[icWasya]

Как-то так

Код:

procedure TForm1.Button1Click(Sender: TObject);
begin
  Memo1.Lines.Clear();

  GenString();
end;

// вычисление строки
function Calc100Sum(S:string):Integer;
var
  Temp:Integer;
  Op:Char;
  I:Integer;
  procedure CalcOp;
  begin
   if Op = '=' then Result:=Temp;
   if Op = '-' then Result:=Result - Temp;
   if Op = '+' then Result:=Result + Temp;
 end;
begin
  Result:=0;
  Temp:=0;
  Op:='=';
  for I:= 1 to Length(S) do
  begin
    case S[i] of
      '0'..'9': Temp:=Temp*10 + Ord(S[i])-Ord('0');
       '+','-': begin CalcOp(); Temp:=0; Op:=S[i]; end;
    end;
  end;
  CalcOp();

end;


// генерация всевозможных строк
procedure TForm1.GenString();
var
  I1,I2,I3,I4,I5,I6,I7,I8:Integer;
  S:string;
  Sum:Integer;
const
  Ops:array[0..2] of string=('','+','-');
begin

  for I1:=0 to 2 do
  for I2:=0 to 2 do
  for I3:=0 to 2 do
  for I4:=0 to 2 do
  for I5:=0 to 2 do
  for I6:=0 to 2 do
  for I7:=0 to 2 do
  for I8:=0 to 2 do
  begin
    S:='1'
       + Ops[I1] + '2'
       + Ops[I2] + '3'
       + Ops[I3] + '4'
       + Ops[I4] + '5'
       + Ops[I5] + '6'
       + Ops[I6] + '7'
       + Ops[I7] + '8'
       + Ops[I8] + '9';

     Sum := Calc100Sum(S);

    if Sum = 100 then
      Memo1.Lines.Add(S+' = 100');

  end;
end;