Problem 11 · 2020 Math Kangaroo
Stretch
Logic & Word Problems
caseworkwork-backward
Adam, Breno and Carlos live in the same apartment and bought a treadmill for exercise. Nobody uses the treadmill on Wednesdays and Sundays, and there is no day on which all three of them use the treadmill. Adam uses the treadmill 4 times a week and Breno 5 times a week. There are 4 consecutive days when Adam uses the treadmill on the first day, he does not use it on the second day, and Breno does not use it on the fourth day. Carlos uses the treadmill on one day of the week. Which day?
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Answer: A — Friday
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Hint 1 of 2
Only Mon, Tue, Thu, Fri, Sat are usable; Breno’s 5 sessions fill them all.
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Hint 2 of 2
Carlos’s day can’t be one where all three use it, so it’s Adam’s single off-day — find it from the four-day clue.
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Approach: pin down Adam's missing day using the consecutive-day clue
- Breno uses all five active days, so Adam’s skipped day is Carlos’s day (no day has all three).
- The four consecutive days with 'Breno off on day 4' must be Thu, Fri, Sat, Sun.
- Then Adam uses Thu (day 1) but not Fri (day 2), so Adam’s off-day is Friday.
- Hence Carlos uses the treadmill on Friday.
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