yours question is slightly unclear.....,if u need to count all possible number of triangle,why i need to divide in 3 parts...,what i think u r looking for is dividing in 3 parts which give me maximum number of possible triangle....if it is so, divide in more or less equal parts... i.e..floor(n/3),floor(n+1/3),floor(n+2/3)..number of ways to do so will be then(n!/(1st term)!(2nd)!(3rd term)!(3-(n%3))!)..take one element from each floor(n/3) elements of each group ....,if you are asking something different please clarify the question more.....!!
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