Discovering Mathematics: A Case Study

As a broad generalisation we might say that research in mathematics consists of two parts: finding out what is true, and proving that it is true.  Mathematical articles (even those written for school students) traditionally concentrate on the second of these, covering up the investigator's tracks and offering only the final, beautifully clear path to the proved theorem.  Readers may find it of interest to see where the ideas came from in a problem I tackled recently.