 <p>The answer is 1/4. Here is the explanation.</p> <p>Let x is the length of the leftmost stick and y is the length of the rightmost stick. Then the middle stick has length n-x-y, if the original stick's length was n.</p> <p>The possible values for x,y are those for which:</p> <ol> <li>x > 0</li> <li>y > 0</li> <li>x + y &lt; n</li> </ol> <p>In the plane Oxy this is equivalent to say that the point (x,y) lies within the triangle with vertices (0, 0), (n, 0), (0, n).</p> <p>Now these three numbers (x, y, n-x-y) form a triangle if all of the three are satisfied:</p> <ol> <li>x + y > n - x - y &lt;=> x + y &lt; n/2</li> <li>x + (n - x - y) > y &lt;=> y &lt; n/2</li> <li>y + (n - x - y) > x &lt;=> x &lt; n/2</li> </ol> <p>Again in the Oxy plane these are satisfied when the point (x,y) lies within the triangle with vertices (0, n/2), (n/2, n/2), (n/2, 0).</p> <p>The area of this triangle is a quarter of the area of the (0, 0), (n, 0), (0, n) triangle, since it's the 'middle' triangle (whose vertices are the midpoints) of the bigger one.</p> <p>Here is a simple C# program to verify the answer:</p> <pre><code>Random r = new Random(); int count = 0, total = 0, tries = 1000000; double x, y; for (int i = 0; i &lt; tries; i++) { x = r.NextDouble(); y = r.NextDouble(); if (x + y &gt; 0.5 &amp;&amp; x &lt; 0.5 &amp;&amp; y &lt; 0.5) ++count; if (x + y &lt; 1.0) ++total; } Console.WriteLine((double)count / total); </code></pre>