THE FIFTEEN PUZZLE
“Do you know the game called the Fifteen Puzzle?” asked the man, who had introduced himself simply as “Mr. Smith.” Jule replied that he didn’t think so. “It was invented around 1870 by Sam Loyd,” the man went on, “one of America’s greatest puzzlists, and at the time it became very popular, much as Rubik’s cube did a century later.”
Jule remembered his fascination with Rubik’s cube as a teenager. The twenty-six brightly colored little cubes he had endlessly rotated searching for the elusive solution, a configuration with a single color on each of the cube’s six faces. He also recalled wondering how many different arrangements were possible. Johanna, his twin sister, believed that the number of combinations was infinite, and also that once properly scrambled it was impossible to restore the cube to its original position. He knew that she was wrong on both counts, but was unable to prove his point back then. Not until many years later, long after he had forgotten all about the game and his fascination with it, did he come across the answer in one of the dozens of mathematical articles that Rubik’s invention had spawned. “There are exactly 43, 252, 003, 274, 489, 856, 000 different configurations, not infinitely many,” he had triumphantly announced to Johanna. But she would not quite concede defeat. “Well,” she had said after a short moment of reflection, “such a big number is almost infinity.”
The man reached into one of his pockets and produced a small wooden square with numbers on it. There was something vaguely familiar about the object but Jule could not quite tell what it was.