Problem 20 · 2012 Math Kangaroo
Stretch
Logic & Word Problems
casework
The runners Kann, Gu and Ru are favourites to win the marathon. Before the race three experts gave their predictions for the outcome of the race.
Expert 1: “Either Kann or Gu will win.”
Expert 2: “If Gu is second Ru will win.”
Expert 3: “If Gu is third Kan will not win.”
Expert 4: “Either Gu or Ru will come second.”
After the race all four predictions were proven correct. In which order, did the three runners finish the race?
Show answer
Answer: D — Gu, Ru, Kan
Show hints
Hint 1 of 2
List the possible finishing orders and test each against all four statements.
Still stuck? Show hint 2 →
Hint 2 of 2
All four predictions are true at once, so eliminate any order that breaks even one.
Show solution
Approach: test each finishing order against all four statements
- Try the finishing orders of the three runners; require all four experts correct at once.
- The order Gu first, Ru second, Kan third works: Expert 1 (Kann or Gu wins) holds since Gu wins; Expert 4 (Gu or Ru second) holds since Ru is second; Experts 2 and 3 are 'if Gu is 2nd/3rd...' which never happen, so they hold automatically.
- The finishing order is Gu, Ru, Kan (D).
Mark:
· log in to save