Recreational mathematics as defined by Wikipedia is a term for mathematics carried out for recreation (entertainment) rather than as a strictly research and application-based professional activity, although it is not necessarily limited to being an endeavor for amateurs. It often involves mathematical puzzles and games.

Perhaps the greatest proponent of recreational mathematics was Martin Gardner, with his Mathematical Games column than ran in Scientific American from 1956 to 1986. The entire collection of Gardner's columns is available here.

In The Mathematics of Various Entertaining Subjects: Research in Recreational Math (Princeton University Press 978-0691164038), editors Jennifer Beineke & Jason Rosenhouse have gathered 17 chapters on various entertaining subjects.

The use of recreational math here is meant for those with a very strong math background.  While chapters such as Minimalist Approaches to Figurative Maze Design, Solving the Tower of Hanoi with Random Moves and Groups Associated to Tetraflexagons (folded flexagons) will challenge most readers.  Advanced chapters such as From the Outside In: Solving Generalizations of the Slothouber-Graatsma-Conway Puzzle, An Introduction to Gilbreath Numbers and Representing Numbers Using Fibonacci Variants requires the reader to have a strong background in academic mathematics.

While not directly an information security title, The Mathematics of Various Entertaining Subjects will stimulate and entertain those looking for a highly rigorous book of recreational mathematics to challenge their mind.