Brain Teaser: Constraint programming

Aaron Feng — Wed, 27 Jun 2007 22:15:00 -0500

I had never heard of constraint programming until a co-worker wrote the following problem on the board a few days ago:

A/BC + D/EF + G/HI = 1

All variables are unique digits from 1 - 9. Two variables next to each other is equivalent to 10 * var1 + var2. For example, if B = 2, C = 5 then the result is 10 * 2 + 5 which equals 25.

I decided to whip up a program to find out the answer.

class Program {
  static List<int> ints = new List<int>();
  static Random r = new Random();

  static void Main(string[] args) {
  double A = 0, B = 0, C = 0, D = 0, E = 0, F = 0, G = 0, H = 0, I = 0;

    while (!(((A / (10 * B + C)) + (D / (10 * E + F)) + (G / (10 * H + I))) == 1)) {
      GenerateUniqueInts();
      A = ints[0]; B = ints[1]; C = ints[2]; 
      D = ints[3]; E = ints[4]; F = ints[5]; 
      G = ints[6]; H = ints[7]; I = ints[8];
      }

    Console.WriteLine(String.Format("{0}/{1}{2} + {3}/{4}{5} + {6}/{7}{8} = 1", 
      A, B, C, D, E, F, G, H, I));
  }

  public static void GenerateUniqueInts() {
    ints.Clear();
    int value = (r.Next() % 9) + 1;

    while (!(ints.Count == 9)) {
      if (!ints.Contains(value)) ints.Add(value);
      value = (r.Next() % 9) + 1;
    }
  }
}

It only takes a couple of seconds for the program to figure out the answer. It turns out there is only one solution to this problem. However, on my first implementation I instantiated the Random object in the GenerateUniqueInts() method. For some reason, that can take up 10 minutes to run. If you are interested in the answer, try the program out.

Aaron Feng: Brain Teaser: Constraint programming

Brain Teaser: Constraint programming