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番外 · 题谱 · 1907 · P2

Canterbury Puzzle 14 · Pilgrim’s Count 14

算术 · P2/P5 · 中段题

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 14 arithmetic

When the Weaver brought out a square piece of beautiful cloth, daintily embroidered with lions and castles, as depicted in the illustration, the pilgrims disputed among themselves as to the meaning of these ornaments. The Knight, however, who was skilled in heraldry, explained that they were probably derived from the lions and castles borne in the arms of Ferdinand III., the King of Castile and Leon, whose daughter was the first wife of our Edward I. In this he was undoubtedly correct. The puzzle that the Weaver proposed was this. "Let us, for the nonce, see," saith he, "if there be any of the company that can show how this piece of cloth may be cut into four several pieces, each of the same size and shape, and each piece bearing a lion and a castle." It is not recorded that anybody mastered this puzzle, though it is quite possible of solution in a satisfactory manner. No cut may pass through any part of a lion or a castle.

当织工拿出一块美丽的方形布,上面绣着如图所示的狮子和城堡时,朝圣者们就这些装饰品的含义争论不休。然而,精通纹章的骑士解释说,它们可能源自卡斯蒂利亚和莱昂国王斐迪南三世怀中的狮子和城堡,他的女儿是爱德华一世的第一任妻子。在这一点上,他无疑是正确的。织工提出的谜题是这样的。 “让我们暂时看看,”他说,“是否有人能够展示如何将这块布切成四块,每块的大小和形状都相同,并且每块上都有一只狮子和一座城堡。”尽管很有可能以令人满意的方式解决这个难题,但没有记录表明有人解决了这个难题。任何切口都不能穿过狮子或城堡的任何部分。

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 - 14,第三人得 x + 17。三人总和给出 4x + 17 - 14 = 79,所以 x = 19。三份分别是 24、19、36 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。