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番外 · 题谱 · 1907 · P6

Dudeney 谜题 42

组合 / 文字游戏 · P3/P6 · 压轴题

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。

组合与机巧 1907 P6 combinatoricswordplay

The inhabitants of Slocomb-on-Sea were greatly excited over the visit of a certain flying man. All the town turned out to see the flight of the wonderful hydroplane, and, of course, Dobson and his family were there. Master Tommy was in good form, and informed his father that Englishmen made better airmen than Scotsmen and Irishmen because they are not so heavy. "How do you make that out?" asked Mr. Dobson. "Well, you see," Tommy replied, "it is true that in Ireland there are men of Cork and in Scotland men of Ayr, which is better still, but in England there are lightermen." Unfortunately it had to be explained to Mrs. Dobson, and this took the edge off the thing. The hydroplane flight was from Slocomb to the neighbouring watering-place Poodleville—five miles distant. But there was a strong wind, which so helped the airman that he made the outward journey in the short time of ten minutes, though it took him an hour to get back to the starting point at Slocomb, with the wind dead against him. Now, how long would the ten miles have taken him if there had been a perfect calm? Of course, the hydroplane's engine worked uniformly throughout.

海上斯洛科姆的居民对某个飞人的到来感到非常兴奋。全镇的人都来观看这架美妙的水上飞机的飞行,当然,多布森和他的家人也在场。汤米大师状态良好,并告诉他的父亲,英国人比苏格兰人和爱尔兰人更适合成为飞行员,因为他们没有那么重。 “你怎么看出来的?”多布森先生问道。 “嗯,你看,”汤米回答道,“确实,在爱尔兰有科克人,在苏格兰有艾尔人,后者更好,但在英格兰有驳船人。”不幸的是,这件事必须向多布森夫人解释,这让事情变得更加紧张。水上飞机从斯洛科姆飞往邻近的 Poodleville 饮水场——相距五英里。但有一阵强风,这对飞行员很有帮助,他在短短十分钟内就完成了向外的旅程,尽管他花了一个小时才回到斯洛科姆的出发点,而且风势对他来说很不利。现在,如果完全平静的话,这十英里需要多长时间?当然,水上飞机的发动机自始至终都是一致工作的。

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 42 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。