Points on integer x-axis
Source: nigerian mathematics olympiad round 3 problem 3
February 21, 2020
combinatoricsanalytic geometry
Problem Statement
given any 3 distinct points on the integer coordinates of the x-axis,the following operation is allowed:A point say is reflected over another point say . Note that after each operation only one among three points is moved.
we perform these operations till 2 out of the 3 points coincide.
let denote the minimum number of operations before we are forced to stop.(this could happen in different ways).
show that there are at most coordinates that point could end up if we are forced to stop after operations