Using LINQ to solve puzzles

The diagram below provided by Luke shows a mobile. It consists in a bunch of weights (A-M) hanging from a system of bars. Each weight has an integer value between 1 and 13, and the goal is to figure out what each weight must be for the the diagram below to balance correctly as shown:

                          |
                          |
              +--+--+--+--+--+--+--+
              |                    |
              |                    |
           +--+--+--+--+--+        |
           |     L        M        |
           |                       |
  +--+--+--+--+--+--+     +--+--+--+--+--+
  H              |  I     |  J        K  |
                 |        |              |
        +--+--+--+--+--+  |     +--+--+--+--+--+
        E              F  |     G              |
                          |                    |
              +--+--+--+--+--+  +--+--+--+--+--+--+
              A              B  C                 D

The puzzle can be solved relatively easily using a LINQ query:

var solveForWeights =
  from a in Enumerable.Range(1, 13)
  join b in Enumerable.Range(1, 13) on 4 * a equals b
  from c in Enumerable.Range(1, 13)
  join d in Enumerable.Range(1, 13) on 5 * c equals d
  from e in Enumerable.Range(1, 13)
  join f in Enumerable.Range(1, 13) on 3 * e equals 2 * f
  join g in Enumerable.Range(1, 13) on 2 * (c + d) equals 3 * g
  from h in Enumerable.Range(1, 13)
  join i in Enumerable.Range(1, 13) on 3 * h - 2 * (e + f) equals 3 * i
  from j in Enumerable.Range(1, 13)
  join k in Enumerable.Range(1, 13) on 3 * (a + b) + 2 * j - 2 * (g + c + d) equals k
  from l in Enumerable.Range(1, 13)
  join m in Enumerable.Range(1, 13) on (h + i + e + f) - l equals 4 * m
  where (4 * (l + m + h + i + e + f) == 3 * (j + k + g + a + b + c + d))
  select new { a, b, c, d, e, f, g, h, i, j, k, l, m,
               Total = a + b + c + d + e + f + g + h + i + j + k + l + m };

solveForWeights.ToList().ForEach(result => Console.WriteLine(result));

This is an interesting approach and an innovative use of LINQ! See the details in Luke's post.