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番外 · 题谱 · 1907 · P1

Dudeney 谜题 7

算术 / 谜题 · P1/P4 · 起手题

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。

算术与计数 1907 P1 arithmeticpuzzle

Though the following little puzzle deals with the purchase of chestnuts, it is not itself of the "chestnut" type. It is quite new. At first sight it has certainly the appearance of being of the "nonsense puzzle" character, but it is all right when properly considered. A man went to a shop to buy chestnuts. He said he wanted a pennyworth, and was given five chestnuts. "It is not enough; I ought to have a sixth," he remarked! "But if I give you one chestnut more." the shopman replied, "you will have five too many." Now, strange to say, they were both right. How many chestnuts should the buyer receive for half a crown?

虽然下面这个小谜题是关于购买栗子的,但它本身并不是“栗子”类型的。这是相当新的。乍一看确实有“无意义拼图”的特征,但仔细考虑一下也没什么问题。一个男人去一家商店买栗子。他说他想要一便士,结果给了五个栗子。 “这还不够;我应该有第六个,”他说! “但如果我再给你举一个栗子。”店主回答说:“你买的太多了,五个。”现在,奇怪的是,他们都是对的。买家应该用半克朗收到多少个栗子?

提示 1

先说出现象:哪些量会变,哪些约束不会变。

提示 2

找守恒量、相似关系、平衡条件或不变量,不急着代公式。

提示 3

把物理图景或谜题结构翻成一个最小方程组,再处理边界情况。

完整解答

解题主线是先把 Dudeney 谜题 7 的条件整理成一个稳定模型,再选择最少的变量。第一步确认约束,第二步写出关键关系,第三步检查特殊情形。这里给的是原创解法骨架;若要核对原始题面,请回到公版来源。

这类题最怕一上来套公式。先把图景或语言条件说清楚,答案通常会少绕很多路。