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.
Cross-posted from http://linqinaction.net