---
tag: 2B4A8GQMKN
kind: concept
name: Sparse ruler
aliases: [optimal-ruler-conjecture]
sources:
  - wikipedia: en:22809664@r1322859680
    locator: Sparse ruler
    note: adopted
    mention: wikipedia://en/22809664
    sections: [Summary]
same_as:
  wikidata: Q7573797
  wikipedia: Sparse ruler
inventory: [HAZ248ZNDM]
---

## Summary

A **sparse ruler** is a ruler in which some of the distance marks may be missing. More abstractly, a sparse ruler of length $L$ with $m$ marks is a sequence of integers $a_1, a_2, ..., a_m$ where $0 = a_1 < a_2 < ... < a_m = L$. The marks $a_1$ and $a_m$ correspond to the ends of the ruler. In order to measure the distance $K$, with $0\le K\le L$ there must be marks $a_i$ and $a_j$ such that $a_j-a_i=K$.