Ionizing radiation induces DNA double-strand breaks (DSB), which interact pairwise to produce chromosome aberrations. There have long been two main competing theories of such pairwise DSB-DSB interactions. The "classical" theory asserts that an unrepaired DSB makes two ends that separate within the cell nucleus, with each end subsequently able to join any similar (nontelomeric) end. The "exchange" theory asserts that at a DSB the chromatin does not separate completely; rather the DSB ends remain associated until repair, or an illegitimate recombination involving another DSB, occurs. The DSB-DSB interaction mechanism was tested by using three-color fluorescence in situ hybridization to paint chromosomes and observe "three-color triplets": three broken and misrejoined chromosomes having cyclically permuted colors. We observed 18 "three-color triplets" in 2000 cells after 2.25 Gy of gamma-irradiation. On the exchange model in its standard form such three-color triplets cannot occur, so this model is inconsistent with the observations. On the classical model, formalized as a discrete time Markov chain embedded at the transitions of a continuous time Markov chain, the frequency of occurrence of three-color triplets can be computed by Monte Carlo simulations. The number of three-color triplets predicted mathematically by the classical model was found to be slightly larger than the observed number. Thus our data, together with our computer simulations, exclude the standard form of the exchange model but are compatible with the classical model. The results are also compatible with other, more complicated models.