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Perfect ruler

A perfect ruler of length ℓ{\displaystyle \ell } is a ruler with integer markings a1=0<a2<⋯<an=ℓ{\displaystyle a_{1}=0<a_{2}<\dots <a_{n}=\ell }, for which there exists an integer m{\displaystyle m} such that any positive integerk≤m{\displaystyle k\leq m} is uniquely expressed as the differencek=ai−aj{\displaystyle k=a_{i}-a_{j}} for some i,j{\displaystyle i,j}.

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