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Canterbury Puzzle 10 · Market Weights 10

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 10 arithmetic

Chaucer says of the Squire's Yeoman, who formed one of his party of pilgrims, "A forester was he truly as I guess," and tells us that "His arrows drooped not with feathers low, And in his hand he bare a mighty bow." When a halt was made one day at a wayside inn, bearing the old sign of the "Chequers," this yeoman consented to give the company an exhibition of his skill. Selecting nine good arrows, he said, "Mark ye, good sirs, how that I shall shoot these nine arrows in such manner that each of them shall lodge in the middle of one of the squares that be upon the sign of the 'Chequers,' and yet of a truth shall no arrow be in line with any other arrow." The diagram will show exactly how he did this, and no two arrows will be found in line, horizontally, vertically, or diagonally. Then the Yeoman said: "Here then is a riddle for ye. Remove three of the arrows each to one of its neighbouring squares, so that the nine shall yet be so placed that none thereof may be in line with another." By a "neighbouring square" is meant one that adjoins, either laterally or diagonally.

乔叟谈到乡绅的自耕农,他组成了他的朝圣者队伍之一,“正如我猜想的那样,他确实是一位护林员”,并告诉我们“他的箭不低垂,手里拿着一把强大的弓。”有一天,当我们在路边一家挂着“支票”标志的小旅馆停下来时,这位自耕农同意向连队展示他的技能。他选了九支好箭,说道:“请注意,先生们,我该如何射出这九支箭,使每一支箭都落在‘支票’标志上的一个方格的中间,但事实上,没有一支箭与任何其他箭在一条线上。”该图将准确地显示他是如何做到这一点的,并且不会在直线、水平、垂直或对角线上找到两个箭头。然后自耕农说:“这里给你们出一个谜语。将三支箭头移到其相邻的一个方格上,这样九个箭头的位置就不会相互对齐。” “相邻的正方形”是指横向或对角地相邻的正方形。

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 - 10,第三人得 x + 13。三人总和给出 4x + 13 - 10 = 63,所以 x = 15。三份分别是 20、15、28 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。