// P92 (***) Von Koch's conjecture.
//     Several years ago I met a mathematician who was intrigued by a problem
//     for which he didn't know a solution.  His name was Von Koch, and I don't
//     know whether the problem has been solved since.  [The "I" here refers to
//     the author of the Prolog problems.  <PMG>]
//
//     d e-f      1 5-4  * *1*
//     | |        | |    6 2
//     a-b-c  ->  7-3-6  *4*3*
//     |          |      5
//     g          2      *
//
//     Anyway the puzzle goes like this: Given a tree with N nodes (and hence
//     N-1 edges), find a way to enumerate the nodes from 1 to N and,
//     accordingly, the edges from 1 to N-1 in such a way, that for each edge K
//     the difference of its node numbers is equal to K.  The conjecture is that
//     this is always possible.
//
//     For small trees the problem is easy to solve by hand.  However, for
//     larger trees, and 14 is already very large, it is extremely difficult to
//     find a solution.  And remember, we don't know for sure whether there is
//     always a solution!
//
//     Write a function that calculates a numbering scheme for a given tree.
//     What is the solution for the larger tree pictured below?
//
//     i g d-k   p
//      \| |     |
//       a-c-e-q-b
//      /| |   |
//     h b f   m