This section contains many difficult puzzles that can be used to motivate advanced students. Many of the puzzles are distinct and require different levels of student mathematical abilities ranging from elementary algebra to number theory and beyond. Although most are not within the scope of a normal high school student's mathematical ability, these puzzles are quite brief and understandable. Very often, they will lead to the investigation of other interesting topics in mathematics. However, some explanation by the teacher may be necessary to enhance the understanding and appreciation of the puzzle by the students.