题面摘自 Henry E. Dudeney 公版文本;英文为古腾堡原文整理,中文为本站自译,提示、解答骨架和闲谈保留本站原创结构。
Young Mrs. Perkins, of Putney, writes to me as follows: "I should be very glad if you could give me the answer to a little sum that has been worrying me a good deal lately. Here it is: We have only been married a short time, and now, at the end of two years from the time when we set up housekeeping, my husband tells me that he finds we have spent a third of his yearly income in rent, rates, and taxes, one-half in domestic expenses, and one-ninth in other ways. He has a balance of £190 remaining in the bank. I know this last, because he accidentally left out his pass-book the other day, and I peeped into it. Don't you think that a husband ought to give his wife his entire confidence in his money matters? Well, I do; and—will you believe it?—he has never told me what his income really is, and I want, very naturally, to find out. Can you tell me what it is from the figures I have given you?" Yes; the answer can certainly be given from the figures contained in Mrs. Perkins's letter. And my readers, if not warned, will be practically unanimous in declaring the income to be—something absurdly in excess of the correct answer!
帕特尼的年轻帕金斯夫人给我写了这样的信:“如果你能告诉我最近一直让我担心的一小笔钱的答案,我会非常高兴。事情是这样的:我们结婚不久,现在,从我们建立家政服务开始两年后,我丈夫告诉我,他发现我们把他年收入的三分之一花在了房租、差饷和税收上,二分之一花在了家庭开支上,九分之一花在了家庭开支上。”我知道他在银行里还有 190 英镑的余额,因为有一天他不小心遗漏了他的存折,你不认为丈夫应该对他的钱完全信任吗?而且——你相信吗?——他从来没有告诉过我他的实际收入,我很自然地想从我给你的数字中找出答案。”是的;帕金斯夫人信中的数字当然可以给出答案。而我的读者,如果没有得到警告,几乎会一致宣布收入是——超出正确答案的荒谬的东西!
提示 1
先说出现象:哪些量会变,哪些约束不会变。
提示 2
找守恒量、相似关系、平衡条件或不变量,不急着代公式。
提示 3
把物理图景或谜题结构翻成一个最小方程组,再处理边界情况。
完整解答
解题主线是先把 Dudeney 谜题 1 的条件整理成一个稳定模型,再选择最少的变量。第一步确认约束,第二步写出关键关系,第三步检查特殊情形。这里给的是原创解法骨架;若要核对原始题面,请回到公版来源。
这类题最怕一上来套公式。先把图景或语言条件说清楚,答案通常会少绕很多路。