Salvage A Broken Stick

Exactly same way :)

The problem does not state very clearly what the probability distribution is of the breakage. However, it is perfectly reasonable to assume that the stick is broken at points $X$ and $Y$ where $X, Y$ are independent stochastic variables homogeneously distributed on $[0, L]$ .

Then Dipanjan's solution is correct. Not only did I end up with the same graph as he did, I also verified it by simulation. Here is my simulation pseudo code:

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x = random(0, L)           # choose breaking points
y = random(0, L)
if  x > y  then  swap(x, y)    # now x <= y

a = x
b = y - x
c = L - y                   # the lengths of the three pieces

u = min(a,b,c)
w = max(a,b,c)
v = a+b+c-u-w           # u, v, w are the lengths in ascending order

if  u + v > w  then  makes up a triangle

I consistently find values near 25%.

Ive got no idea :@

Shouldn't this be 100%? A single stick is broken into 3 different parts of random size. Under what circumstances will you not be able to form a triangle from these 3 parts together? I can't think of any.

Or have I not understood the question?