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{\bf Adrian Dumitrescu and Minghui Jiang}
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{\bf On a Covering Problem for Equilateral Triangles}
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Let $T$ be a unit equilateral triangle, and $T_1,\dots,T_n$ be $n$
equilateral triangles that cover $T$ and satisfy the following two
conditions: (i)~$T_i$ has side length $t_i$ ($0<t_i<1$); (ii)~$T_i$ is
placed with each side parallel to a side of $T$.  We prove a
conjecture of Zhang and Fan asserting that any covering that meets the
above two conditions (i) and (ii) satisfies $\sum_{i=1}^n t_i \geq 2$.
We also show that this bound cannot be improved.

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