Problem 28 · 2024 Math Kangaroo
Stretch
Logic & Word Problems
casework
Captain Flint asks four of his pirates to note down how many gold, silver and bronze coins there were in the treasure chest. Their answers are shown in the diagram. Unfortunately, part of the paper was damaged. Only one of the four pirates told the truth; the other three lied on every single one of their answers. The total number of coins was 30. Who told the truth?
Show answer
Answer: B — Al
Show hints
Hint 1 of 3
The visible numbers are: Tom 9 silver and 11 bronze; Al 7 gold and 12 bronze; Pit 10 gold and 10 bronze; Jim 9 gold and 10 silver.
Still stuck? Show hint 2 →
Hint 2 of 3
Whoever is honest gives the real counts, so every other pirate's visible numbers must each be wrong, and the real gold, silver and bronze add to 30.
Still stuck? Show hint 3 →
Hint 3 of 3
Try each pirate as the honest one and check that the three real counts (totalling 30) make every other pirate wrong on each entry.
Show solution
Approach: assume each pirate honest in turn and force the real counts to total 30
- Suppose Al is honest: then gold = 7 and bronze = 12, so silver = 30 − 7 − 12 = 11.
- Check the liars against (gold, silver, bronze) = (7, 11, 12): Tom's 9 silver and 11 bronze are both wrong, Pit's 10 gold and 10 bronze are both wrong, and Jim's 9 gold and 10 silver are both wrong.
- So every other pirate lied on every answer, exactly as required, and trying any other pirate as honest forces a clash, so this is the only possibility.
- The truthful pirate is Al.
Mark:
· log in to save