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Canterbury Puzzle 17 · Broken Window 17

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 17 geometric

The Monk that went with the party was a great lover of sport. "Greyhounds he had as swift as fowl of flight: Of riding and of hunting for the hare Was all his love, for no cost would he spare." One day he addressed the pilgrims as follows:— "There is a little matter that hath at times perplexed me greatly, though certes it is of no great weight; yet may it serve to try the wits of some that be cunning in such things. Nine kennels have I for the use of my dogs, and they be put in the form of a square; though the one in the middle I do never use, it not being of a useful nature. Now the riddle is to find in how many different ways I may place my dogs in all or any of the outside kennels so that the number of dogs on every side of the square may be just ten." The small diagrams show four ways of doing it, and though the fourth way is merely a reversal of the third, it counts as different. Any kennels may be left empty. This puzzle was evidently a variation of the ancient one of the Abbess and her Nuns.

参加聚会的僧侣是一位运动爱好者。 “他拥有像飞翔的家禽一样敏捷的灰狗:骑马和狩猎野兔是他的全部爱,他不惜一切代价。”有一天,他对朝圣者们说:“有一件小事,有时让我大为困惑,虽然它确实不是什么大事;但它可以用来考验一些狡猾的人的智慧。我有九个狗舍供我的狗使用,它们被放在一个正方形的形状中;虽然中间的那个我从来没有使用过,但它没有什么用处。现在的谜语是找出有多少种不同的方式我可以把我的狗放在所有或任何一个外面的狗舍里,这样广场每边的狗的数量就只有十只。”小图显示了四种方法,虽然第四种方法只是第三种方法的逆转,但它算作是不同的。任何狗舍都可以空着。这个谜题显然是女修道院院长和她的修女们的古老谜题的变体。

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。