title: How to find one hamiltonian path in cube((2n)^3)?
body: <p>I solve acm-icpc problem a kind of graph theory.</p>
  
  <blockquote>
    <p>Traveling Spiders is a logical puzzle that needs a sequence of
    systematic choices among many alternatives. The puzzle assumes a
    geometric object whose surface is partitioned into a set of areas
    called cells that are usually congruent, or very similar in their
    shapes and sizes. A spider may move around freely on the surface of
    the object, but, can move forward from a cell to only one of its
    neighboring cells in each step. Now, given some pairs of male and
    female spiders, initially positioned all in different cells, we want
    to find a set of paths that, respectively, leads each male spider to
    his partner. The only condition is that every cell of the object must
    be visited once and only once by a male spider during their traversal.</p>
  </blockquote>
  
  <p>the cube exists in the space [0, 2n] x [0, 2n] x [0, 2n], and n can be 2 &lt;= n &lt;= 50.</p>
  
  <p>we have to find one hamiltonian path when I game two position start from A to B.</p>
  
  <p>and print all of path(1 0 1 -> 1 0 3 -> .... -> 3 1 4).</p>
  
  <p>My friend said it is can't see general answer. because It is quite difficult to exact planar graph. and It cannot judge hamiltonian path or not.</p>
  
  <p>how I can find hamiltonian path in general case?;</p>