HMMT 二月 2000 · 代数 · 第 8 题
HMMT February 2000 — Algebra — Problem 8
题目详情
英文原题
- A man has three daugh ters. The pro du t of their ages is 168, and he remem b ers that the sum of their ages is the number of trees in his y ard. He oun ts the trees but annotdetermine an y of their ages. What are all p ossible ages of his oldest daugh ter?
p pa b 3
2 2 2 2
解析
英文解析
- 168 = 2 3 7. There are only 2 om binations of these whose sums allo w indistinguishabilit y of the ages. If there are 27 trees, 2, 4, 21 and 1, 12, 14 y ears are p ossible. Ifthere are 21 trees, 2, 7, 12 and 3, 4, 14 are p ossible. So, the p ossible ages of the oldestdaugh ter are 12, 14, 21 .