The Princess and Some Roses

Abstract: Impartial combinatorial game theory will be explained briefly and used to analyze two impartial take-away heap games, ”The Princess and the Roses” (P&R) and ”The Princess and Two Roses” (P2R). P2R is a variant of P&R that only allows taking one chip from two different heaps. Sprague-Grundy values are calculated by computer for positions up to six heaps and thirty chips in each heap for both games. From patterns out of the data achieved, P-positions are described for any amount of chips in five heaps or less for P&R and P2R. In P2R the pattern of P-positions, for five heaps where the smallest heap is odd, is not proven and is therefore stated as a conjecture.