The History of Sim: A Hidden Gem of Mathematical Gaming

Sim was invented in 1969 by the cryptographer Gustavus Simmons, who published it in the Journal of Recreational Mathematics. It became a favourite teaching example among mathematicians — a playable piece of Ramsey theory — yet never became a household name the way chess or Go did. This is the story of that quiet classic, and of its revival as Triad.

Triad is a free online version of Sim, the 1969 pencil-and-paper game by Gustavus Simmons where two players draw lines between six dots and the first to complete a triangle in their own colour loses. For the rules, see what is Sim.

At a Glance

• Inventor: Gustavus J. Simmons, cryptographer
• Introduced: 1969, in the Journal of Recreational Mathematics
• Board: K6 — six dots, fifteen edges
• Solved: 1974 — the second player wins with perfect play

The Birth of Sim

Unlike traditional games that evolved over centuries, Sim was designed deliberately and with a purpose beyond entertainment: to make an abstract mathematical idea tangible. At its core it is a playable demonstration of a result from Ramsey theory, the branch of mathematics that studies unavoidable patterns. The outcome was a game that is simultaneously a puzzle, a strategy contest, and a small proof — colour the edges of six points two ways and a one-colour triangle is forced. The full argument is in the Ramsey theory behind Triad.

Why Mathematicians Loved It

Most games are analysed only after they become popular; Sim drew attention precisely because of the mathematics inside it, transforming a theorem about unavoidable structure into something you could feel emerging move by move. Its profile rose further when Martin Gardner covered Sim in his “Mathematical Games” column in Scientific American in January 1973, introducing it to a wide recreational-mathematics audience. For many readers, that column was their first encounter with the game.

The 1974 Solution

Five years after Sim appeared, it was solved. In 1974, Mead, Rosa and Huang — all at McMaster University — proved that the second player can always force a win, publishing the result as “The Game of Sim: A Winning Strategy for the Second Player” in Mathematics Magazine. The proof settled the theoretical question early, though a winning strategy simple enough for humans to follow would not arrive until decades later.

Why Sim Never Became Famous

Given its elegance, Sim might have joined the canon of classic abstract games. Several things kept it obscure. It spread through mathematical circles rather than families and toy stores, so people met it as a classroom curiosity rather than a competitive game. Its name never developed a strong identity and now collides with SIM cards and simulation games. And because it needs nothing but paper and six dots, there was never a commercial product — or a marketing budget — to push it. When classic games moved online, attention went to chess, Go, and later Sudoku and Wordle, while Sim stayed tucked away in university pages and puzzle collections.

From Sim to Triad

The game is brilliant; the name and presentation held it back. A modern, polished edition can fix that without touching what makes Sim special — the objective, the mathematics, and the elegance all stay the same. Triad is that edition — Sim’s modern home, built to introduce the game to people who would love it but have never heard of it. More than fifty years on, it remains one of the most elegant strategy games most people have never played.

References

• Simmons, G. J., “The game of SIM,” Journal of Recreational Mathematics 2, 1969, p. 66.
• Mead, E., Rosa, A., Huang, C., “The Game of Sim: A Winning Strategy for the Second Player,” Mathematics Magazine, Vol. 47, No. 5 (1974), pp. 243–247.
• Gardner, M., “Mathematical Games,” Scientific American, January 1973.