On an infinite “squared” sheet six squares are shaded as in the diagram. On some squares there are pieces. It is possible to transform the positions of the pieces according to the following rule: if the neighbour squares to the right and above a given piece are free, it is possible to remove this piece and put pieces on these free squares.
The goal is to have all the shaded squares free of pieces. Is it possible to reach this goal if
(a) In the initial position there are 6 pieces and they are placed on the 6 shaded squares?
(b) In the initial position there is only one piece, located in the bottom left shaded square?
https://cdn.artofproblemsolving.com/attachments/2/d/0d5cbc159125e2a84edd6ac6aca5206bf8d83b.png
(M Kontsevich, Moscow) combinatoricscombinatorial geometryinfinite board