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Perfect ruler

From Wikipedia, the free encyclopedia

A perfect ruler of length is a ruler with integer markings , for which there exists an integer such that any positive integer is uniquely expressed as the difference for some . This is referred to as an -perfect ruler.

An optimal perfect ruler is one of the smallest length for fixed values of and .

Example

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A 4-perfect ruler of length is given by . To verify this, we need to show that every positive integer is uniquely expressed as the difference of two markings:

See also

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This article incorporates material from perfect ruler on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.