History
John Spilsbury's "Europe divided into its kingdoms, etc." (1766). He created them for education, and called them “Dissected Maps”.
History of the Jigsaw Puzzle
Jigsaw puzzles were originally made by painting a picture onto a piece of wood, and then cutting that picture into small pieces. Modern day jigsaw puzzles are usually made of cardboard cut into oddly shaped, usually interlocking, pieces.
The jigsaw puzzle has a long and distinguished history. John Spilsbury, a mapmaker from London is credited with selling the first jigsaw puzzles around 1760. It is said that, in order to teach his children geography, he took a map of Europe and pasted it onto a piece of wood. He cut around the borders of each of the European countries, gave his children the pieces all mixed up, and asked them to make a map of Europe. Word spread of his invention, and by 1820 it had become a very popular educational aid.
History of Squaring the Square
An interesting question can be asked: Is it possible to construct a square puzzle where each of the constituent tiles of the square are also squares, but where each of these squares is a different size. This is known as a perfect squared square ("PSS"). It was said to be impossible until this assertion was proved erroneous when a 55-square PSS was published by R. Sprague in 1939. Theophilus Harding Willcocks ("THW") discovered (in 1946) and subsequently published, a PSS with 24 squares, shown below. This was, for more than 30 years, the smallest and most widely known perfect squared square. On March 22 1978, A. J. W. Duijvestijn found by computer search a PSS having only 21 squares. This was subsequently proved to be unique and to have the lowest possible number of constituent squares, i.e., the PSS having the lowest possible order. A lot of other PSSs can be found in: Bouwkamp, C. J. and Duijvestijn, A. J. W. "Catalogue of Simple Perfect Squared Squares of Orders 21 Through 25.", Eindhoven Univ. Technology, Dept. Math, Report 92-WSK-03, Nov. 1992.
These perfect squared squares are an interesting way to make a jigsaw puzzle. As noted above, if the side length of the completed puzzle is known and if the edge length of each of the individual tiles is known, then we have important clues to help to solve the complete puzzle; now, however, because each square is a different size, the puzzle is quite to complete. There are many sums of side lengths that must equal the overall side length. This makes it quite a challenge to find the unique way they all fit together. Although there is only one unique solution to nearly every PSS jigsaw, obviously 90 degree rotations or a mirror image are trivial transformations of that unique solution and these are also solutions.
It is possible to search online for the solutions to these puzzles, but don't be tempted. It will take all the fun out of it
