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番外 · 题谱 · 1907 · P3

Canterbury Puzzle 15 · The Locked Chest 15

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 15 combinatorial

We find that there was a cook among the company; and his services were no doubt at times in great request, "For he could roast and seethe, and broil and fry, And make a mortress and well bake a pie." One night when the pilgrims were seated at a country hostelry, about to begin their repast, the cook presented himself at the head of the table that was presided over by the Franklin, and said, "Listen awhile, my masters, while that I do ask ye a riddle, and by Saint Moden it is one that I cannot answer myself withal. There be eleven pilgrims seated at this board on which is set a warden pie and a venison pasty, each of which may truly be divided into four parts and no more. Now, mark ye, five out of the eleven pilgrims can eat the pie, but will not touch the pasty, while four will eat the pasty but turn away from the pie. Moreover, the two that do remain be able and willing to eat of either. By my halidame, is there any that can tell me in how many different ways the good Franklin may choose whom he will serve?" I will just caution the reader that if he is not careful he will find, when he sees the answer, that he has made a mistake of forty, as all the company did, with the exception of the Clerk of Oxenford, who got it right by accident, through putting down a wrong figure. Strange to say, while the company perplexed their wits about this riddle the cook played upon them a merry jest. In the midst of their deep thinking and hot dispute what should the cunning knave do but stealthily take away both the pie and the pasty. Then, when hunger made them desire to go on with the repast, finding there was nought upon the table, they called clamorously for the cook. "My masters," he explained, "seeing you were so deep set in the riddle, I did take them to the next room, where others did eat them with relish ere they had grown cold. There be excellent bread and cheese in the pantry."

我们发现公司里有一个厨师;毫无疑问,他的服务有时会受到很大的要求,“因为他可以烤、煮、烤、煎,还可以做馅饼,还可以烤馅饼。”一天晚上,当朝圣者们坐在一家乡村旅馆里,正要开始用餐时,厨师来到富兰克林主持的餐桌前,说道:“请听我说,我的主人,我确实在问你们一个谜语,而圣莫登,这是一个我无法回答自己的谜语。有十一位朝圣者坐在这块桌子上,上面放着一份典狱长馅饼和一份鹿肉馅饼,每人都可以吃现在,注意一下,十一个朝圣者中有五个可以吃馅饼,但不会碰馅饼,而四个人会吃馅饼,但不会吃馅饼,而且,我的哈利达姆,有谁可以告诉我,好心的富兰克林可以用多少种不同的方式来选择他要服务的人呢?我只是提醒读者,如果他不小心,当他看到答案时,他会发现他犯了四十个错误,就像所有公司所做的那样,除了奥克森福德的职员,他偶然通过写错数字而得到了正确的结果。说来也奇怪,正当大家为这个谜语困惑不已时,厨师却给他们开了一个愉快的玩笑。在他们的深思熟虑和激烈争论中,狡猾的无赖除了偷偷地把馅饼和馅饼都拿走之外,还能做什么呢?然后,当饥饿使他们想继续吃饭时,发现桌子上什么也没有,他们大声叫厨师。 “我的主人,”他解释道,“看到你们对谜语如此深陷,我确实把它们带到了隔壁房间,其他人在它们变冷之前津津有味地吃着它们。食品储藏室里有美味的面包和奶酪。”

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。