Mathematicians have found a way to simultaneously touch 7 cylinders

More than 50 years ago, Martin Gardner, the author of popular articles on mathematics in Scientific American magazine, offered his readers the task: “Can you place seven cigarettes in such a way that each of them is in contact with everyone else?”

Gardner himself found a solution, but it did not satisfy him, because the bases of some cylinders were in contact with the side surfaces. He wanted a solution in which the cylinder bases would not be used. That is, for the case with infinitely long cylinders.

Half a century later, on March 20, 2014, at the Gathering 4 Gardner conference in honor of Gardner, mathematician from the Hungarian Academy of Sciences Sándor Bozóki announced the same solution. Last summer, it was published in a scientific article on ArXiv.

Bozoki and colleagues spent three months of computer time searching for a good configuration. They compiled a system of polynomial equations describing the position of the generators of cylinders in three-dimensional space.

The number of possible configurations was estimated at about 121 billion, and it was not possible to verify all of them. But scientists were lucky: after checking 80 million configurations, two solutions were found.



Both results were checked using the AlphaCertified program to prove that the solutions found were not the result of some computer rounding errors. Scientists even made a real physical model of wood. However, in the manufacture of wooden parts there are even more errors than there may be rounding errors in computer calculations, so this model is made solely for demonstration purposes.