How would I set up a test to determine if a magic square was actually
magic or not using visual basic 6 ?

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Request for Question Clarification by xemion-ga on 02 Sep 2002 23:24 PDT

An easier way of doing this might be some advanced Excel macro.  Would
you consider such an answer?  That allows the basic Visual Basic math
computations without creating a whole data entry interface.

xemion-ga

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Clarification of Question by makossa-ga on 03 Sep 2002 03:31 PDT

No, I need to work in visual basic 6. What I am looking for is the
correct syntax needed to work through a for..next loop that
will add the rows, columns, and diagonals of a magic square,  and
compare it against a boolean, to determine if the square is
truely magic or not.

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Clarification of Question by makossa-ga on 03 Sep 2002 03:34 PDT

I will actually be entering magic squares into this test, one at a
time to test them.

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Clarification of Question by makossa-ga on 03 Sep 2002 14:30 PDT

Thank you, but I don't even know what delphi is. I am teaching myself
visual basic 6. I have no other programming languages.I guess I'm
looking for help on a fairly empirical level, in VB6.

Here's a Delphi solution which might help you get started.

type
  TMatrixRow = array of Integer;
  TMatrix = array of TMatrixRow;

function IsMagicSquare(const Matrix: TMatrix): Boolean;

var
  I: Integer;    // row index
  J: Integer;    // column index
  Sum: Integer;  // ideal sum of cells in any row, column, or main diagonal
  Temp: Integer; // actual sum of cells
  N: Integer;    // number of rows

begin
  Result := True;

  N := Length(Matrix);

  // matrix must be square
  for I := 0 to High(Matrix) do
    if (Length(Matrix[I]) <> N) then
      begin
      Result := False;
      Break;
      end;

  Sum := N * (N * N + 1) div 2;

  // check row sums
  if (Result) then
    for I := 0 to (N - 1) do
      begin
      Temp := 0;

      for J := 0 to (N - 1) do
        Inc(Temp, Matrix[I, J]);

      if (Temp <> Sum) then
        begin
        Result := False;
        Break;
        end;
      end;

  // check column sums
  if (Result) then
    for J := 0 to (N - 1) do
      begin
      Temp := 0;

      for I := 0 to (N - 1) do
        Inc(Temp, Matrix[I, J]);

      if (Temp <> Sum) then
        begin
        Result := False;
        Break;
        end;
      end;

  // check diagonal #1
  if (Result) then
    begin
    Temp := 0;

    for I := 0 to (N - 1) do
      Inc(Temp, Matrix[I, I]);

    if (Temp <> Sum) then
      Result := False;
    end;

  // check diagonal #2
  if (Result) then
    begin
    Temp := 0;

    for I := 0 to (N - 1) do
      Inc(Temp, Matrix[I, N - I - 1]);

    if (Temp <> Sum) then
      Result := False;
    end;
end;

procedure Demo;

var
  Matrix: TMatrix;

begin
  SetLength(Matrix, 3, 3);

  Matrix[0, 0] := 8;
  Matrix[0, 1] := 1;
  Matrix[0, 2] := 6;

  Matrix[1, 0] := 3;
  Matrix[1, 1] := 5;
  Matrix[1, 2] := 7;

  Matrix[2, 0] := 4;
  Matrix[2, 1] := 9;
  Matrix[2, 2] := 2;

  if (IsMagicSquare(Matrix)) then
    ShowMessage('Yes')
  else
    ShowMessage('No');
end;

In my example code, you can replace the one occurence of

High(Matrix)

with

(N - 1)

to make it clearer.

I found your question quite interesting so I tried it out... here's my
solution.. tested on 3x3 matrix but not guaranteed to work on higher
ones tho (it should be). Also I've written it on ASP (VBScript) but I
guess VB should be the same.

  function checkMagicSquare (mx, dimension)
    dim compareSum,correctSum, i
    correctSum = dimension * (dimension * dimension + 1) / 2

    ' first check to make sure the size of the array is correct
    checkMagicSquare = ((ubound(mx, 1) = dimension - 1) AND
(ubound(mx, 2) = dimension - 1))

    if checkMagicSquare then
    ' Check the fist diagonal
      compareSum = 0
      for i = 0 to dimension - 1
        compareSum = compareSum + mx(i,i)
      next
      checkMagicSquare = (compareSum = correctSum)
    end if

    if checkMagicSquare then
    ' Check the second diagonal
      compareSum = 0
      for i = 0 to dimension - 1
        compareSum = compareSum + mx(i,dimension - 1 - i)
      next
      checkMagicSquare = (compareSum = correctSum)
    end if

    if checkMagicSquare then
    ' Check each row
      for i = 0 to dimension - 1
        compareSum = 0
        if not checkMagicSquare then exit for
        'If the previous test fails, ignore the rest of the tests
        for j = 0 to dimension - 1
          compareSum = compareSum + mx(i,j)
        next
        checkMagicSquare = (compareSum = correctSum)
      next
    end if

    if checkMagicSquare then
    ' Check each column
      for i = 0 to dimension - 1
        compareSum = 0
        if not checkMagicSquare then exit for
        'If the previous test fails, ignore the rest of the tests
        for j = 0 to dimension - 1
          compareSum = compareSum + mx(j,i)
        next
        checkMagicSquare = (compareSum = correctSum)
      next
    end if
  end function

  Dim mx3x3(2,2)
  mx3x3(0,0) = 8
  mx3x3(0,1) = 1
  mx3x3(0,2) = 6
  mx3x3(1,0) = 3
  mx3x3(1,1) = 5
  mx3x3(1,2) = 7
  mx3x3(2,0) = 4
  mx3x3(2,1) = 9
  mx3x3(2,2) = 2