Problem 8 · 2024 Math Kangaroo
Medium
Logic & Word Problems
work-backward
There are five different kinds of fruit in a bowl: apples, grapes, cherries, strawberries and bananas. Anna likes apples, cherries, strawberries and bananas. Berta likes apples. Conny likes grapes, cherries, strawberries and bananas. Doris likes apples, grapes and cherries. Eva likes apples and cherries. The fruits are shared out so that each person gets a different kind of fruit, but everybody gets a kind of fruit that they like. Who gets the cherries?
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Answer: E — Eva
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Hint 1 of 2
Find the person with the fewest choices first; they are forced.
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Hint 2 of 2
Once a forced person takes their only option, that fruit is gone, which may force the next person.
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Approach: assign the forced choices in order
- Berta likes only apples, so Berta must get the apples.
- Eva likes only apples and cherries; with apples taken, Eva must get the cherries.
- So the cherries go to Eva.
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