2019 point grasshoppers sit on a line, jumping around
Source: Tournament of Towns, Junior A-Level , Spring 2019 p2
May 9, 2020
Linegamegame strategycombinatoricsTournament of TownsToTKvant
Problem Statement
point grasshoppers sit on a line. At each move one of the grasshoppers jumps over another one and lands at the point the same distance away from it. Jumping only to the right, the grasshoppers are able to position themselves so that some two of them are exactly mm apart. Prove that the grasshoppers can achieve the same, jumping only to the left and starting from the initial position.(Sergey Dorichenko)