// to search for the solution we must
// find the 126 possible selections for X
// and determine the set difference set Y. We then must test
// the various orders of X and Y. In total we
// end up checking about 10^6 combinations.
static void Main()
{
List <int> t = new List <int>()
{
1, 2, 3, 4, 5, 6, 7, 8, 9, 10
};
for (int i = 1; i <= 9; ++i)
{
for (int j = i + 1; j <= 9; ++j)
{
for (int k = j + 1; k <= 9; ++k)
{
for (int m = k + 1; m <= 9; ++m)
{
for (int n = m + 1; n <= 9; ++n)
{
// for each set of i,j,k,l,m, and n
// we want to check the linear solution
// using all possible permutations of these numbers
// as well as the possible permutations of the difference
// set with [1,10]
List <int> dSet = new List <int>();
List <int> X = new List <int>();
X.Add(i);
X.Add(j);
X.Add(k);
X.Add(m);
X.Add(n);
foreach (int x in t)
{
if (x != i &&
x != j &&
x != k &&
x != m &&
x != n)
{
dSet.Add(x);
}
}
// now that we have the difference set, we need
// to operate on all the permutations of these numbers
// and compute the constant we need for our computations
int constant = 0;
foreach (int item in dSet)
{
constant += item;
}
foreach (int item in X)
{
constant += 2 * item;
}
constant /= 5;
List <List <int> > permsX = Permutator.getIntPermutations(X);
List <List <int> > permsDSet = Permutator.getIntPermutations(dSet);
foreach (List <int> u in permsDSet)
{
foreach (List <int> v in permsX)
{
if (u[0] + v[0] + v[1] == constant &&
u[1] + v[1] + v[2] == constant &&
u[2] + v[2] + v[3] == constant &&
u[3] + v[3] + v[4] == constant &&
u[4] + v[4] + v[0] == constant)
{
// print the solution sets, but print
// the solution in the format as described in the problem description
int min = 10, index = 0;
for (int x1 = 0; x1 < u.Count; ++x1)
{
if (u[x1] <= min)
{
min = u[x1];
index = x1;
}
}
for (int x1 = 0; x1 < u.Count; ++x1)
{
int x2 = (x1 + index) % u.Count;
Console.Write(u[x2] + "," + v[x2 % 5] + "," + v[(x2 + 1) % 5] + "; ");
}
Console.WriteLine();
}
}
}
}
}
}
}
}
// Keep the console window open in debug mode.
Console.WriteLine("Press any key to exit.");
Console.ReadKey();
}
