Alice and Bob are playing a game. The rule is as follows:. '). And the string contains at least one question mark.Alice hopes the final score of this game is as large as possible, but Bob hopes the final score is as small as possible. Assume they both play the game with the best strategy, what's the final score of this game?
Alice and Bob are playing a game. The rule is as follows: 1. Initially, they are given a string consisted of digits '0' sim ∼ '9' and question marks ('?'). And the string contains at least one question mark. 2. Each player takes turn alternately. If the number of question marks is odd, the turns start with Alice. Otherwise, the turns start with Bob. 3. In each turn, the player can choose one of the question marks and change it to any digits ('0' sim ∼ '9') he/she likes. 4. The game ends when all question marks are changed to digits. 5. Assume the number represented by the final string is x. If x is a multiple of 11, the final score of this game is x. Otherwise, the final score of this game is -x. Alice hopes the final score of this game is as large as possible, but Bob hopes the final score is as small as possible. Assume they both play the game with the best strategy, what's the final score of this game?
