Scaling up inference-time compute has proven to be a valuable strategy in improving the performance of Large Language Models (LLMs) without fine-tuning. An important task that can benefit from additional inference-time compute is self-repair; given an initial flawed response, or guess, the LLM corrects its own mistake and produces an improved response, or fix. We leverage the in-context learning ability of LLMs to perform self-repair in the coding domain. The key contribution of our paper is an approach that synthesises and selects an ordered set of golden example pairs, or AuPairs, of these initial guesses and subsequent fixes for the corresponding problems. Each such AuPair is provided as a single in-context example at inference time to generate a repaired solution. For an inference-time compute budget of $N$ LLM calls per problem, $N$ AuPairs are used to generate $N$ repaired solutions, out of which the highest-scoring solution is selected as the final answer. The underlying intuition is that if the LLM is given a different example of fixing an incorrect guess each time, it can subsequently generate a diverse set of repaired solutions. Our algorithm selects these AuPairs in a manner that maximises complementarity and usefulness. We demonstrate the results of our algorithm on 5 LLMs across 7 competitive programming datasets for the code repair task. Our algorithm yields a significant boost in performance compared to best-of-$N$ and self-repair, and also exhibits strong generalisation across datasets and models. Moreover, our approach shows significantly stronger scaling with inference-time compute budget compared to baselines.