Computational Diversions: WordWiring, a Network-Themed Party Game

Abstract

Fans of ‘‘mathematical games’’ (I’m one) often end up with a small library of books on the subject, collectively containing descriptions of a vast trove of games. There are board games, or informal pencil-and-paper games, with applications to (e.g.) graph theory, number theory, combinatorics, logic, and many other branches of mathematics. In fact, the range and variety of mathematical games is so wide—and so rich in content—that one could plausibly base a pretty good introductory mathematics curriculum on these pastimes. Perhaps a few of the more advanced subjects would be underrepresented in this exercise (real analysis? differential geometry?); but a typical library of mathematical games provides, overall, a broad portrait of mathematics in general. Now, coverage of mathematics is one thing; but does our library provide reasonable coverage of what we mean by games? Interestingly, there are certain important types of games that tend to be near-invisible in recreational mathematics. For one thing, almost all the examples in our library are either solitaire games (which by some definitions of the term would hardly qualify as ‘‘games’’ at all), or two-person games. Think of the standards: tic-tac-toe, Nim, Sim, Sprouts, chess, Go, and so forth. Occasionally there are threeor four-person variations of these games, but for the most part we’re talking about n players, where n is a small positive integer. (Perhaps, if we program a computer to play a mathematical game against itself, we could say that n = 0 in that case?) Not all games are like this. After all, baseball is a game, isn’t it? You need to round up 18 people at the very least to play a weekend-afternoon informal game of baseball. Even a pick-up basketball game will usually have at least six players; touch football would require a dozen or so. And how about children’s favorites, such as musical chairs? Starting a game of musical chairs with only two or three kids on hand seems hardly worth the effort. Other children’s classics—Tag, Duck-Duck-Goose, Capture the Flag—are best played with numbers ranging from a half-dozen (at the low end) to twenty or more. For older children and adults, there are games such as charades, or twenty questions, and these are typically played in moderate-sized groups (three would be a bit small for these games). In other