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A tale of touching tubes

Mathematicians find way to put seven cylinders in contact without using their ends

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4:13pm, April 2, 2014

NO IFS, ASHES OR BUTTS  Seven cylinders can each touch each other using only their sides, not their ends, mathematicians have discovered.

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

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