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。
Three countrymen met at a cattle market. "Look here," said Hodge to Jakes, "I'll give you six of my pigs for one of your horses, and then you'll have twice as many animals here as I've got." "If that's your way of doing business," said Durrant to Hodge, "I'll give you fourteen of my sheep for a horse, and then you'll have three times as many animals as I." "Well, I'll go better than that," said Jakes to Durrant; "I'll give you four cows for a horse, and then you'll have six times as many animals as I've got here." No doubt this was a very primitive way of bartering animals, but it is an interesting little puzzle to discover just how many animals Jakes, Hodge, and Durrant must have taken to the cattle market.
三个同胞在牛市场相遇。 “看这里,”霍奇对杰克斯说,“我可以用我的六头猪换你的一匹马,然后你这里的动物数量就会是我的两倍。” “如果这就是你做生意的方式,”杜兰特对霍奇说,“我会给你十四只羊换一匹马,然后你的动物数量将是我的三倍。” “好吧,我会做得更好,”杰克斯对杜兰特说。 “我给你四头牛换一匹马,然后你的动物数量将是我这里的六倍。”毫无疑问,这是一种非常原始的动物交换方式,但要了解杰克、霍奇和杜兰特到底带了多少动物到牛市场,这是一个有趣的小谜题。
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。