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 Sompnour, or Summoner, who, according to Chaucer, joined the party of pilgrims, was an officer whose duty was to summon delinquents to appear in ecclesiastical courts. In later times he became known as the apparitor. Our particular individual was a somewhat quaint though worthy man. "He was a gentle hireling and a kind; A better fellow should a man not find." In order that the reader may understand his appearance in the picture, it must be explained that his peculiar headgear is duly recorded by the poet. "A garland had he set upon his head, As great as if it were for an ale-stake." One evening ten of the company stopped at a village inn and requested to be put up for the night, but mine host could only accommodate five of them. The Sompnour suggested that they should draw lots, and as he had had experience in such matters in the summoning of juries and in other ways, he arranged the company in a circle and proposed a "count out." Being of a chivalrous nature, his little plot was so to arrange that the men should all fall out and leave the ladies in possession. He therefore gave the Wife of Bath a number and directed her to count round and round the circle, in a clockwise direction, and the person on whom that number fell was immediately to step out of the ring. The count then began afresh at the next person. But the lady misunderstood her instructions, and selected in mistake the number eleven and started the count at herself. As will be found, this resulted in all the women falling out in turn instead of the men, for every eleventh person withdrawn from the circle is a lady. "Of a truth it was no fault of mine," said the Sompnour next day to the company, "and herein is methinks a riddle. Can any tell me what number the good Wife should have used withal, and at which pilgrim she should have begun her count so that no other than the five men should have been counted out?" Of course, the point is to find the smallest number that will have the desired effect.
根据乔叟的说法,桑普诺(Sommpnour)或召唤者加入了朝圣者队伍,是一名官员,其职责是传唤罪犯到教会法庭出庭。后来他被称为幻影师。我们这个人是一个有点古怪但有价值的人。 “他是一个温柔而善良的雇工;一个人应该找不到更好的人了。”为了让读者了解他在画中的样子,必须说明他特有的头饰是由诗人适当记录的。 “他头上戴了一个花环,就像是为了啤酒桩一样伟大。”一天晚上,连队十人在一家乡村旅馆停下来,要求留宿一晚,但矿主只能容纳五人。桑普努尔建议他们应该抽签,因为他在召集陪审团和其他方面有处理此类问题的经验,所以他把公司排成一个圆圈,并提议“抽签”。出于侠义之心,他的小阴谋就是安排男人们全部闹翻,把女人留给女人。因此,他给巴斯的妻子一个数字,并指示她以顺时针方向一圈又一圈地数数,落在这个数字上的人立即走出圆圈。然后从下一个人开始重新计数。但这位女士误解了她的指示,错误地选择了数字十一,并开始自己数数。将会发现,这导致所有女性依次退出,而不是男性,因为退出圈子的每 11 个人中就有一位是女性。 “说实话,这不是我的错,”第二天,桑普诺尔对同伴们说道,“我认为这是一个谜语。谁能告诉我,善良的妻子应该用什么数字,她应该从哪位朝圣者开始计数,这样除了这五个人之外,就不会再有其他人被算出来了?”当然,关键是找到能够达到预期效果的最小数字。
提示 1
先只保留连接关系,把多余长度和角度擦掉。
提示 2
数端点、奇偶穿越和连通块,看看有没有不变量。
提示 3
最后再把抽象关系放回原图,确认没有偷换路径。
完整解答
一笔画回到起点需要所有路口度数为偶数;若有四个奇度路口,就不可能每条路恰好走一次并回到原点。至少要改变两条端点关系,或增加一条连接两个奇度点的路,把奇度点数降到 0。
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。