Winning Strategy with Addition to X=0 Problem:
Two players play the following game. Initially, X=0. The players take turns adding any number between 1 and 10 (inclusive) to X. The game ends when X reaches 100. The player who reaches 100 wins. Find a winning strategy for one of the players.
This is my solution, which hopefully you can comment on and verify:
If I have 100 and win, then I must have had a number between 90 and 99 on my last turn. On the turn before that, my opponent must have 89 because then we will have a number between 90 and 99 on our last turn. On the turn before that, I want a number between 79 and 88 so that I could force my opponent to have 89 on their turn. On the turn before that, my opponent should have a 78 so that I can get to a number between 79 and 88. On the turn before that, I want a number between 68 and 77 so that I could force my opponent to have a 78 sum on his/her turn. Continuing in this manner,
we see that our opponent must have the sums on his/her turn: 89,78,67,56,45,34,23,12, and 1.
As the winner, I want to be in the following intervals of sums at each of my turns: 90-99,79-88,68-77,57-66,46-55,35-44,24-33,14-22,2-11.
Thus, the winning strategy is to go first and add 1 to X=0. Then, no matter how our opponent plays, we can always choose a number between 1 and 10 to force our opponent to have one of the losing positions above and so I will win...

Community wiki answer so the question can be marked as answered:
Yes, you are correct. Also note the links in the comments for further reading about similar games and a systematic way of solving them.
