{A tetrahedron (triangular pyramid) has
 1,3,6,10, etc in successive layers.  A two layer
 tetrahedron has 4 marbles, a perfect square.  What is
 the next larger with a total that is a perfect square?}
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{generated code snipped here}.

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procedure TForm1.SolveBtnClick(Sender: TObject);
{User clicked solve button}
{pretty much self commenting - isn't Delphi great?}
const maxmarbles=1000;
var {the 4 variables}
PyramidNbr  :integer; {also nbr of marbles on a side} 

  layer  :integer; {nbr of marbles in layer}

  total  :integer; {total in pyramid}

  root :integer;  {square root of total}
begin
layer:=0;
  total:=0;
  PyramidNbr:=0;
repeat
inc(PyramidNbr);
    layer:=layer+PyramidNbr;
    total:=total+layer;
    root:=trunc(sqrt(total));
until ((PyramidNbr>3) and  (root*root=total)) or (PyramidNbr>maxMarbles);

If root*root=total
then  showmessage ('Side '+inttostr(PyramidNbr)
              +', Layer '+ inttostr(layer)
              +', Total '+inttostr(total)
              +', Sqrt(Total) '+inttostr(root))
else Showmessage('No solutions with sides less than '+inttostr(maxmarbles));
end;

end.