Toucanwin is exactly what it sounds like – solving a jigsaw puzzle in a particular way, in a specific number of moves.
“It’s not easy,” said Roberttie Johnson, retired professor of mathematics at Eastern Oregon University, and author of Toucan-Piece Puzzles in Mathematical Success, when I asked him how difficult the puzzles could be. “There are some really clever people who have mastered the game.”
Johnson is the author of numerous math books, and he said one of his favorites was his 2015 book, Toucan-Piece Puzzles in Mathematics. I loved the title of his earlier book, Toucan-P (2001), after the logo of the Royal Canadian Mint, and his earlier stage name.
I knew this stage name from childhood, but had forgotten all about it, and nearly missed its significance in this discussion. The punch line, of course, being his surname—Toucan, which he has long had in his name.
Here is an article on the hit Broadway musical “Million Dollar Quartet”, based on the recording of the famous 1955 concert in Memphis. It was from this recording that Johnson discovered the title of his book.
His first book was Toucan Win, Toucan Win II, Toucan Win II Plus, and Toucan Win Plus Plus. Toucan Win is still a seller, despite the competition from newer jigsaw puzzles.
In Toucanwin III, written for the 2007 World Puzzle Championship, he solved a 36-piece jigsaw puzzle in 28 moves using a strategy called “staying with the options.” He used the same strategy for this jigsaw, but set the option apart by removing four pieces after a certain number of moves.
“That was the signature move in Toucan-Win III,” Johnson said.
In Toucan Win IV, he did a version of “distraction jigsaw puzzle” – one in which each jigsaw piece has two colors, so that a jigsaw puzzle has 60 pieces (32 colors).
To solve the problem in his book, he used the colored pieces, each with two colors, and marked the color of an available spot in each of the 54 box sizes. By counting the number of colored pieces of an available color, he determined which box size would have an available spot.
“That way you could move through the entire set and look for colors and colors,” Johnson said.
The positions of all the colors and combinations are marked in this diagram.
Then he counted the number of consecutive moves to each box – the number of moves to that box could be calculated as well, by noting the number of open spaces, and finding the number of colors that could fill those open spaces.
“Once you know that number, you know how many moves it would take to find all those colors,” Johnson said.
When he put the puzzle back together, he found one square of the large box with no color, as indicated by the mark below.
This creates two different possibilities: either the puzzle can be completed, or the puzzle could be completed in more moves, in which case he would add six more spaces. If he reached a point in which the puzzle could be completed in fewer moves, then he could solve the puzzle in fewer moves.