Pentomino (1965) — How Solomon Golomb's Five-Square Shape Became Tetris

Introduction

What I wish to exhume this time is not a game but a book. In 1965, the American mathematician Solomon W. Golomb (1932-2016) published Polyominoes. The first edition came bundled with a set of plastic pieces: all twelve shapes formed by joining five unit squares edge to edge, shapes later known as pentominoes.

The book itself has the modest appearance of a mathematics text. What interests me is the sheer reach of its contents, tracing back to a 1907 English newspaper puzzle column and forward to a Soviet computer screen in 1984, and on to today's shelf of puzzle games.

In this essay I trace the years from 1953, when Golomb gave the shape its name, through 1957, when Martin Gardner carried it to the world, to 1975, when a Russian translation appeared, and on to 1984, when Alexey Pajitnov drew Tetris out of it. I want to confirm, from history's side, why a five-square shape traveled so far.

1965, an impression of the book Polyominoes (illustration, AI-generated)

The Context of the Era

Golomb was born in 1932 in Baltimore, Maryland. An engineer by training, he earned his bachelor's degree from Johns Hopkins University and a doctorate in mathematics from Harvard in 1957. His specialty was coding theory and number theory, but it was his after-hours work in recreational mathematics that made his name widely known.

In 1953, in a talk to the Harvard Mathematics Club, he systematically introduced shapes formed by joining unit squares edge to edge. He is said to have named the five-square shapes 'pentominoes' as a play on 'domino' (two squares). The following year, 1954, he published a paper formally coining the word 'polyomino' as a back-formation from 'domino'.

The shape itself is older still. The earliest known reference to this style of puzzle is said to appear in Henry Dudeney's The Canterbury Puzzles of 1907 (the very book covered in this site's separate piece 'Dudeney, 1907'). Golomb himself, in his book, relates an anecdote that an ancient Go master had already noticed the twelve patterns five stones can form on a Go board — suggesting that interest in the shape predates his own naming by a good deal.

In May 1957, Martin Gardner covered pentominoes in his 'Mathematical Games' column in Scientific American. A shape born in a single Harvard lecture thus reached the hands of ordinary readers. From a lecture to a magazine column to a Russian translation (illustration, AI-generated)

Mechanics

The rule of pentominoes is simple. Shapes formed by joining five unit squares edge to edge number exactly twelve, once mirror images and rotations are treated as identical. Using these twelve pieces to tile rectangular boards of 6x10, 5x12, 4x15, or 3x20 without gaps, or to tile a board while leaving a hole of a specified shape, is the basic 'packing' game of pentominoes.

In his 1965 book, Golomb went so far as to explain exhaustive-search methods for these twelve-piece combinations and combinatorial tools for counting the total number of tilings. It is this book's achievement to have elevated an idle pastime into a mathematics textbook.

In a 2024 interview, Alexey Pajitnov said the pentomino sets he owned came in two kinds: 'a more modern Japanese version' and 'a traditional Russian set.' Taking the twelve wooden pieces out of the box, arranging them into free shapes, and then packing them back into the rectangular box — a back-and-forth that could take an experienced player 30 to 40 minutes — was, by his own account, a puzzle he had enjoyed for years.

A diagram of twelve pieces tiling a 6x10 rectangle (illustration, AI-generated)

Legacy

In 1975, Golomb's book was published in the Soviet Union as Полимино (Polymino), translated by I. Yaglom and issued by the Mir publishing house; this edition additionally included papers by Golomb and David Klarner. Nine years later, in 1984, a young computer scientist named Alexey Pajitnov, working at a computing research institute in Moscow, began experimenting with moving shapes on an Electronika 60 — an experimental machine with neither graphics nor sound — drawing on pentomino memories from his own childhood.

Pajitnov himself, in a 2024 interview, stated plainly that 'the main inspiration for Tetris came from the game Pentominoes.' He recalls simplifying the five-square shapes into four-square ones, and that while building the rotation routine and watching a shape turn on the screen, the idea struck him that the game could be played in real time. This is the moment at which pentominoes, as a plaything, were recast as falling blocks on a computer screen.

The pentomino shape itself did not vanish into Tetris's shadow, either. Tiling problems remain a subject of research in computational geometry and combinatorial optimization to this day, and Golomb's book continues to be cited in papers dealing with polyomino tiling. A single shape has managed to survive simultaneously in a toy box, an academic journal, and a home game console.

From the 1965 book to the 1984 falling-block well (illustration, AI-generated)

References

Sources consulted for this article:

・Wikipedia: Solomon W. Golomb (dates, career, the 1953 naming, mentions of influence on Tetris)

・Wikipedia: Polyominoes: Puzzles, Patterns, Problems, and Packings (1965 Scribner's edition, 1975 Russian translation, 1994 second edition)

・Wikipedia: Pentomino (definition of the shapes, the twelve forms)

・Thought Economics: Tetris Creator & Leaders on Gaming's Greatest Success (2024 interview in which Alexey Pajitnov himself states pentominoes as the main inspiration for Tetris)

・NPR: Happy Birthday, Tetris. 35 Years Later You're As Addictive And Tetromino-y As Ever (on the relationship between pentominoes and Tetris)

・Wikipedia: Henry Dudeney (author of The Canterbury Puzzles, 1907)

・Wikipedia: The Canterbury Puzzles

・ETH Library: Polyominoes (on the 1953 Harvard lecture)

・Wikipedia: Tetris (1984 development on the Electronika 60)

Closing

Let us count the years it took for one book to travel the world. Twelve years from the 1953 lecture to the 1965 publication, ten more to the Russian translation, and nine more before Pajitnov turned it into Tetris — about thirty-one years in all. Information that circles the globe in weeks today once had to cross the Atlantic and the Urals riding on the heavy medium of a printed book.

What I want to stress is that what Pajitnov 'invented' was not the act of stacking blocks itself, but the addition of rotation and falling time to a back-and-forth motion — taking pieces out, scattering them, packing them back — that already existed in a toy. Seen as a historian would see it, Tetris is not a miracle born from nothing, but the next move placed atop a long lineage of a five-square shape.

Whenever a modern puzzle game deals in rearranging shapes or tiling space, I believe some trace of this 1965 book's shadow still lingers in its handling.

Still one book on the shelf, sixty years on (illustration, AI-generated)