title: Algorithm for placement of 32 seeded players in a 128 person tournament
body: <p>I am trying to create a tennis tournament simulator, where the outcomes of the games are random (sort of). At Grand Slams there are 128 players, 32 of which are seeded. At the moment I am trying to place the seeds in the draw at the appropriate position. I have the generated strengths of the players according to a normal distribution (which will substitute for their rankings) and stored them in an ascending sorted std::array. I thought to simply represent the draw initially as <code>vector&lt;double&gt; Draw(128)</code>. Ideally I would have an algorithm to put each player in the proper position in the draw, but I haven't been able to come up with one yet, so I decided to just type in the positions into an array and select the appropriate array depending on how many players there are in the tournament. </p>
  
  <p>The positions are as follows: 0,127,95,32,64,96,31,63,16,112,79,48,15,111,80,47,41,72,8,119,23,104,55,87,71,39,24,7,56,88,103,120</p>
  
  <p>The first few terms of which in terms as multiples of 32 are: 0*32,4*32-1,3*32-1,1*32,2*32,3*32,1*32-1,2*32-1,0.5*32,3.5*32-1,2.5*32-1,1.5*32,0.5*32-1,3.5*32,2.5*32.</p>
  
  <p>I haven't figured out a pattern from this yet. Is there a known algorithm for this?</p>