Problem 13 · 2023 Math Kangaroo
Medium
Logic & Word Problems
casework
Maria, Peter, Richard and Tina were playing football in the classroom when a window pane broke. The head teacher asked who did it and got these answers. Maria: “It was Peter.” Peter: “It was Richard.” Richard: “It wasn’t me.” Tina: “It wasn’t me.” It later turned out that only one child told the truth. Who broke the window pane?
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Answer: B — Tina
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Hint 1 of 2
Try assuming each child is the culprit in turn and see how many of the four statements come out true.
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Hint 2 of 2
Only the case with exactly one true statement can be correct.
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Approach: test each suspect and count how many statements are true
- Suppose Tina broke it. Then Maria's “it was Peter” is false, Peter's “it was Richard” is false, Richard's “it wasn't me” is true, and Tina's “it wasn't me” is false.
- That gives exactly one true statement, matching the rule that only one child told the truth.
- Testing the other suspects gives either zero or more than one true statement, so they fail.
- Therefore Tina broke the window, answer B.
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