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About special rulers

Source: Romania TST 2 2009, Problem 1

May 4, 2012
combinatorics proposedcombinatorics

Problem Statement

We call Golomb ruler a ruler of length ll, bearing k+1≥2k+1\geq 2 marks 0<a1<…<ak−1<l0<a_1<\ldots <a_{k-1}<l, such that the lengths that can be measured using marks on the ruler are consecutive integers starting with 11, and each such length be measurable between just two of the gradations of the ruler. Find all Golomb rulers.
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