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A easy math question.
發問:
In how many different ways can a pair of parallel diagonals be chosen in a regular 20-sided polygon?
最佳解答:
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.
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