Finite number of moves to yield a configuration
Source: Germany Bundeswettbewerb Mathematik 2008, Round 1, Problem 4
July 19, 2008
analytic geometryalgebra unsolvedalgebra
Problem Statement
In a planar coordinate system we got four pieces on positions with coordinates. You can make a move according to the following rule: You can move a piece to a new position if there is one of the other pieces in the middle of the old and new position. Initially the four pieces have positions . Given a finite number of moves can you yield the configuration \{(0,0), (1,1), (3,0), (2, \minus{} 1)\} ?