Problem 21 · 2025 Math Kangaroo
Stretch
Logic & Word Problems
casework
Fabio never tells the truth on Tuesdays, Thursdays and Saturdays, while he always tells the truth on the other days of the week. One day Mateo had the following conversation with Fabio:
Mateo: “What day is today?”
Fabio: “Saturday”
Mateo: “What day will tomorrow be?”
Fabio: “Wednesday”
On which day of the week did the conversation take place?
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Answer: D — Thursday
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Hint 1 of 2
On a truth day both of Fabio’s answers are true; on a lying day both are false.
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Hint 2 of 2
Test each weekday against his two statements until one fits.
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Approach: check each day for consistency
- Fabio lies on Tue/Thu/Sat and tells the truth otherwise; both his answers share that day’s truth status.
- He says ‘today is Saturday’ and ‘tomorrow is Wednesday’.
- Only Thursday works: it is a lying day, and both statements are indeed false (it isn’t Saturday, and tomorrow is Friday not Wednesday).
- So the conversation happened on Thursday.
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