Birth of a Problem: The Story of Creation in Seven Stages

摘要

Problem solving requires the existence of problems. Somebody has to create them. But how? I will share here an example of how it works for me. Nearly every March I attend the Southeastern International Conference on Combinatorics, Graph Theory, and Computing at the Florida Atlantic University. Listening to talks there accelerates the gears of my mind. Ideas of research mathematics inspire my problem creation. Of course, research mathematics often deals with a sophisticated topic matter, uses a break-through-the-wall by all available means solutions, and so the first task is to extract "naked" beautiful ideas out of it. The second task is to dress up these ideas and present them to the high school Olympians in a form of an enjoyable story. Consequently, some of our problems have special titles, such as "Football for 23", "Chess 7x7", "Old Glory", "Stone Age Entertainment", "King Arthur and the Knights of the Round Table", "Crawford Cowboy Had a Farm, Ee i ee i oh!", etc. I would like to illustrate here how a problem of the 29~(th) Colorado Mathematical Olympiad has been created during March-April 2012. You will witness the construction of a two-way bridge between problems of mathematical Olympiads and research problems of mathematics. Let us begin.