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Dudeney 谜题 36

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 P6 geometricpuzzle

A facetious individual who was taking a long walk in the country came upon a yokel sitting on a stile. As the gentleman was not quite sure of his road, he thought he would make inquiries of the local inhabitant; but at the first glance he jumped too hastily to the conclusion that he had dropped on the village idiot. He therefore decided to test the fellow's intelligence by first putting to him the simplest question he could think of, which was, "What day of the week is this, my good man?" The following is the smart answer that he received:— "When the day after to-morrow is yesterday, to-day will be as far from Sunday as to-day was from Sunday when the day before yesterday was to-morrow." Can the reader say what day of the week it was? It is pretty evident that the countryman was not such a fool as he looked. The gentleman went on his road a puzzled but a wiser man.

一个爱开玩笑的人在乡间散步时,遇到一个坐在栅栏上的乡巴佬。由于这位先生不太清楚他的路,他想向当地居民打听;但乍一看,他太仓促地得出了自己爱上了村里白痴的结论。因此,他决定测试一下这个家伙的智力,首先向他提出他能想到的最简单的问题,那就是:“我的好朋友,今天是星期几?”以下是他收到的聪明答案:“当后天是昨天时,今天与星期日的距离就如同前天是明天时今天与星期日的距离一样远。”读者能说出今天是星期几吗?很明显,这个乡下人并不像他看上去那么傻。这位绅士继续他的道路,虽然感到困惑,但也是一个明智的人。

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 36 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。