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番外 · 题谱 · 1907 · P5

Canterbury Puzzle 11 · Seating the Pilgrims 11

组合游戏 · 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 11 combinatorial

"I trow there be not one among ye," quoth the Nun, on a later occasion, "that doth not know that many monks do oft pass the time in play at certain games, albeit they be not lawful for them. These games, such as cards and the game of chess, do they cunningly hide from the abbot's eye by putting them away in holes that they have cut out of the very hearts of great books that be upon their shelves. Shall the nun therefore be greatly blamed if she do likewise? I will show a little riddle game that we do sometimes play among ourselves when the good abbess doth hap to be away." The Nun then produced the eighteen cards that are shown in the illustration. She explained that the puzzle was so to arrange the cards in a pack, that by placing the uppermost one on the table, placing the next one at the bottom of the pack, the next one on the table, the next at the bottom of the pack, and so on, until all are on the table, the eighteen cards shall then read "CANTERBURY PILGRIMS." Of course each card must be placed on the table to the immediate right of the one that preceded it. It is easy enough if you work backwards, but the reader should try to arrive at the required order without doing this, or using any actual cards.

“我想你们当中没有一个人,”修女后来说道,“不知道许多僧侣经常通过玩某些游戏来打发时间,尽管这些游戏对他们来说是不合法的。这些游戏,例如纸牌和国际象棋,他们巧妙地将它们放在从书架上的伟大书籍的中心切出的孔中,以躲避院长的眼睛。修女应该吗?因此,如果她也这样做,我会受到很大的责备吗?我会展示一个小谜语游戏,当好心的女院长碰巧不在时,我们会玩这个游戏。”然后修女拿出了图中所示的十八张牌。她解释说,这个谜题是将卡片排列成一叠,将最上面的一张放在桌子上,将下一张放在卡片的底部,下一张放在桌子上,下一张放在卡片的底部,依此类推,直到所有卡片都放在桌子上,十八张卡片上应写着“坎特伯雷朝圣者”。当然,每张牌都必须放在桌子上紧邻前一张牌的右侧。如果您向后工作,这很容易,但是读者应该尝试在不这样做或不使用任何实际卡片的情况下达到所需的顺序。

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。