先到 50
First to 50
题目详情
鲍勃和吉尔正在玩一场竞争性游戏，他们轮流喊出数字。第一个叫出50号的人获胜。游戏规则如下：
开始游戏的玩家必须喊出1到10之间的整数
每个新呼叫的号码必须比前一个号码大至少 1 且不超过 10。
如果鲍勃和吉尔都发挥最佳状态，鲍勃是否应该首先赢得比赛？
Bob and Jill are playing a competitive game in which they take turns calling out numbers. The first person to call the number 50 wins. The rules of the game are as follows:
The player who starts the game must call out an integer between 1 and 10
Each new number called must be larger than the previous number by at least 1 and by no more than 10.
If Bob & Jill both play optimally, should Bob want to go first to win the game?
解析
为了解决这个问题，我们要逆向思考。
- 我们知道如果鲍勃能够跟注，他就会赢得比赛 号码 50。如果 Bob 拨打 50，这意味着 Jill 一定拨打了 数量在 40 - 49 之间。
- Bob 可以拨打的下一个最大号码是 39。如果他拨打 39，Jill 必须 拨打 29 - 38 之间的号码。
- Bob 可以拨打的下一个最大号码是 28。如果他拨打 28，Jill 必须 拨打 18 - 27 之间的号码。
- Bob 可以拨打的下一个最大号码是 17。如果他拨打 17，Jill 必须 拨打 7 - 16 之间的号码。
- Bob 可以拨打的下一个最大号码是 6。 因此，Bob 应该想要开始游戏以及他想要开始的数字。 应该选择以6开始游戏。
Original Explanation
To solve this problem, let’s work backwards.
- We know that Bob will win the game if he is the one that is able to call the number 50. If Bob calls 50, this means that Jill must have called a number between 40 - 49.
- The next highest number that Bob can call is 39. If he calls 39, Jill must call a number between 29 - 38.
- The next highest number that Bob can call is 28. If he calls 28, Jill must call a number between 18 - 27.
- The next highest number that Bob can call is 17. If he calls 17, Jill must call a number between 7 - 16.
- The next highest number that Bob can call is 6. Therefore, Bob should want to start the game and the number that he should choose to start the game with is 6.