Q#1: A pair of positive integers x0 and y0 are selected and further pairs are generated according to the following rule: After the values of xn and yn have been found, a coin is tossed. If it lands heads, then xn+1 = xn −1 and yn+1 = xn. Otherwise, if it lands tails, then xn+1 = yn − 2 and yn+1 = xn + 1. The process ends when a non-positive value of x or y is generated. Is there a choice of initial values for x0 and y0 and sequence of coin toss outcomes for which the sequence of x’s and y’s does not terminate?