Jigsaw puzzle makers face a COVID-induced shortage of product, NPR reported. Prices and complications of manufacturing puzzles are causing demand to outpace supply. Meanwhile, the classic “slider puzzle” has a secret math-based solution.
According to NPR, the jigsaw puzzle industry has faced such a surge in sales that it’s been difficult to keep items in stock. “Whether it’s farm animals, fine art, landscapes, or ladies in fancy hats at a cake contest, the market for jigsaw puzzles has exploded,” the article said. Not only are more people at home looking for things to do, but international business has been affected as well. It used Puzzle Huddle, a company owned by Matthew Goins, as a microcosm of the issue that sprang from the pandemic.
“Puzzle Huddle designs and licenses artwork in the U.S. and the puzzles are manufactured in China. Goins says they started seeing delays back in January before the pandemic hit the U.S.”
All puzzles require patience and brainpower, but some classic puzzles can also be solved by using math. Even the well-known “slider puzzle,” in which a picture is jumbled with just one free space and must be shifted around to make a picture, is rooted in mathematics.
Slider puzzles involve a picture cut up into square pieces that are usually movable tiles locked onto a board. One piece is missing, meaning you can only slide one puzzle piece at a time to rearrange the puzzle and make the picture look proper. They’re based on a 19th-century puzzle called the Fifteen Puzzle.
“In its classic form, you have the numbers one through 15 in a four by four square and a blank space that allows the squares to move,” said Dr. Arthur T. Benjamin, Professor of Mathematics at Harvey Mudd College. “The solution is pretty intuitive; you basically get the numbers in the right place one at a time with just an occasional twist.”
The first step in solving a Fifteen Puzzle is to get numbers one through four into their proper places. Don’t worry about any other number yet. Once one through four have been placed, they won’t move again for the rest of the puzzle, leaving you with 11 pieces to worry about instead of 15. The second row—numbers five through eight—are the same. And again, once they’re set, they never move again.
“The next tiles we place are not nine and 10, but nine and 13,” Dr. Benjamin said. In other words, the final two rows of leftmost tiles. “Next we want to move the 10 and 14 to their final positions. Finally, we’re just left with the 11, 12, and 15 in some order. If the original puzzle was solvable, then they can simply be rotated to reach the goal position.”
Dr. Benjamin said that world chess champion Bobby Fischer could consistently solve the Fifteen Puzzle in under 25 seconds.
With a slider puzzle, the same logic can be applied if you can figure out which tiles belong in which positions. By sorting the top two rows first, then the leftmost row of tiles, then the next leftmost row, you can skip the classic headache that comes from having two misplaced tiles near the top and everything else settled.
Dr. Arthur T. Benjamin contributed to this article. Dr. Benjamin is Professor of Mathematics at Harvey Mudd College. He earned a PhD in Mathematical Sciences from Johns Hopkins University in 1989.