Problem 13 · 2011 Math Kangaroo
Medium
Logic & Word Problems
substitutioncasework
Anna, Bob, Cleo, Dido, Eva, and Ferdl each roll a die. Each person rolls a different number. Anna’s number is twice as big as Bob’s. Anna’s number is three times as big as Cleo’s. Dido’s number is four times as big as Eva’s. Which number did Ferdl roll?
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Answer: D — 5
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Hint 1 of 2
Anna's number is both double and triple of someone's — what must it be?
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Hint 2 of 2
Once Anna is fixed, the other multiples force every name, leaving Ferdl's.
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Approach: pin down Anna first
- Anna is 2×Bob and 3×Cleo, so Anna is divisible by 2 and 3 — on a die that means Anna = 6, Bob = 3, Cleo = 2.
- Dido = 4×Eva forces Eva = 1, Dido = 4. The five used numbers are 6, 3, 2, 1, 4, so Ferdl rolled 5, answer D.
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