procedure TForm1.Button1Click(Sender: TObject);
var
  IntSum: Integer;
  IntArray: array[1..4] of Integer;

  function GetIntFromRange(Low, High: Integer): Integer;
  begin
    Result := Low + Random(High - Low + 1);
  end;

begin
  IntSum := 0;
  IntArray[1] := GetIntFromRange(2, 7);
  IntSum := IntSum + IntArray[1];
  IntArray[2] := GetIntFromRange(Max(2, 8 - IntArray[1]), 7);
  IntSum := IntSum + IntArray[2];
  IntArray[3] := GetIntFromRange(Max(2, Min(7, 15 - IntSum)), Max(2, Min(7, 20 - IntSum)));
  IntSum := IntSum + IntArray[3];
  IntArray[4] := 22 - IntSum;
end;