A tale of touching tubes

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

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

D. Mackenzie

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.