The purpose of this paper is to provide issues related to student understanding of logical components that arise when solving word problems. We designed a logic problem called the King and Prisoner Puzzle--a linguistically simple, yet logically challenging problem. In this paper, we describe various student solutions to the puzzle and discuss the issues with students' logic. In particular, it is thought-provoking that invalid arguments in students' solutions to the puzzle are based on a lack of precise understanding of some basic logical components. This emphasizes the necessity of additional teaching to form mutual understanding of the meaning of the logical components.