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Canterbury Puzzle 1 · Tiled Yard 1

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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 1 geometric

The Reve was a wily man and something of a scholar. As Chaucer tells us, "There was no auditor could of him win," and "there could no man bring him in arrear." The poet also noticed that "ever he rode the hindermost of the route." This he did that he might the better, without interruption, work out the fanciful problems and ideas that passed through his active brain. When the pilgrims were stopping at a wayside tavern, a number of cheeses of varying sizes caught his alert eye; and calling for four stools, he told the company that he would show them a puzzle of his own that would keep them amused during their rest. He then placed eight cheeses of graduating sizes on one of the end stools, the smallest cheese being at the top, as clearly shown in the illustration. "This is a riddle," quoth he, "that I did once set before my fellow townsmen at Baldeswell, that is in Norfolk, and, by Saint Joce, there was no man among them that could rede it aright. And yet it is withal full easy, for all that I do desire is that, by the moving of one cheese at a time from one stool unto another, ye shall remove all the cheeses to the stool at the other end without ever putting any cheese on one that is smaller than itself. To him that will perform this feat in the least number of moves that be possible will I give a draught of the best that our good host can provide." To solve this puzzle in the fewest possible moves, first with 8, then with 10, and afterwards with 21 cheeses, is an interesting recreation.

里夫是一个狡猾的人,也是一位学者。正如乔叟告诉我们的那样,“没有任何审计员可以让他获胜”,并且“没有人可以拖欠他的钱”。诗人还注意到“他曾经骑过最阻碍的路线”。他这样做是为了更好地不间断地解决他活跃的大脑中出现的奇特问题和想法。当朝圣者在路边的一家小酒馆停下来时,许多大小不一的奶酪引起了他警惕的目光;他要了四张凳子,并告诉大家他会向他们展示一个他自己设计的拼图,让他们在休息时感到开心。然后,他将八块大小逐渐变化的奶酪放在最后一张凳子上,最小的奶酪位于顶部,如图所示。 “这是一个谜语,”他说,“我曾经在诺福克郡巴尔德斯韦尔的同胞面前做过这个谜语,而且,圣乔斯,他们中间没有人能正确地解开这个谜语。然而,这很容易,因为我真正想要的是,通过一次将一块奶酪从一个凳子移到另一个凳子上,你们将把所有的奶酪移到另一端的凳子上,而不要在比它更小的凳子上放任何奶酪。对于能够以尽可能少的动作完成这一壮举的人,我将提供我们好东道主所能提供的最好的草案。”用尽可能少的步数解决这个难题,首先用 8 块奶酪,然后用 10 块奶酪,最后用 21 块奶酪,是一种有趣的游戏。

A B C D M N P Q
fig-1

Dudeney 几何重排题的工作图:把 4×6 方格先看成一个总面积,再试两道栅栏如何保持四块全等。

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。