ABSTRACT
This chapter introduces the notion of a “nimber,” which arises in the study of combinatorial games but turns out to have many applications in mathematics. A nimber is at its heart just a non-negative integer, but doesn't add the same way ordinary numbers do; instead, nimbers are written in binary and added without carrying. As a result, the sum of a nimber and itself is always zero, and subtracting nimbers is the same as adding them. Seven puzzles and a theorem are presented. Three of the puzzles concern variations of the game of Nim, from which the name “nimber” is derived; the rest introduce the reader to two unusual hat-puzzle variations, and a couple of problems involving spies. The theorem introduces the reader to error-correcting codes, in particular by showing that the Hamming code can correct any single error.
