Perfect Packings of Squares Using the Stack-Pack Strategy

   Abstract. We consider the problem of packing an infinite set of square tiles into a finite number of rectangular boxes. We introduce a simple packing strategy that we call stack-pack. Using this strategy, we prove that if 1/2 < t < 2/3, then the squares of side n ^-t , for positive integers n , can be packed into some finite collection of square boxes of the same area ζ(2t) as the total area of the tiles.