type
  TRandomValues = array[1..4] of Integer;

procedure GetRandomValues(out Values: TRandomValues);
var
  IntSum: Integer;

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

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

procedure TForm1.Button1Click(Sender: TObject);
var
  I, J: Integer;
  IntSum: Integer;
  Values: TRandomValues;
begin
  for I := 1 to 10000 do
  begin
    GetRandomValues(Values);

    IntSum := 0;
    for J := 1 to 4 do
    begin
      if (Values[J] < 2) or (Values[J] > 7) then
        raise Exception.CreateFmt('Value out of range! [%d,%d,%d,%d]',
          [Values[1], Values[2], Values[3], Values[4]]);

      IntSum := IntSum + Values[J];
    end;
    if IntSum <> 22 then
      raise Exception.CreateFmt('Sum differs from 22! [%d,%d,%d,%d]',
        [Values[1], Values[2], Values[3], Values[4]]);
  end;
end;