Anyone who’s ever moved furniture knows how frustrating it can be to get big items around tight corners, but surely you haven’t been struggling with a sofa for more than 50 years. Mathematicians have, though.
The so-called “moving sofa problem” has been causing plenty of mathematical headaches since it was formally published by Leo Moser in 1966. It sounds simple enough: What’s the largest sofa that will fit around a corner? To be more specific, “largest” means the greatest seating area, the hallway is a meter (3.3 feet) wide, the corner is 90 degrees, and the sofa must be pulled, not inclined or turned upright.
Although some promising solutions have been proposed over the years — Joseph Gerver’s 1992 answer is the current favorite — to actually solve the problem, you have to demonstrate with an irrefutable mathematical proof that a particular sofa is the largest possible. And no one has done that … yet.
Of course, mathematicians refuse to let the sofa problem lie and have even come up with variants to make matters more complicated. One such variant asks for the optimal shape of a sofa that must fit through a hallway with two right angles: one on the right and one on the left.
One suggestion: If you choose to tackle any of the sofa problems, take a nice nap first.
The magic of math:
There’s a 50-50 chance that two people in a room of 23 will share a birthday and a 99 percent chance of such an occurrence in a room with 75 people.
It’s a virtual certainty that the order of cards in a well-shuffled deck has never existed before.
The only number in the English language that is spelled with the same number of letters as its name is “four.”