A census-taker calls at a house. He asks the woman living there the ages of her

游客2023-10-17  18

问题 A census-taker calls at a house. He asks the woman living there the ages of her three daughters. The woman says, "If you multiply their ages the total is 72; if you add their ages the total is the same as the number on my front door, which you can see. "
The census-taker says, "That is not enough information for me to calculate their ages. “The woman says, "Well, my eldest daughter has a cat with a wooden leg. “The census-taker replies, "Ah! Now I can calculate their ages. “What are the ages of the three girls?

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答案 8,3,3

解析 (由于三个孩子年龄相乘得72,可以得出的组合有:72×1×1,36×2×1,18×4×1。9×4×2,9×8×1,6 x 6×2,8×3×3, 12×6×1, 12×3×2, 18×2×2,6×4 x 3.24×3×1。各组合相加之后得到:74,39,23,15,18,14,14,19,17,22,13,28。人口普查员一定知道门牌号码,可是仍然无法确定是哪个组合,说明门牌号码是14,可知是6×6×2,8×3×3这两种情况中的一种,房主人又提到eldest daughter,说明,较大的两个孩子不可能同岁,故可以确定三个孩子的年龄分别是8岁,3岁,3岁。)
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