# Sparse Rulers

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A sparse ruler is a rod of integer length with a minimal number of marks so that all distances 1 to can be measured. Many lengths, such as 36, have unique rulers with a twin by subtracting marks from , as seen here:

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Contributed by: Ed Pegg Jr (June 2019)

Open content licensed under CC BY-NC-SA

## Details

Snapshot 1: a simple case with extra marks at 1, 2 and 4 on a ruler of length 7; all the lengths from 1 to 7 can be measured as , , , , , and .

## Snapshots

## Permanent Citation