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Canterbury Puzzle 18 · Innkeeper’s Bill 18

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 Canterbury Puzzles 1907 18 arithmetic

Of this person we are told, "He knew well all the havens, as they were, From Gothland to the Cape of Finisterre, And every creek in Brittany and Spain: His barque yclepéd was the Magdalen." The strange puzzle in navigation that he propounded was as follows. "Here be a chart," quoth the Shipman, "of five islands, with the inhabitants of which I do trade. In each year my good ship doth sail over every one of the ten courses depicted thereon, but never may she pass along the same course twice in any year. Is there any among the company who can tell me in how many different ways I may direct the Magdalen's ten yearly voyages, always setting out from the same island?" CHART of ye MAGDALEN

关于这个人,我们被告知,“他熟悉所有的港口,从哥特兰到菲尼斯特雷海角,以及布列塔尼和西班牙的每一条小溪:他的三桅帆船是抹大拉号。”他提出的奇怪的航海难题如下。 “这里有一张海图,”船夫说道,“上面有五个岛屿,我与这些岛屿上的居民进行贸易。每年,我的好船都会航行在上面所描绘的十个航线中的每一个航线上,但在任何一年里,她都不会经过同一条航线两次。公司中有谁能告诉我,我可以用多少种不同的方式来指挥马格达伦号的十年航行,总是从同一个岛屿出发?”抹大拉的图表

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 - 18,第三人得 x + 21。三人总和给出 4x + 21 - 18 = 95,所以 x = 23。三份分别是 28、23、44 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。