Reward hacking is a form of misalignment in which models overoptimize proxy rewards without genuinely solving the underlying task. Precisely measuring reward hacking occurrence remains challenging because true task rewards are often expensive or impossible to compute. We introduce Countdown-Code, a minimal environment where models can both solve a mathematical reasoning task and manipulate the test harness. This dual-access design creates a clean separation between proxy rewards (test pass/fail) and true rewards (mathematical correctness), enabling accurate measurement of reward-hacking rates. Using this environment, we study reward hacking in open-weight LLMs and find that such behaviors can be unintentionally learned during supervised fine-tuning (SFT) when even a small fraction of reward-hacking trajectories leak into training data. As little as 1\% contamination in distillation SFT data is sufficient for models to internalize reward hacking which resurfaces during subsequent reinforcement learning (RL). We further show that RL amplifies misalignment and drives its generalization beyond the original domain. We open-source our environment and code to facilitate future research on reward hacking in LLMs. Our results reveal a previously underexplored pathway through which reward hacking can emerge and persist in LLMs, underscoring the need for more rigorous validation of synthetic SFT data. Code is available at https://github.com/zohaib-khan5040/Countdown-Code.