奥数之家
奥数论坛
简短留言
| 首页 | 竞赛大纲 | 优秀前辈 | 视频提示 | 专题讲座 | 论文锦集 | 综合训练 | 修身养性 | 家教平台 | 奥数论坛 |
 
The 18th Balkan Mathematical Olympiad
2001年第18届巴尔干地区数学奥林匹克
  1. If 2n - 1 = ab and 2k is the highest power of 2 dividing 2n - 2 + a - b then k is even.
  2. A convex pentagon has rational sides and equal angles. Show that it is regular.
  3. a, b, c are positive reals whose product does not exceed their sum.
    Show that a2 + b2 + c2 ≥ (√3)abc.
  4. A cube side 3 is divided into 27 unit cubes. The unit cubes are arbitrarily labeled 1 to 27 (each cube is given a different number). A move consists of swapping the cube labeled 27 with one of its neighbours. Is it possible to find a finite sequence of moves at the end of which cube 27 is in its original position, but cube n has moved to the position originally occupied by 27-n (for n = 1, 2, ... , 26) ?
点击此处查看相关视频讲解
在方框内输入单词或词组
建议使用:IE 6.0及以上版本浏览器。不支持 Netscape浏览器。 本站空间由北京师范大学提供
Copyright © 2005-2007 aoshoo.com All Rights Reserved 滇ICP备05000048号
MSN:shuxvecheng@hotmail.com QQ:316180036 E-mail:aoshoo@sina.com 电话:15810289082