1969年荷兰数学家汉斯$\cdot$弗洛伊登塔尔提出的``和与积之谜'', 涉及到整数分拆和因子分解的基本性质, 这个表述非常简单的问题表面上看是一个不可能解决的谜题. 文章从自动推理智能体的视角, 用浅显而严格的语言解释弗洛伊登塔尔问题的求解过程, 可作为计算机搜索程序的设计参照. 文章从弗洛伊登塔尔问题延伸定义了弗洛伊登塔尔数(Freudenthal numbers, F数)序列, 通过计算机数学实验探讨了F数序列的性质, 提出了几个有趣的未解决问题.

This article presents a rigorous and step-by-step explanation to the automated reasoning procedure of the famous Impossible Puzzle (the Puzzle of Sum and Products) raised by Hans Freudenthal from the point of view of intelligent agents. The discussion provides an example of automated reasoning and searching of multi-agents in artificial intelligence. The original puzzle has also been extended to generating the Freudenthal numbers and several other sequences integers existed in the The On-Line Encyclopedia of Integer Sequences. Several interesting unsolved problems related to Freudenthal numbers are given in the last section for further investigation.