This note discusses a possible method for teaching an example of problem solving to intermediate grade students. Under the guidance of the instructor, students may see the links between the 'guess' method and the arithmetic operation 'strings'. This may help enhance their logical thinking ability as well as arithmetic operation skills. For more mathematically talented students, this example also offers them an opportunity to see the connections among relatively prime numbers, combinations of numbers, algorithmic procedures, and their applications. Sections include: Introduction; The 'Guess' Method; More Systematic Procedure; How to Find A Combination; and Conclusions.