integers of form 81x+100y
Source: India tst 2003, p5
March 14, 2012
geometrygeometric transformationreflectioncombinatorics unsolvedcombinatorics
Problem Statement
On the real number line, paint red all points that correspond to integers of the form , where and are positive integers. Paint the remaining integer point blue. Find a point on the line such that, for every integer point , the reflection of with respect to is an integer point of a different colour than .