Mathematicians find way to put seven cylinders in contact without using their ends
ATLANTA — Over 50 years ago, the popular mathematics writer Martin Gardner and readers of Scientific American pondered a challenge: Can you place seven cigarettes so that each cigarette touches every one of the others?
Gardner had a solution, but it was unsatisfying because some of the cigarettes’ ends touched others’ sides. If that end of a cigarette were lit, it would no longer touch its neighbor. Mathematicians wondered whether an arrangement could be found with only side-to-side contacts using infinitely long cylinders.
On March 20 at Gathering 4 Gardner, a conference to celebrate Gardner, mathematician Sándor Bozóki of the Hungarian Academy of Sciences in Budapest presented a solution of this more challenging problem, which was also posted online last summer at arXiv.org. Bozóki and colleagues used three months of computer time to solve 20