In this article, we discuss how to use a diagrammatic approach to solve the classic sailors and the coconuts problem. It provides us an insight on how to tackle this type of problems in a novel and intuitive way. This problem-solving approach will be found useful to mathematics teachers or lecturers involved in teaching elementary number theory, recreational mathematics or mathematics problem solving. Copyright © 2009 The Author. Published by Oxford University Press on behalf of The Institute of Mathematics and its Applications.