We consider a sufficient condition on the number of hidden units in multilayer perceptrons for two-category classification (TCC) problems. Multilayer perceptrons considered here have one hidden layer and units take binary values. The outputs of the input units are represented by vertices of a hypercube. A sufficient number of hidden units for TCC problems is estimated by studying the number of vertices belonging to the same category and being placed between two parallel hyperplanes. We show that 2[(I(A)+2)/3]-1 or 2[(I(A)+2/3] hidden units are sufficient in the case of I(A)=3n+1, n=O,1,2,…, or I(A)≠3n+1, respectively, where I(A) means the number of input patterns belonging to category A and [x] is the largest integer not larger than x. We also show that the above result is the best one when we estimate the number of hidden units by the number of vertices placed between two parallel hyperplanes.