  The Abstraction and Reasoning Corpus (ARC) was recently introduced by
Fran\c{c}ois Chollet as a tool to measure broad intelligence in both humans and
machines. It is very challenging, and the best approach in a Kaggle competition
could only solve 20% of the tasks, relying on brute-force search for chains of
hand-crafted transformations. In this paper, we present the first steps
exploring an approach based on descriptive grid models and the Minimum
Description Length (MDL) principle. The grid models describe the contents of a
grid, and support both parsing grids and generating grids. The MDL principle is
used to guide the search for good models, i.e. models that compress the grids
the most. We report on our progress over a year, improving on the general
approach and the models. Out of the 400 training tasks, our performance
increased from 5 to 29 solved tasks, only using 30s computation time per task.
Our approach not only predicts the output grids, but also outputs an
intelligible model and explanations for how the model was incrementally built.
