A easy math question.

Exclude the longest diagonals(10 lines) , a diagonal have and only have 1 diagonal parallel to it.So the number of ways of a pair of parallel diagonals can be chosen= (The numbers of the diagonals - 10) / 2= [(20C2 - 20) - 10] / 2= 80 ways


2010-11-13 12:11:59 補充：
Corrections :

Case 1 :
Consider a diagonal which is across 2 continous sides , there are 8 other diagonals parallel to it. So the number of ways of a pair of parallel diagonals can be chosen from
these 9 diagonals = 9C2 , there are 20 diagonals across 2 continous sides ,
(20/2) (9C2) = 360 ways.

2010-11-13 12:12:28 補充：
Case 2 :
Consider a diagonal which is across 3 continous sides , there are 7 other diagonals parallel to it. So the number of ways of a pair of parallel diagonals can be chosen from these 8 diagonals = 8C2 ,

2010-11-13 12:12:36 補充：
there are also 20 diagonals across 3 continous sides ,
(20/2) (8C2) = 280 ways.

So the number of ways of a pair of parallel diagonals can be chosen

= 360 + 280 = 640 ways.