We introduce \emph{Humanoid Hanoi}, a challenge problem for long-horizon humanoid skill composition that requires a robot to repeatedly sequence pickup, locomotion, and placement skills to rearrange stacked boxes in simulation and on hardware. This symbolically simple task exposes a weakness in a common modular humanoid architecture, where reusable high-level skills are learned on top of a shared, task-agnostic whole-body controller (WBC). While such a WBC provides a unified low-level interface for skill composition, it may not be sufficiently hardened to execute the full collection of learned skills under domain randomization and long-horizon closed-loop execution. We compare strategies for addressing this issue, including skill-specific WBC fine-tuning, residual low-level adaptation, and task-driven data aggregation that expands the shared-WBC training distribution with closed-loop trajectories induced by learned skills while preserving its original tracking objective. In our evaluated system, the shared-WBC approach achieves the strongest long-horizon robustness. A direct transition-smoothing intervention further shows that low-level controller handoffs account for a substantial part of the composition loss observed with non-shared controllers. Project page: https://osudrl.github.io/Humanoid_Hanoi/

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