IMO 2011 simple solution or...

1)

A={ai,aj,ak,al}   ai<aj<ak<al,(ai+aj)/(ak+al),(aj+ak)/(aj+al) ,(ai+al)/(aj+ak)and(aj+ak)/(ai+al).

2) Strong Induction and contradiction Method.

3) f(x)=ff(x)=fffff(x)

  f(-1)=f(0)=0...f(-|x|)=0.

4) (n-i+1)*(i-1)!*(n-i)!

5)f(m)=f(n)

6) Too simple.

所有跟帖： 

• 4) Sigma(......) i from 1 to n. -jinjing- ♀ (0 bytes) () 08/01/2011 postreply 08:41:39

• 4)Too old to be fast, It should be (n+1)!/2 by recursive. -jinjing- ♀ (0 bytes) () 08/01/2011 postreply 14:01:06

• 1).....and (ai+al)/(aj+ak)or(aj+ak)/(ai+al). and changed to or. -jinjing- ♀ (0 bytes) () 08/01/2011 postreply 09:30:54