Problem 11 · 2014 Math Kangaroo
Medium
Number Theory
caseworksum-constraint
A grandmother, her daughter and her granddaughter each have their birthday in February. Together they are 100 years old, and each person’s age is a power of 2. In which year was the granddaughter born?
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Answer: C — 2010
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Hint 1 of 2
Three ages, each a power of 2, add to 100.
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Hint 2 of 2
Try the largest powers of 2 first and see what is left.
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Approach: find three powers of 2 summing to 100
- Powers of 2 available: 1, 2, 4, 8, 16, 32, 64.
- 64 + 32 + 4 = 100, so the ages are 64, 32 and 4 (grandmother, mother, granddaughter).
- The granddaughter is 4, born 2014 − 4 = 2010.
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