91Ó°ÊÓ

"Escape of the clones" is a nice puzzle, originally proposed by Maxim Kontsevich. The game is played on an infinite checkerboard restricted to the first quadrant - that is the squares may be identified with points having integer coordinates \((x, y)\) with \(x>0\) and \(y>0 .\) The "clones" are markers (checkers, coins, small rocks, whatever... ) that can move in only one fashion \(-\) if the squares immediately above and to the right of a clone are empty, then it can make a "clone move." The clone moves one space up and a copy is placed in the cell one to the right. We begin with three clones occupying cells (1,1),(2,1) and \((1,2)-\) we'll refer to those three checkerboard squares as "the prison." The question is this: can these three clones escape the prison? You must either demonstrate a sequence of moves that frees all three clones or provide an argument that the task is impossible.