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。
In the illustration we have a sketch of Sir Edwyn de Tudor going to rescue his lady-love, the fair Isabella, who was held a captive by a neighbouring wicked baron. Sir Edwyn calculated that if he rode fifteen miles an hour he would arrive at the castle an hour too soon, while if he rode ten miles an hour he would get there just an hour too late. Now, it was of the first importance that he should arrive at the exact time appointed, in order that the rescue that he had planned should be a success, and the time of the tryst was five o'clock, when the captive lady would be taking her afternoon tea. The puzzle is to discover exactly how far Sir Edwyn de Tudor had to ride.
插图中描绘了埃德温·德·都铎爵士去营救他的爱人、美丽的伊莎贝拉,她被邻近的邪恶男爵俘虏了。埃德温爵士计算出,如果他以每小时十五英里的速度骑行,他就会早一个小时到达城堡,而如果他以每小时十英里的速度骑行,他就会晚一个小时到达那里。现在,最重要的是,他必须在约定的时间到达,才能让计划中的营救成功,而幽会的时间是五点钟,俘虏女士正在喝下午茶。谜题是要弄清楚埃德温·德·都铎爵士到底要骑多远。
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 41 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。