚠️Common mistake: checking only the Honest card holder. The Fox must have exactly one true statement, and both of the Liar's must be false.
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