Abstract Raven’s Progressive Matrices (RPMs) are a popular family of general intelligence tests, and provide a non-verbal measure of a test subject’s reasoning abilities. Traditionally RPMs have been manually designed. To make them readily available for both practice and examination, we tackle the problem of automatically synthesizing RPMs. Our goal is to efficiently generate a large number of RPMs that are authentic (i.e. similar to manually written problems), interesting (i.e. diverse in terms of difficulty), and well-formed (i.e. unambiguous). The main technical challenges are: How to formalize RPMs to accommodate their seemingly enormous diversity, and how to define and enforce their validity? To this end, we (1) introduce an abstract representation of RPMs using first-order logic, and (2) restrict instantiations to only valid RPMs. We have realized our approach and evaluated its efficiency and effectiveness. We show that our system can generate hundreds of valid problems per second with varying levels of difficulty. More importantly, we show, via a user study with 24 participants, that the generated problems are statistically indistinguishable from actual problems. This work is an exciting instance of how logic and reasoning may aid general learning.