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 ?
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.
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$i$&lt;1/2(sum) wher  1&lt;=i&lt;=n
.Here a$1$,a$2$..... ,a$n$ are the lengths of sticks given to us and every time the above condition a$i$&lt;1/2(sum) is violated for any i,increase the count by 1.