You are here

The 15 Puzzle: How It Drove the World Crazy

The Slocum Puzzle Foundation
Number of Pages: 

Probably everyone has seen a modern version of the "15 puzzle." As sold in drugstores today, the puzzle usually consists of 15 sliding plastic squares and one empty space, all within a square case, looking something like this:


















In the modern incarnation of this puzzle, the squares are usually attached to each other using a tongue-and-groove system, so they can be slid within the case but not removed from it. An earlier version of the 15 puzzle had the squares (or sometimes circles) made of separate blocks of wood or other material, which could be dumped out of the box and replaced in random order. In either case, solving the puzzle meant getting the blocks back into numerical order by sliding them within the case.

This simple puzzle enjoyed a huge wave of popularity in the United States in the years 1879–1880, and its popularity was not confined to the U.\S: if the 15 puzzle were a disease, we might say it there was something of a global pandemic in 1880, with cases documented as far away as Europe, Asia, New Zealand and Australia. Numerous variants on the 15 puzzle were manufactured, and it was mentioned in both high and low culture of the day: learned societies held lectures and published articles about the puzzle, popular newspapers carried stories on it, and it was featured in contemporary popular songs and theatrical performances. All this is documented, in sometimes excruciating detail, by Slocum and Sonneveld, who seem to have taken the approach "when in doubt, leave it in." That quibble aside, this is a beautifully-illustrated volume which contains a wealth of information of interest to fans of the puzzle as well as those interested in American popular culture and history.

Interestingly, the invention of the 15 puzzle has long been attributed to Sam Loyd, a chess champion, puzzle creator and author. Loyd was known to stretch the truth in his writings, for instance having claimed that tangrams were invented around 3000 BC (rather than the truer date of 1800 AD) and that he invented the dexterity puzzle "Pigs in Clover" (in which the goal is to get several balls to the center of a series of concentric circles) and the game Parcheesi. Slocum and Sonneveld convincingly demonstrate that his claim to have invented the 15 puzzle is yet another fabrication. In so doing, they provide an interesting case history of how an incorrect piece of information can become established as historical "fact."

Just in case you were wondering, the 15 puzzle can only be solved for half of the beginning positions, and the 15–14 position shown at the top of this article is one that cannot be solved. Perhaps this is the source of contemporary newspaper reports of people having been driven insane by the puzzle? Two articles proving that the 15–14 position (and similar positions in which two pieces are interchanged) were published in 1879–1880 and the proofs are presented in this book. Further explanation about the mathematics of the 15 puzzle is presented in an online article partly written by Slocum, available at

Jerry Slocum studied engineering, psychology and management in college and retired in 1993 from the position of Acting President of the Transport Sector of Hughes Aircraft, after a 38-year career with that company. He is a collector of mechanical puzzles and books about puzzles and has curated several museum exhibits about puzzles at sites including The Museum of Science and Industry in Chicago and The Science Center in Saint Louis. Slocum is founder of The Slocum Puzzle Foundation, whose purpose is to educate the public about puzzles and their history. As part of this mission, the Foundation has published six books, including The 15 Puzzle. More information about Slocum and his other publications is available from his website:

Sarah Boslaugh, PhD, MPH, ( ) is a Senior Statistical Data Analyst in the Department of Pediatrics at the Washington University School of Medicine in St. Louis, MO. She wrote An Intermediate Guide to SPSS Programming: Using Syntax for Data Management with Sage Publications in 2005 and is currently writing Secondary Data Sources for Public Health: A Practical Guide for Cambridge University Press. She is also Editor-in-Chief of The Encyclopedia of Epidemiology which will be published by Sage in 2007.

Date Received: 
Tuesday, May 30, 2006
Include In BLL Rating: 
Jerry Slocum and Dic Sonneveld
Publication Date: 
Sarah Boslaugh
Publish Book: 
Modify Date: 
Monday, July 10, 2006