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In this paper, we present a novel unsupervised domain adaptation (UDA) method, named Domain Adaptive Relational Reasoning (DARR), to generalize 3D multi-organ segmentation models to medical data collected from different scanners and/or protocols (domains). Our method is inspired by the fact that the spatial relationship between internal structures in medical images is relatively fixed, e.g., a spleen is always located at the tail of a pancreas, which serves as a latent variable to transfer the knowledge shared across multiple domains. We formulate the spatial relationship by solving a jigsaw puzzle task, i.e., recovering a CT scan from its shuffled patches, and jointly train it with the organ segmentation task. To guarantee the transferability of the learned spatial relationship to multiple domains, we additionally introduce two schemes: 1) Employing a super-resolution network also jointly trained with the segmentation model to standardize medical images from different domain to a certain spatial resolution; 2) Adapting the spatial relationship for a test image by test-time jigsaw puzzle training. Experimental results show that our method improves the performance by 29.60% DSC on target datasets on average without using any data from the target domain during training.