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Interpretable Learning to Rank (LtR) is an emerging field within the research area of explainable AI, aiming at developing intelligible and accurate predictive models. While most of the previous research efforts focus on creating post-hoc explanations, in this paper we investigate how to train effective and intrinsically-interpretable ranking models. Developing these models is particularly challenging and it also requires finding a trade-off between ranking quality and model complexity. State-of-the-art rankers, made of either large ensembles of trees or several neural layers, exploit in fact an unlimited number of feature interactions making them black boxes. Previous approaches on intrinsically-interpretable ranking models address this issue by avoiding interactions between features thus paying a significant performance drop with respect to full-complexity models. Conversely, ILMART, our novel and interpretable LtR solution based on LambdaMART, is able to train effective and intelligible models by exploiting a limited and controlled number of pairwise feature interactions. Exhaustive and reproducible experiments conducted on three publicly-available LtR datasets show that ILMART outperforms the current state-of-the-art solution for interpretable ranking of a large margin with a gain of nDCG of up to 8%.