Numbers in a circle
Source: Problem 4, Centroamerican Olympiad 2009
October 7, 2009
combinatorics proposedcombinatorics
Problem Statement
We wish to place natural numbers around a circle such that the following property is satisfied: the absolute values of the differences of each pair of neighboring numbers are all different.
a) Is it possible to place the numbers from 1 to 2009 satisfying this property
b) Is it possible to suppress one of the numbers from 1 to 2009 in such a way that the remaining 2008 numbers can be placed satisfying the property