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。
Two youths, bearing the pleasant names of Moggs and Snoggs, were employed as junior clerks by a merchant in Mincing Lane. They were both engaged at the same salary—that is, commencing at the rate of £50 a year, payable half-yearly. Moggs had a yearly rise of £10, and Snoggs was offered the same, only he asked, for reasons that do not concern our puzzle, that he might take his rise at £2, 10 s. half-yearly, to which his employer (not, perhaps, unnaturally!) had no objection. Now we come to the real point of the puzzle. Moggs put regularly into the Post Office Savings Bank a certain proportion of his salary, while Snoggs saved twice as great a proportion of his, and at the end of five years they had together saved £268, 15 s. How much had each saved? The question of interest can be ignored.
两个年轻人,有着好听的名字,莫格斯和斯诺格斯,被明辛巷的一个商人雇用为初级职员。他们的工资相同,即起薪为每年 50 英镑,每半年支付一次。莫格斯每年加薪 10 英镑,斯诺格斯也得到了同样的待遇,只是他要求以 2 英镑、10 秒的价格加薪,原因与我们的困惑无关。半年一次,他的雇主对此没有反对(也许不是不自然!)。现在我们来到了难题的真正关键点。莫格斯定期将自己工资的一定比例存入邮局储蓄银行,而斯诺格斯则将两倍的比例存入邮局储蓄银行,五年后,他们总共存了 268 英镑 15 先令。每人存了多少钱?利息问题可以忽略不计。
提示 1
先列小例,不要凭直觉猜最大或最小。
提示 2
看奇偶、整除、余数和总量是否已经锁住选择。
提示 3
最后用上下界排除所有漏网情形。
完整解答
设第二人得 x 枚,则第一人得 2x - 26,第三人得 x + 29。三人总和给出 4x + 29 - 26 = 127,所以 x = 31。三份分别是 36、31、60 枚。
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。