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番外 · 题谱 · 1907 · P2

Dudeney 谜题 26

几何趣题 / 谜题 · P2/P5 · 中段题

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。

几何与棋盘 1907 P2 geometricpuzzle

"Speaking of perplexities——" said Mr. Wilson, throwing down a magazine on the table in the commercial room of the Railway Hotel. "Who was speaking of perplexities?" inquired Mr. Stubbs. "Well, then, reading about them, if you want to be exact—it just occurred to me that perhaps you three men may be interested in a little matter connected with myself." It was Christmas Eve, and the four commercial travellers were spending the holiday at Grassminster. Probably each suspected that the others had no homes, and perhaps each was conscious of the fact that he was in that predicament himself. In any case they seemed to be perfectly comfortable, and as they drew round the cheerful fire the conversation became general. "What is the difficulty?" asked Mr. Packhurst. "There's no difficulty in the matter, when you rightly understand it. It is like this. A man named Parker had a flying-machine that would carry two. He was a venturesome sort of chap—reckless, I should call him—and he had some bother in finding a man willing to risk his life in making an ascent with him. However, an uncle of mine thought he would chance it, and one fine morning he took his seat in the machine and she started off well. When they were up about a thousand feet, my nephew suddenly——" "Here, stop, Wilson! What was your nephew doing there? You said your uncle," interrupted Mr. Stubbs. "Did I? Well, it does not matter. My nephew suddenly turned to Parker and said that the engine wasn't running well, so Parker called out to my uncle——" "Look here," broke in Mr. Waterson, "we are getting mixed. Was it your uncle or your nephew? Let's have it one way or the other." "What I said is quite right. Parker called out to my uncle to do something or other, when my nephew——" "There you are again, Wilson," cried Mr. Stubbs; "once for all, are we to understand that both your uncle and your nephew were on the machine?" "Certainly. I thought I made that clear. Where was I? Well, my nephew shouted back to Parker——" "Phew! I'm sorry to interrupt you again, Wilson, but we can't get on like this. Is it true that the machine would only carry two?" "Of course. I said at the start that it only carried two." "Then what in the name of aerostation do you mean by saying that there were three persons on board?" shouted Mr. Stubbs. "Who said there were three?" "You have told us that Parker, your uncle, and your nephew went up on this blessed flying-machine." "That's right." "And the thing would only carry two!" "Right again." "Wilson, I have known you for some time as a truthful man and a temperate man," said Mr. Stubbs, solemnly. "But I am afraid since you took up that new line of goods you have overworked yourself." "Half a minute, Stubbs," interposed Mr. Waterson. "I see clearly where we all slipped a cog. Of course, Wilson, you meant us to understand that Parker is either your uncle or your nephew. Now we shall be all right if you will just tell us whether Parker is your uncle or nephew." "He is no relation to me whatever." The three men sighed and looked anxiously at one another. Mr. Stubbs got up from his chair to reach the matches, Mr. Packhurst proceeded to wind up his watch, and Mr. Waterson took up the poker to attend to the fire. It was an awkward moment, for at the season of goodwill nobody wished to tell Mr. Wilson exactly what was in his mind. "It's curious," said Mr. Wilson, very deliberately, "and it's rather sad, how thick-headed some people are. You don't seem to grip the facts. It never seems to have occurred to either of you that my uncle and my nephew are one and the same man." "What!" exclaimed all three together. "Yes; David George Linklater is my uncle, and he is also my nephew. Consequently, I am both his uncle and nephew. Queer, isn't it? I'll explain how it comes about." Mr. Wilson put the case so very simply that the three men saw how it might happen without any marriage within the prohibited degrees. Perhaps the reader can work it out for himself.

“说到困惑——”威尔逊先生说着,把一本杂志扔到了铁路宾馆商务间的桌子上。 “谁在谈论困惑?”斯塔布斯先生问道。 “好吧,那么,如果你想准确地说,读到关于他们的文章——我突然想到,也许你们三个人可能对与我有关的一件小事感兴趣。”那是平安夜,四位商务旅客正在格拉斯敏斯特度假。也许每个人都怀疑其他人没有家,也许每个人都意识到自己正处于这种困境之中。无论如何,他们看起来都很舒服,当他们围着欢快的火堆时,谈话变得很普遍。 “有什么困难吗?”帕克赫斯特先生问道。 “如果你正确理解的话,这件事并不困难。事情是这样的。一个名叫帕克的人有一架可以搭载两个人的飞行器。他是一个喜欢冒险的小伙子——我应该称他为鲁莽——他费了很大力气才找到一个愿意冒着生命危险和他一起上升的人。然而,我的一个叔叔认为他会碰碰运气,一个晴朗的早晨,他坐在飞行器里,她出发得很好。当他们上升到大约一千英尺时,我的侄子突然——” “喂,停下来,威尔逊!你说你的侄子在那里做什么?”斯塔布斯先生打断道。 “是吗?好吧,没关系。我的侄子突然转向帕克,说发动机运转不正常,所以帕克对我的叔叔喊道——”“听着,”沃特森先生插话道,“我们搞混了。是你叔叔还是你侄子?我们就这样吧。” “我说的很对。帕克喊我叔叔做点什么,这时我的侄子——” “你又来了,威尔逊,”斯塔布斯先生喊道。 “总而言之,我们是否可以理解,你的叔叔和侄子都在机器上?” “当然。我想我已经说得很清楚了。我在哪里?好吧,我的侄子对帕克喊道——” “唷!我很抱歉再次打断你,威尔逊,但我们不能这样相处。这台机器真的只能运载两个吗?” “当然,我一开始就说了,只能带两个。” “那么,以航空站的名义,你所说的机上共有三人是什么意思?”斯塔布斯先生喊道。 “谁说是三个?” “你告诉我们帕克、你的叔叔和你的侄子乘坐这架神圣的飞行器升空了。” “这是正确的。” “而且那东西只能承载两个!” “又对了。” “威尔逊,我认识你已有一段时间了,你是一个诚实、温和的人,”斯塔布斯先生严肃地说。 “但我担心自从你开始从事新产品线以来,你就已经过度劳累了。” “半分钟,斯塔布斯,”沃特森先生插话道。 “我清楚地看到我们都在哪里出了问题。当然,威尔逊,你想让我们明白帕克要么是你的叔叔,要么是你的侄子。现在,如果你能告诉我们帕克是你的叔叔还是侄子,我们就没事了。” “他和我没有任何关系。”三人叹了口气,面面相觑。斯塔布斯先生从椅子上站起来去拿火柴,帕克赫斯特先生开始给手表上发条,沃特森先生拿起拨火棍去救火。这是一个尴尬的时刻,因为在这个善意的季节,没有人愿意准确地告诉威尔逊先生他的想法。 “这很奇怪,”威尔逊先生非常刻意地说,“有些人的头脑是多么厚颜无耻,这很可悲。你们似乎没有掌握事实。你们似乎从来没有想到过,我的叔叔和我的侄子是同一个人。” “什么!”三人齐声惊呼。 “是的;大卫·乔治·林克莱特是我的叔叔,他也是我的侄子。因此,我既是他的叔叔,又是他的侄子。很奇怪,不是吗?我会解释一下这是怎么回事。”威尔逊先生把这个案子说得非常简单,以至于这三个人看到了在禁止范围内不结婚的情况下会发生什么。或许读者可以自己思考一下。

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 26 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。