Problem 18 · 2021 Math Kangaroo
Medium
Logic & Word Problems
casework
Three pirates were asked how many coins and how many diamonds their friend Graybeard had. Each of the three told the truth to one question but told a lie to the other. Their answers were: (1) He has 8 coins and 6 diamonds. (2) He has 7 coins and 4 diamonds. (3) He has 7 coins and 7 diamonds. What is the total number of coins and diamonds that Graybeard has?
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Answer: C — 13
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Hint 1 of 2
Each pirate is right about exactly one of the two counts (coins or diamonds).
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Hint 2 of 2
Two pirates name the same coin count, 7; that is a good place to test the truth.
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Approach: make each statement half-true
- Two pirates say 7 coins, so try coins = 7: then pirates 2 and 3 are truthful about coins and must be lying about diamonds (4 and 7 are both wrong), while pirate 1's coin count 8 is the lie.
- Pirate 1 must then be truthful about diamonds, giving 6 diamonds — and 6 is not 4 or 7, so pirates 2 and 3 are indeed lying there. Everything fits.
- Total = 7 coins + 6 diamonds = 13.
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