In context learning (ICL) is an attractive method of solving a wide range of problems. Inspired by Garg et al. (2022), we look closely at ICL in a variety of train and test settings for several transformer models of different sizes trained from scratch. Our study complements prior work by pointing out several systematic failures of these models to generalize to data not in the training distribution, thereby showing some limitations of ICL. We find that models adopt a strategy for this task that is very different from standard solutions.