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Lines tangent to $2n-2$ spheres in ${\mathbb R}^n$

Lines tangent to $2n-2$ spheres in ${\mathbb R}^n$

We show that for $n \ge 3$ there are $3 \cdot 2^{n-1}$ complex common tangent lines to $2n-2$ general spheres in $\mathbb {R}^n$ and that there is a choice of spheres with all common tangents real.