Rick and his cousin are playing a game where they pick up colored sticks. Rick currently has 11 points and likes to pick up the pink sticks, earning 7 points every turn. His cousin just lost all her points on the previous turn, and has a strategy to catch up by getting all the purple ones, earning 18 points per turn. In a certain number of turns, the score will be tied. How many points will they each have? How long will that take?
To catch up to 11 points, Rick's cousin needs to earn 11 points. Since she earns 18 points per turn by picking up purple sticks, it will take her 11/18 = <<11/18=0.6111111111111112>>0.61... turns to catch up to Rick's score.
Since they can't split turns, it will take Rick's cousin 1 turn to catch up to him. At the end of this turn, Rick will have 11 + 7 = <<11+7=18>>18 points
Rick's cousin will have 0 + 18 = <<0+18=18>>18 points.
Thus, they will both have 18 points when they tie. Answer: \boxed{18}.