I suggest you the next game: I tell you a number between 1 and 5, and then you add to that number a number between 1 and 5 and tell it to me. I then add another number between 1 and 5 (not necessarily different from the precedents) t the number you told me, and tell it to you. So forth, until one of us reaches 45.
"No fair," you say, "you will always win". And you are in fact right. How come?
For the general case of allowed numbers between x and y (y>x>0) and destination N, find a strategy that you'll win the game for sure. You may choose who starts based on x, y, N.