Let r>1 be a rational number. Alice plays a solitaire game on a number line. Initially there is a red bead at 0 and a blue bead at 1. In a move, Alice chooses one of the beads and an integer k∈Z. If the chosen bead is at x, and the other bead is at y, then the bead at x is moved to the point x′ satisfying x′−y=rk(x−y).Find all r for which Alice can move the red bead to 1 in at most 2021 moves. number theorycombinatoricsconstruction