### Author Topic: 每周一题: 桌面上的表 (11/29/04 -- 12/05/04)  (Read 8275 times)

#### 万精油

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• Posts: 1831
##### 每周一题: 桌面上的表 (11/29/04 -- 12/05/04)
« on: 十一月 29, 2004, 09:58:05 am »

« Last Edit: 十月 08, 2009, 09:38:03 pm by 万精油 »

#### idiot95

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##### 每周一题: 桌面上的表 (11/29/04 -- 12/05/04)
« Reply #1 on: 十一月 29, 2004, 10:35:08 am »
For each watch, (a circle O), denote the center of the table as C, at any time t, the end of the minute hand is T1, consider T2 which is the position of this hand at time t+30s. T2 will be the other end of the diameter passing OT1. Apparently (hehe..) CT1+CT2 > CO*2. (draw a symmetric image of CT1T2 w.r.t. O)

Then you add all of these kind of things up (as the watches are all good, so t+30s would be the same for all of them, i.e. they reach their T2 at the same time). The sum of the T1 group + the sum of T2 > 2*the sum of TO group. Then at least one of them is greater than TO group.

#### 万精油

• Hero Member
• Posts: 1831
##### 每周一题: 桌面上的表 (11/29/04 -- 12/05/04)
« Reply #2 on: 四月 08, 2005, 09:06:36 am »
I just digged one of my old articles up, it is related to clocks. I thought people who's interested in this forum will also be interested in reading such articles. Here it is

http://www.zhipingyou.com/qqsh/index.php?topic=303

My other writings (old and new) will appear gradually in the mother forum of the above link, which is the following

http://www.zhipingyou.com/qqsh/index.php?board=7
« Last Edit: 三月 31, 2011, 01:44:12 pm by 万精油 »