论文部分内容阅读
1.是否存在正实数a使得不等式|cos x|+|cos ax|>sin x+sin ax恒成立?2.别佳和瓦萨在一个n×n的方格棋盘上玩游戏.开始时,除了一个角上的格为黑色以外,所有的格均为白色,在黑格中有一个“车”.由别佳开始,两人轮流将车沿水平或垂直方向移动若干格,车经过和到达的格立即变为黑色,车不能经过和到达黑格.当某人无法按规则移动车时,此人失败.游戏结束.问:谁有必胜策略?
1. Is there a positive real number a such that the inequality | cos x | + | cos ax |> sin x + sin ax is constant? 2. Beatrice and Vaasa play on an n × n chessboard. At the beginning, In addition to a corner of the grid is black, all the grid are white, there is a In the Haig from the good start, the two take turns moving the car along the horizontal or vertical direction of a number of grid, the car through And arriving grids turn black immediately, the car can not pass through and arrive at the Haig grid. When someone can not move the car according to the rules, the person fails. The game is over. Q: Who has the winning strategy?