## If a stick is broken at random into three pieces, what is the probability
## that the pieces can be put together in a triangle.

# counter
c = 0

# the number of trials
n = 1000

for(i in 1:n) {

	## a, b in (0, 1) and a < b
	v <- sort(runif(2));

	## calculate the length of each edge
	e <- c(v[1], v[2] - v[1], 1 - v[2]);

	## ensure e[1] < e[2] < e[3]
	e <- sort(e)

	## if they can be put together in a triangle
	if( e[1] + e[2] > e[3] ) {
		c = c + 1;
	}
}

print( c / n )