this is problem strategy and choice problem pls help asap

20.6 Consider the game Turning Turtles, but in this case a player, having turned an O to an X in position n, may now, if he or she wishes, flip the turtle in position n - 1 (either from O to X or from X to O). Prove that this version of Turning Turtles is strategically the same as Two-Pile Nim