Small-angle X-ray scattering (SAXS) measurements reveal a striking difference in intermolecular interactions between two short highly charged peptides - deca-arginine (R10) and deca-lysine (K10). Comparison of SAXS curves at high and low salt concentration shows that R10 self-associates, while interactions between K10 chains are purely repulsive. The self-association of R10 is stronger at lower ionic strengths, indicating that the attraction between R10 molecules has an important electrostatic component. SAXS data are complemented by NMR measurements and potentials of mean force between the peptides, calculated by means of umbrella-sampling molecular dynamics (MD) simulations. All-atom MD simulations elucidate the origin of the R10 - R10 attraction by providing structural information on the dimeric state. The last two C-terminal residues of R10 constitute an adhesive patch formed by stacking of the side chains of two arginine residues and by salt bridges formed between the like-charge ion pair and the C-terminal carboxyl groups. A statistical analysis of the Protein Data Bank reveals that this mode of interaction is a common feature in proteins.