Problem 24 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
casework
Carlos always tells the truth on alternate days. On the other days, he tells only lies. Today he made exactly four of the five statements that follow. Which one was not made today by him?
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Answer: C — My name is Carlos.
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Hint 1 of 2
On a truth day every statement he makes is true; on a lie day every one is false.
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Hint 2 of 2
Check whether all of A, B and D could be true together — if not, today must be a lie day.
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Approach: rule out a truth day, forcing a lie day
- If today were a truth day, A (prime total) and B (equal counts) force exactly 1 male and 1 female friend, contradicting D (three older male friends).
- So today is a lie day: every statement he makes is false.
- 'My name is Carlos' is true, so on a lie day he cannot make it.
- The statement not made today is C.
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