高中

Hello everybody!

After doing several Tournament of Towns (TOT) problems on this forum, I am wondering if anyone can give me more information about the competition:

1. When is the competition?
2. Where do we take it?
3. What are the levels and their difficulties?

Feel free to type in chinese! Any additional comments are welcome too.

x^3-3x-4=0之三根為a,b,c,求(a-b)(b-c)(c-a)之值為?

何為"封閉表達式"??

我想請問一下,參加下面的奧林匹亞研討會有要考試嗎?我怕哪種題目我半題都做不出來,怕被笑ㄝ!＞＜
但是我還是想參加，只是在這理想確認一下而已，怕會去那裡丟臉，如果只是聽他們討論就沒問題了，但如果要考試或來解題我就會怕怕的ㄝ．．．
知道相關的人能幫幫說明嗎？？謝謝～

任給在球面{(x,y,z) | x^2+y^2+z^2=1}上n個點.
證明: 這些點之間距離的平方之總和小於或等於n^2

這題困擾了我真的好久好久了
希望只要有一點點的想法就可以打上來

1.1*3*5*7*9.......*2005)/1004*1005*1006........*2006=？
2.[1/(1*2)+1/(3*4)+1/(5*6).......+1/(2005*2006)]/
1/(1004*2006)+1/(1005*2005)+.......+1/(2006*1004)]
=
3.證：n的5次方減n 恆為30的倍數
4.證:Sm=Sn 則Sm+n=0