---
tag: PREBFXNC7M
kind: concept
name: Perfect ruler
sources:
  - wikipedia: en:2515712@r1372901448
    locator: Perfect ruler
    note: adopted
    mention: wikipedia://en/2515712
    sections: [Summary]
same_as:
  wikidata: Q7168097
  wikipedia: Perfect ruler
inventory: [P7NKQS516F]
---

## Summary

A **perfect ruler** of length $\ell$ is a ruler with [[integer|0C4JS9RF5M]] markings $a_1=0 < a_2 < \dots < a_n=\ell$, for which there exists an integer $m$ such that any positive integer $k\leq m$ is uniquely expressed as the difference $k=a_i-a_j$ for some $i,j$. This is referred to as an $m$-perfect ruler.