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

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

游客2023-10-17  30
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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