On Solving an Amusing Puzzle

Abstract

The study of Diophantine equations has been of great interest to mathematicians of long time. In this paper, we will introduce an amusing puzzle, and solve it using the idea of continued fraction method. It turns out that the puzzle gives rise to a quadratic Diophantine equation. We will be solving this equation using a nice continued fraction. Finally, we have obtained closed expressions forming infinitely many solutions to the given puzzle.