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
In the sports-day house relay final, Red, Yellow, Blue and Green each field a team, starting in lanes 2, 1, 8 and 4 (Red lane 2, Yellow lane 1, Blue lane 8, Green lane 4).
Before the race, 4 pupils each guess two teams' places.
Kit says, "Green fourth, Red second."
Lok says, "Red fourth, Green first."
Ming says, "Blue fourth, Yellow first."
Fan says, "Green second, Yellow third."
In the end no two teams tie, and each pupil got exactly one of their two guesses right.
Write the lane numbers of the 1st- to 4th-placed teams in order as a four-digit number. What is it?
Show the hints (3)
💡Hint 1: Everyone has one right and one wrong. Assume one of someone's guesses is right and see where it leads.
💡Hint 2: Try assuming Kit's "Green fourth" is right, so "Red second" is wrong. What happens to the others?
💡Hint 3: If someone ends up with both wrong or both right, the assumption fails. In fact Kit's right guess is "Red second".
Worked solution
Have a go first, then read the solution step by step.
1.Case 1: suppose Kit's "Green fourth" is right and "Red second" wrong.
2.Lok's "Red fourth" is wrong (fourth is already Green) and "Green first" is wrong too (Green is already fourth): both wrong, a contradiction.
3.So case 1 is impossible.
4.Case 2: suppose Kit's "Red second" is right and "Green fourth" wrong.
5.Lok's "Red fourth" is wrong (Red is already second), so the other guess, "Green first", is right.
6.Ming's "Yellow first" is wrong (first is already Green), so the other guess, "Blue fourth", is right.
7.Yellow can only be third.
8.Only case 2 works: 1st to 4th are Green (lane 4), Red (lane 2), Yellow (lane 1), Blue (lane 8), and everyone has exactly one right. The number is 4218.
⚠️Common mistake: stopping at the first order that works without ruling out the other case. Both cases must be checked to know the answer is the only one.
Play more like this in Numsprite (unlimited questions, instant marking) →A free maths game: every level free from Easy to Expert (★ to ★★★★), unlimited questions, no download