The Moving Sofa Problem: 50 Years Unsolved

5 min readAug 11, 2022
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It was 1966 when renowned mathematician Leo Moser asked a simple question that completely confused the world of mathematics. Moser likely came up with the problem after struggling to move his sofa into a new house and thinking he could solve it simply using mathematics. After a while, however, he was stuck. He then published the problem in an article to recruit other mathematicians to his aid.

Moser had asked a very simple question that affects our everyday lives. After all, most of us have struggled to move a sofa from one room to another at least once. This goes to show the originality of mathematicians, however. While everyone struggles with moving sofas, mathematicians try to solve the problem permanently in order to not come across it in the future.

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In its simplest form, Moser’s problem is as follows: In a two-dimensional “L” shaped corridor with a width equal to that of the width of the sofa, what is the maximum area the sofa can occupy while still being able to turn the L shaped corner?I will simplify the question further. Firstly, imagine the corridor as two-dimensional. Although this goes against real-life intuition, it is necessary for the problem. Below is an illustration of the corridor in question.By the way, after publishing this article, I learned that Douglas Adams used this problem for his book Dirk Gently's Holistic Detective Agency! It seems a nice read!
A unit length L-hallway

While some sofas can make the turn quite easily, others will simply not be able to make it. Moser asks us simply the maximum size of a sofa that needs to make the corner, and he honestly doesn’t know. Also, because we imagine this in the two-dimensional plane, we need to find the object’s area instead of its volume.

First, we will brainstorm the problem and then look at some proposed solutions. To come up with our own solution, we need to think simply. For example, if we have a square sofa with a length of 1cm, we find…


Math Teacher. Content Curator. Soccer player. Maradona fan. Mostly write about the lectures I love to learn better.

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