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。
"A neighbour of mine," said Aunt Jane, "bought a certain quantity of beef at two shillings a pound, and the same quantity of sausages at eighteenpence a pound. I pointed out to her that if she had divided the same money equally between beef and sausages she would have gained two pounds in the total weight. Can you tell me exactly how much she spent?" "Of course, it is no business of mine," said Mrs. Sunniborne; "but a lady who could pay such prices must be somewhat inexperienced in domestic economy." "I quite agree, my dear," Aunt Jane replied, "but you see that is not the precise point under discussion, any more than the name and morals of the tradesman."
“我的一个邻居,”简姨妈说,“以每磅两先令的价格买了一定数量的牛肉,以每磅十八便士的价格买了同样数量的香肠。我向她指出,如果她把同样的钱平分在牛肉和香肠上,她的总重量会增加两磅。你能告诉我她到底花了多少钱吗?” “当然,这不关我的事,”桑尼伯恩夫人说。 “但是能支付这样的价格的女士一定对国内经济有些缺乏经验。” “我完全同意,亲爱的,”简姨妈回答道,“但是你看,这不是我们讨论的确切问题,就像商人的名字和道德一样。”
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 - 20,第三人得 x + 23。三人总和给出 4x + 23 - 20 = 103,所以 x = 25。三份分别是 30、25、48 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。