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番外 · 题谱 · 1907 · P5

Canterbury Puzzle 5 · Lantern Field 5

几何趣题 · 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。

The Canterbury Puzzles 1907 5 geometric

The frolicsome Wife of Bath, when called upon to favour the company, protested that she had no aptitude for such things, but that her fourth husband had had a liking for them, and she remembered one of his riddles that might be new to her fellow pilgrims: "Why is a bung that hath been made fast in a barrel like unto another bung that is just falling out of a barrel?" As the company promptly answered this easy conundrum, the lady went on to say that when she was one day seated sewing in her private chamber her son entered. "Upon receiving," saith she, "the parental command, 'Depart, my son, and do not disturb me!' he did reply, 'I am, of a truth, thy son; but thou art not my mother, and until thou hast shown me how this may be I shall not go forth.'" This perplexed the company a good deal, but it is not likely to give the reader much difficulty.

当巴斯的嬉闹的妻子被要求支持这群人时,她抗议说她没有这种能力,但她的第四任丈夫却喜欢它们,她记得他的一个谜语对她的朝圣者伙伴来说可能是新的:“为什么一个牢牢地装在桶里的塞子和另一个刚刚从桶里掉下来的塞子一样?”当公司迅速回答这个简单的难题时,这位女士接着说,有一天她坐在自己的私人房间里缝纫时,她的儿子进来了。 “收到父母的命令后,”她说,“‘走吧,我的儿子,不要打扰我!’”他确实回答说:“我确实是你的儿子;”但你不是我的母亲,除非你向我展示这可能是怎么回事,否则我不会出去。”这让大家很困惑,但不太可能给读者带来太大困难。

提示 1

先把图画成可量的对象,标出边、格点或切割线。

提示 2

找面积、长度、对称轴或不变量,不急着剪。

提示 3

若是重排题,检查每一块在移动前后是否保持形状和面积。

完整解答

把题目先放到方格纸上。若四块面积相等,每块面积是总面积的四分之一;“轮廓相同”要求两道切割线在旋转或翻折后能互相对应。解题主线是先画出中心对称或四分旋转的候选,再用方格计数核对每块面积。

Dudeney 的趣题常把难点藏在“看起来可以试”的地方。别急着猜答案;先把图、表或状态画出来,再问哪些限制一直没有变。这也是它和 Carroll 逻辑题互补的地方:一个拆句子,一个拆结构。