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。
The gentle Pardoner, "that straight was come from the court of Rome," begged to be excused; but the company would not spare him. "Friends and fellow-pilgrims," said he, "of a truth the riddle that I have made is but a poor thing, but it is the best that I have been able to devise. Blame my lack of knowledge of such matters if it be not to your liking." But his invention was very well received. He produced the accompanying plan, and said that it represented sixty-four towns through which he had to pass during some of his pilgrimages, and the lines connecting them were roads. He explained that the puzzle was to start from the large black town and visit all the other towns once, and once only, in fifteen straight pilgrimages. Try to trace the route in fifteen straight lines with your pencil. You may end where you like, but note that the omission of a little road at the bottom is intentional, as it seems that it was impossible to go that way.
温和的赎罪券商请求原谅,“那笔钱直接来自罗马宫廷”。但公司不会放过他。 “朋友们,朝圣者们,”他说,“事实上,我编的这个谜语虽然很可怜,但它是我能设计出的最好的谜语。如果不符合你们的喜好,那就怪我对这些事情缺乏了解。”但他的发明很受欢迎。他制作了随附的计划,并说它代表了他在某些朝圣期间必须经过的六十四个城镇,连接它们的线是道路。他解释说,这个谜题是从那个黑人大城镇开始,在连续十五次朝圣中访问所有其他城镇一次,且仅一次。尝试用铅笔沿着十五条直线描绘路线。你可以在你喜欢的地方结束,但请注意,底部的一条小路是故意省略的,因为似乎不可能走那条路。
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 - 2,第三人得 x + 5。三人总和给出 4x + 5 - 2 = 31,所以 x = 7。三份分别是 12、7、12 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。