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
On a school trip, Yan, Sze-ki, Lok and May race up to a hilltop.
Their bibs:
Yan 7, Sze-ki 6, Lok 3 and May 5.
They arrive one after another, no two together.
We know:
Lok finished right after Sze-ki.
May finished ahead of Sze-ki.
Lok was neither first nor last.
Write the bib numbers of the 1st to 4th finishers in order as a four-digit number. What is it?
Show the hints (2)
💡Hint 1: First find someone whose place is already certain, or narrow down which places each person could have.
💡Hint 2: Start from "Lok finished right after Sze-ki". Once someone's place is fixed, nobody else can have it.
Worked solution
Have a go first, then read the solution step by step.
1.Sze-ki: not first (slower than May); not third (Lok is right behind, and Lok isn't fourth); not fourth (Lok is right behind). So Sze-ki came second.
2.Lok: not first or fourth; not second (right behind Sze-ki, and Sze-ki is second). So Lok came third.
3.May: not second, third or fourth (faster than Sze-ki, who is second). So May came first.
4.Yan: not first (May is first); not second (Sze-ki is second); not third (Lok is third). So Yan came fourth.
5.1st to 4th: May (5), Sze-ki (6), Lok (3), Yan (7), so the number is 5637.
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