Logic as a Matrix for Bierce's Thought: "The Gem Puzzle"

One of the most unusual and atypical non-fictional articles Ambrose Bierce ever wrote appeared in the 22 May 1880 issue of the Argonaut, a San Francisco literary journal. Titled simply "The Gem Puzzle,"¹ it occupies almost half a page and is wholly devoted to the analysis and solution of the mathematical novelty variously known as the "Gem Puzzle" or the "Fifteen Puzzle." There is no doubt that Bierce was the author, for the initial "B." appears at its end, which Bierce used distinctively when he did not sign his name. Bierce apparently never returned to the subject, nor did he ever again write an article with such a level of technicality.

What keeps "The Gem Puzzle" article from being a mere curiosity is its significance as a demonstration of the analytical and organizational powers of Bierce's mind. Although his fame justly rests on his short fiction, particularly his stories of the Civil War and the wickedly cynical definitions of his Devil's Dictionary, in fact the greatest bulk of his writings over the course of more than forty years he spent as a journalist consists of the largely uncollected columns of his running commentary on local, national, and international events. Under different names ("The Town Crier," "Comments, Mostly Frivolous, on the Fad of the Day," "The Passing Show," "The Bald Campaigner," but most extensively and famously "Prattle: A Transient Record of Individual Opinion") Bierce's feature columns appeared prominently once or twice a week in the San Francisco Examiner and in various other periodicals (e.g., newspapers owned by the Hearst syndicate) which published his work. Although Bierce tended to be self-deprecating about his comments and opinions, his uncollected columns contain some of the most thoughtful and incisive analyses of current events in American journalism.

At the time of the composition of "The Gem Puzzle," Bierce was still editing as well as writing for the Argonaut. It is not surprising for the Argonaut to have printed the article for, in addition to Bierce's role in deciding what would go into the journal, the Gem Puzzle was an enormously popular fad that was then sweeping the country, and so the topic was of certain interest. But it is somewhat surprising that Bierce undertook to write about it himself. His formal education after public school consisted of his attendance, at least in 1859 when he was seventeen, at the Kentucky Military Institute. Hitherto, the main influence of that school has always been assumed to be training in topographical engineering, for once Bierce received a commission in the Union army, he was assigned to prepare maps in advance of battles.² With the authorship of this article, however, it is now apparent that Bierce had also acquired some significant, though not professional, mathematical skills. The concise but rather dense style of this article also suggests the model of a formal academic paper. If so, it was a reversion to an early influence that he had left behind when he adopted a brisker expository style more appealing to readers.

The Gem Puzzle that Bierce analyzed remains widely recognizable today as one of the so-called sliding block puzzles encountered during one's childhood. The version Bierce probably used³ consisted of fifteen removable blocks labeled 1 through 15 that were slid around on a 4 × 4 grid. According to the directions on the box, one was to "[p]lace the Blocks in the Box irregularly, then move until in regular order." What made the puzzle so maddening—and interesting—was that for certain "irregular placements of the blocks" it seemed impossible to move the blocks back to the regular order shown in Figure 1 below. Of particular note, starting from the solution, it seemed impossible to slide the blocks around in such a way that in the end blocks 1 through 13 were in their original positions but blocks 14 and 15 were swapped (see the right side of Figure 1). That this task really is hopeless can be rigorously proved using mathematics, although the arguments required are quite...