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 proprietor of a small London café has given me some interesting figures. He says that the ladies who come alone to his place for refreshment spend each on an average eighteenpence, that the unaccompanied men spend half a crown each, and that when a gentleman brings in a lady he spends half a guinea. On New Year's Eve he supplied suppers to twenty-five persons, and took five pounds in all. Now, assuming his averages to have held good in every case, how was his company made up on that occasion? Of course, only single gentlemen, single ladies, and pairs (a lady and gentleman) can be supposed to have been present, as we are not considering larger parties.
伦敦一家小咖啡馆的老板提供了一组有趣的账目：单独来店里用点心的女士平均花费十八便士，单独来的男士平均花费半克朗，而一位男士带一位女士同来时平均花费半几尼。除夕夜，他为二十五个人供应晚餐，总共收了五英镑。若假定这些平均数在当晚每一类客人身上都正好成立，那么那晚的客人构成是怎样的？当然这里只考虑单身男士、单身女士，以及一男一女成对同行的客人，不考虑更大的同行团体。
提示 1
先说出现象：哪些量会变，哪些约束不会变。
提示 2
找守恒量、相似关系、平衡条件或不变量，不急着代公式。
提示 3
把物理图景或谜题结构翻成一个最小方程组，再处理边界情况。
完整解答
解题主线是先把 Dudeney 谜题 19 的条件整理成一个稳定模型，再选择最少的变量。第一步确认约束，第二步写出关键关系，第三步检查特殊情形。这里给的是原创解法骨架；若要核对原始题面，请回到公版来源。
这类题最怕一上来套公式。先把图景或语言条件说清楚，答案通常会少绕很多路。