  We provide a winning strategy for sums of games of MARK-t, an impartial game
played on the nonnegative integers where each move consists of subtraction by
an integer between 1 and t-1 inclusive, or division by t, rounding down when
necessary. Our algorithm computes the Sprague-Grundy values for arbitrary n in
quadratic time. This solves a problem posed by Aviezri Fraenkel. In addition,
we characterize the P-positions and N-positions for the game in mis\`ere play.
