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。
Every one is familiar with the difficulties that frequently arise over the giving of change, and how the assistance of a third person with a few coins in his pocket will sometimes help us to set the matter right. Here is an example. An Englishman went into a shop in New York and bought goods at a cost of thirty-four cents. The only money he had was a dollar, a three-cent piece, and a two-cent piece. The tradesman had only a half-dollar and a quarter-dollar. But another customer happened to be present, and when asked to help produced two dimes, a five-cent piece, a two-cent piece, and a one-cent piece. How did the tradesman manage to give change? For the benefit of those readers who are not familiar with the American coinage, it is only necessary to say that a dollar is a hundred cents and a dime ten cents. A puzzle of this kind should rarely cause any difficulty if attacked in a proper manner.
每个人都熟悉在找零时经常出现的困难,以及口袋里有几枚硬币的第三方的帮助有时会帮助我们解决问题。这是一个例子。一个英国人走进纽约的一家商店,以三十四美分的价格购买了商品。他身上仅有的钱是一美元、三分钱和两分钱。商人只有半美元和四分之一美元。但恰巧有另一位顾客在场,当他要求帮忙时,他拿出了两角硬币、五角硬币、两角硬币和一角硬币。商人是如何找到零钱的?为了方便那些不熟悉美国硬币的读者,只需说一美元是一百美分,一毛钱是十美分。如果以适当的方式攻击,这种谜题很少会造成任何困难。
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。