Problem 19 · 2013 Math Kangaroo
Stretch
Logic & Word Problems
caseworkwork-backward
Andi, Betti, Clara and Dani were born in the same year. Their birthdays are on 20 February, 12 April, 12 May and 25 May, but not necessarily in that order. Betti and Andi were born in the same month. Andi and Clara were born on the same day, in different months. Who is the oldest?
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Answer: D — Dani
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Hint 1 of 2
'Same month' must be the month that has two of the dates.
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Hint 2 of 2
'Same day, different months' must use the day number that appears twice.
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Approach: match the pairs of dates by the clues
- Betti and Andi share a month, and only May has two dates (12 May, 25 May).
- Andi and Clara share a day in different months, and only the 12th repeats (12 April, 12 May), so Andi = 12 May, Clara = 12 April; then Betti = 25 May.
- Dani gets the leftover 20 February, the earliest date, so Dani is the oldest.
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