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番外 · 题谱 · 1907 · P3

Canterbury Puzzle 3 · Signboard Letters 3

组合游戏 · P3/P6 · 压轴题

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 3 combinatorial

The Miller next took the company aside and showed them nine sacks of flour that were standing as depicted in the sketch. "Now, hearken, all and some," said he, "while that I do set ye the riddle of the nine sacks of flour. And mark ye, my lords and masters, that there be single sacks on the outside, pairs next unto them, and three together in the middle thereof. By Saint Benedict, it doth so happen that if we do but multiply the pair, 28, by the single one, 7, the answer is 196, which is of a truth the number shown by the sacks in the middle. Yet it be not true that the other pair, 34, when so multiplied by its neighbour, 5, will also make 196. Wherefore I do beg you, gentle sirs, so to place anew the nine sacks with as little trouble as possible that each pair when thus multiplied by its single neighbour shall make the number in the middle." As the Miller has stipulated in effect that as few bags as possible shall be moved, there is only one answer to this puzzle, which everybody should be able to solve.

磨坊主接下来把公司带到一边,向他们展示了九袋面粉,如图所示。 “现在,听着,所有的人和一些人,”他说,“当我给你们提出九袋面粉的谜语时。请注意,我的大人和主人,外面有一个袋子,旁边有两个袋子,中间有三个袋子。圣本尼迪克特,如果我们将这对 28 乘以一个 7,答案就是 196,这是一个事实是中间麻袋所显示的数字,但另一对 34 乘以它的相邻麻袋 5 也不会等于 196。因此,我恳求你们,先生们,尽可能不麻烦地重新放置这九个麻袋,使每一对乘以它的单个相邻麻袋时,都将得到中间的数字。”由于磨坊主实际上规定要移动尽可能少的行李,因此这个难题只有一个答案,每个人都应该能够解决。

提示 1

先把每一步允许做什么写成状态表。

提示 2

找一个不会随操作改变的量,或把对象分成互斥类别。

提示 3

检查构造是否覆盖全部对象,而不是只给出一个漂亮例子。

完整解答

固定主人面向门口,就消除了旋转重复。先数其余人任意排列,再减去两位指定朝圣者相邻的情形。相邻时把这两人看成一个双人块,块内部有 2 种顺序;最后用总数减去坏排列。

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。