Problem 23 · 2019 Math Kangaroo
Stretch
Logic & Word Problems
casework
One of the 5 children Alex, Bartek, Cora, Dani and Emil has eaten a cake. Alex says: “I did not eat a cake.” Bartek says: “I ate a cake.” Cora says: “Emil has not eaten a cake.” Dani says: “I did not eat a cake.” Emil says: “Alex has eaten a cake.” One of the children lies. Which child has eaten a cake?
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Answer: B — Bartek
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Hint 1 of 2
Exactly one statement is false; test who the eater could be and count the lies.
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Hint 2 of 2
Suppose Bartek is the eater and check whether only one child ends up lying.
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Approach: test the eater so that exactly one lies
- Assume Bartek ate the cake.
- Then Alex, Cora and Dani all speak truthfully, and Bartek's 'I ate' is true.
- Only Emil's 'Alex ate' is false — exactly one liar, as required.
- So the child who ate the cake is Bartek (B).
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