The ability to associate words is an important cognitive skill. In this study we investigate different methods for representing word associations in the brain, using the Remote Associates Test (RAT) as a task. We explore representations derived from free association norms and statistical n-gram data. Although n-gram representations yield better performance on the test, a closer match with the human performance is obtained with representations derived from free associations. We propose that word association strengths derived from free associations play an important role in the process of RAT solving. Furthermore, we show that this model can be implemented in spiking neurons, and estimate the number of biologically realistic neurons that would suffice for an accurate representation.