A perfect ruler of length ℓ {\displaystyle \ell } is a ruler with integer markings a 1 = 0 < a 2 < ⋯ < a n = ℓ {\displaystyle a_{1}=0<a_{2}<\dots <a_{n}=\ell } , for which there exists an integer m {\displaystyle m} such that any positive integer k ≤ m {\displaystyle k\leq m} is uniquely expressed as the difference k = a i − a j {\displaystyle k=a_{i}-a_{j}} for some i , j {\displaystyle i,j} . This is referred to as an m {\displaystyle m} -perfect ruler.
A perfect ruler of length ℓ {\displaystyle \ell } is a ruler with integer markings a 1 = 0 < a 2 < ⋯ < a n = ℓ {\displaystyle a_{1}=0<a_{2}<\dots <a_{n}=\ell } , for which there exists an integer m {\displaystyle m} such that any positive integer k ≤ m {\displaystyle k\leq m} is uniquely expressed as the difference k = a i − a j {\displaystyle k=a_{i}-a_{j}} for some i , j {\displaystyle i,j} . This is referred to as an m {\displaystyle m} -perfect ruler.
Source: Wikipedia "Perfect ruler" · CC BY-SA 4.0
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