Many inference systems used for concept description logics are constraint systems that employ tableaux methods. These have the disadvantage that for reasoning with qualified number restrictions n new constant symbols are generated for each concept of the form (atleast n R C). In this paper we present an alternative method that avoids the generation of constants and uses a restricted form of symbolic arithmetic considerably different from the tableaux method. The method we use is introduced in Ohlbach, Schmidt and Hustadt (1995b) for reasoning with graded modalities. We exploit the exact correspondence between the concept description language ALCN and the multi-modal version of the graded modal logic K and show how the method can be applied to ALCN as well.