The sofa problem that has puzzled science for 6 decades has been solved

For nearly 60 years, scientists have been unable to find a solution to a seemingly simple problem: Moving a sofa through a narrow L-shaped corner.

The problem was posed by Leo Moser , an Austrian-Canadian mathematician in 1966. Moser asked the question: What is the largest sofa and what shape can it be that can move through the right angle of an L-shaped hallway?

While this may seem simple, mathematically it is quite complex, as it involves both optimizing the area and the motion of the object.

The conundrum of moving a sofa through a tight corner has been solved (Photo: Getty).

If you have a square sofa, this will be a piece of cake. However, if the sofa is rectangular and made up of two squares, it will obviously get stuck.

Jineon Baek , a postdoctoral researcher in mathematics at Yonsei University (South Korea), is the one who found the answer to this difficult problem.

In a 100-page report published on November 24, Baek concluded that for a hallway with an assumed width of 1 unit, the maximum area of ​​an imaginary sofa that could be moved through the right angle would be 2.2195 units.

Before Baek, many mathematicians tried to solve this problem.

The solution to the sofa problem as discovered by mathematician Joseph Gerver (Photo: Live Science).

The first was John Hammersley , a British mathematician. It took him just two years after the problem was posed to discover that a rectangular sofa would not solve the problem.

Instead, the sofa had to be adjusted to form a semicircle. In this way, the sofa could have a maximum area of ​​2.2074 units, according to John Hammersley's calculations.

Nearly a quarter of a century later, Joseph Gerver, a mathematician from Rutgers University (USA), proved that the chair can reach an area range of 2.2195 to 2.37 units.

Of these, 2.37 is what Gerver considers the upper limit of what a chair can achieve. The sofa in Gerver's study is a U-shaped chaise longue, made up of 18 separate curves, allowing it to fold around corners without getting stuck.

However, Jineon Baek used computer-aided algorithms to refute Gerver's upper limit, thereby confirming that the largest chair with an area of ​​2.2195 units would need to move through an L-shaped corner that is 1 unit wide.