Playing a game to get to 60 first

Question

If we play a game in which Player 1 picks a number 1-11, and then player 2 can add 1-11 to that (i.e. player 1 picks 5, player 2 can add to make it 6-16), what is the strategy to win this game if Player 1 wants to make 60?

The answer is: Let them go first so they will say anything between 1-11, then you say 12, then they go, then you say 24, then they go, then you say 36, then they go, then you say 48, then they have to go for a number between 49-59 and then you say 60.

I see why this is the answer and it seems very simple after seeing it, but I don't know how to go about getting this answer myself. Would it involve some sort of backward induction?

Note: Not too sure about the Tag for this question.

Thanks

Answer 1

Backwards induction is correct. You accurately note that you need them to pick their last number in the range [49,59]. That means you have to pick 48. In order to pick 48, you need them to pick a number in the range [37,47]. That means you need to pick 36. And so on.

Answer 2

This is a two-person game of complete information. You solve it by backward induction. If you can get the game to 49 through 59, you will win. So in your penultimate move, you want to force that outcome. Hence you will say 48.

Okay, that means you will win, if you can get the game to 37 through 47. So you must say 36, as soon as you can.

You come up with the numbers 24 and 12 by induction.

By the way, there is an old bar game with match sticks called 1-3-5-7 that works exactly in this manner.