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。
This Doctor, learned though he was, for "In all this world to him there was none like To speak of physic and of surgery," and "He knew the cause of every malady," yet was he not indifferent to the more material side of life. "Gold in physic is a cordial; Therefore he lovéd gold in special." The problem that the Doctor propounded to the assembled pilgrims was this. He produced two spherical phials, as shown in our illustration, and pointed out that one phial was exactly a foot in circumference, and the other two feet in circumference. "I do wish," said the Doctor, addressing the company, "to have the exact measures of two other phials, of a like shape but different in size, that may together contain just as much liquid as is contained by these two." To find exact dimensions in the smallest possible numbers is one of the toughest nuts I have attempted. Of course the thickness of the glass, and the neck and base, are to be ignored.
这位医生虽然博学多才，因为“对他来说，在这个世界上，没有人比他更能谈论内科和外科手术”，“他知道每种疾病的原因”，但他对生活中更物质的方面并非漠不关心。 “金在药性上是一种甘露，所以他特别喜爱金。”博士向聚集的朝圣者提出的问题是这样的。他制作了两个球形小瓶，如我们的插图所示，并指出其中一个小瓶的周长正好是一英尺，另外一个小瓶的周长是两英尺。 “我确实希望，”医生对大家说，“能得到另外两个小瓶的精确尺寸，形状相似但大小不同，它们加起来可能含有与这两个小瓶一样多的液体。”以尽可能小的数字找到精确的尺寸是我尝试过的最困难的事情之一。当然，玻璃的厚度、颈部和底座是可以忽略的。
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。