# Seven Touching Cylinders

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## Theorem

It is possible to arrange $7$ identical cylinders so that each one touches each of the others.

The cylinders must be such that their heights must be at least $\dfrac {7 \sqrt 3} 2$ of the diameters of their bases.

## Proof

It remains to be proved that the heights of the cylinders must be at least $\dfrac {7 \sqrt 3} 2$ of the diameters of their bases.

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## Historical Note

Martin Gardner originally raised the similar Six Touching Cylinders, which was an old puzzle, in his *Mathematical Games* column in *Scientific American*.

It was originally written in the context of cigarettes.

On its publication, he received letters from about $15$ readers who had discovered this $7$-cylinder solution.

He credited George Rybicki and John Reynolds for the diagram.

## Sources

- 1965: Martin Gardner:
*Mathematical Puzzles and Diversions*: $12$: Nine More Problems: Answers: $1$. - 1968: Henry Ernest Dudeney:
*536 Puzzles & Curious Problems*... (previous) ... (next): Answers: $312$. The Six Submarines