Guaranteeing that you can take a hot shower is NP complete, at lest in one formalization the problem by Christina Matzke and Damien Challet in a recent paper.
Christina Matzke, Damien Challet, Taking a shower in Youth Hostels: risks and delights of heterogeneity, arXiv:0801.1573v1 , 10 January, 2008. … Tuning one’s shower in some hotels may turn into a challenging coordination game with imperfect information. The temperature sensitivity increases with the number of agents, making the problem possibly unlearnable. Because there is in practice a finite number of possible tap positions, identical agents are unlikely to reach even approximately their favorite water temperature. Heterogeneity allows some agents to reach much better temperatures, at the cost of higher risk.
Spotted on the physics arXiv blog.