In 1901 the American puzzle manufacturer Sam Lloyd offered a puzzle. It requires reconstructing a square in a minimum of pieces, starting from a scooped shape. The mathematicians quickly took up the challenge and several proposals were made. They offer designs in 6 and then 5 pieces, but no one can go below that.
The world of science then tries several approaches to succeed in cutting this shape into only 4 pieces and putting them together to form a perfect square. Sam Lloyd, at the origin of this problem, will propose a simple solution, which will remain for years as the only 4 piece design of this puzzle.
But more than twenty years later, a mathematician named Henry Dudeney demonstrated that Sam Lloyd’s square is in reality a rectangle. He will then estimate that a four-piece solution is simply impossible.
An unsolvable problem ?
The problem will then span the ages and the 20th century. It will be studied by many scientists, mathematicians and students, without any finding a 4-piece solution. We will have to wait until May 28, 2024, 123 years after this problem was first stated, to find a solution. It was puzzle creator Vesa Timonen who discovered it and shared it on social networks.
In order to achieve the expected result, Timonen played with the rules a little. In fact, he overturned a coin, to present it on its hidden side. A unique proposal, which allows the problem to be solved in just 4 parts. An interesting solution, which, he explains, does not really come from him and is far from unanimous among scientists. Some believe that by modifying the pieces of the puzzle in this way, Timonen transgressed the rules given by Sam Lloyd more than 120 years ago.
Computers to the rescue of the human brain
To solve this puzzle, the puzzle designer used an algorithm. He entered the two expected shapes into a computer program and let the machine work, which worked by random cutting. In her article returning to the subject, Vesa Timonen nevertheless explains that she checked many solutions manually, because there is always a risk of machine error.
He assures that by further refining his algorithm, in particular by adding the fact of making fractal or curved cuts, he could find other solutions to assemble this square into 4 pieces. So far, he has discovered around a hundred solutions in 5 pieces (there were only around ten models before he looked into the subject).
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