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。
When the Smileys recently received a visit from the favourite uncle, the fond parents had all the five children brought into his presence. First came Billie and little Gertrude, and the uncle was informed that the boy was exactly twice as old as the girl. Then Henrietta arrived, and it was pointed out that the combined ages of herself and Gertrude equalled twice the age of Billie. Then Charlie came running in, and somebody remarked that now the combined ages of the two boys were exactly twice the combined ages of the two girls. The uncle was expressing his astonishment at these coincidences when Janet came in. "Ah! uncle," she exclaimed, "you have actually arrived on my twenty-first birthday!" To this Mr. Smiley added the final staggerer: "Yes, and now the combined ages of the three girls are exactly equal to twice the combined ages of the two boys." Can you give the age of each child?
当史迈利夫妇最近接待了最喜欢的叔叔来访时，这对可爱的父母把五个孩子都带到了他的面前。首先是比莉和小格特鲁德，叔叔被告知男孩的年龄正好是女孩的两倍。然后亨利埃塔来了，有人指出她和格特鲁德的年龄加起来等于比莉年龄的两倍。然后查理跑进来，有人说现在两个男孩的年龄总和正好是两个女孩年龄总和的两倍。当珍妮特进来时，叔叔正在对这些巧合表示惊讶。“啊！叔叔，”她惊呼道，“你居然到了我二十一岁生日了！”对此，史迈利先生最后补充道：“是的，现在三个女孩的年龄总和正好等于两个男孩年龄总和的两倍。”你能给出每个孩子的年龄吗？
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 12 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。