constructing nondegenerate polygon from n sides by making cuts We are given the length of n sticks and we need to make a polygon using all the n sticks. If it is impossible to construct a nondegenerate polygon from the given n sticks, we can cut one or more sticks into two parts (length of cut part need not be integer).
How many cuts do we need to make for given n values ?
 3(n=3)

 1 2 3

We cannot construct a triangle so we try to make a square and we cut stick 3 into two parts of length 1 and 2.
thus answer is 1.
How can we solve this for any n numbers given to us ?
 A: You always need at most one cut. The sticks can be used to form a polygon as long as there's no stick that's as long as all the others put together. If originally there is such a stick, just cut it in half.
A: You might need 2 cuts in 2 special cases:


*

*You have a single stick: you must chop twice to make a triangle

*You have 2 sticks of exactly equal length, in this case it doesn't matter if you cut one of the sticks in exactly 1/2 or make one side longer, you won't be able to construct a polygon without also cutting the other stick. 
But for most cases: 


*

*make 1 cut if the longest(sticks) $\ge$ sum(rest of sticks) 

*Otherwise, 0 cuts are necessary.

A: I just got the correct solution in some discussion forum of another platform
For a polygon  to be non degenerate polygon,each side of the polygon must satisfy this condition   sum=a$1$ +a$2$+........+a$n$
and a$i$<1/2(sum) wher  1<=i<=n
.Here a$1$,a$2$..... ,a$n$ are the lengths of sticks given to us and every time the above condition a$i$<1/2(sum) is violated for any i,increase the count by 1.
