We present a framework capable of producing contact plans describing complex multiped motions (including humanoid): standing up, climbing stairs using a handrail, crossing rubble and getting out of a car. Our framework answers a need demonstrated at the Darpa Robotics Challenge, where the lack of an automatic acyclic contact planner was recognized a major issue. Our novel key idea is the reachability condition. Informally, it verifies that the root configuration of a robot is " close, but not too close " from obstacles: close to allow contact creation, not too close to avoid collision. With this approximation of the space of admissible root configurations we decompose the hard contact planning problem into simpler sub-problems: first, to plan a guide path for the root without considering the whole-body configuration; then, to generate a discrete sequence of whole-body configurations in static equilibrium along this path. The reachability condition turns the high-dimensional computation of the guide into a collision checking problem, solved in less than a few seconds. Then a deterministic contact selection algorithm tackles the combinatorial issue of generating of a discrete sequence along the guide path. Several innovations make it computationally efficient: a criterion for verifying static equilibrium, and a set of heuristics used to enforce desirable properties on the configuration. Our approach results from the pragmatic choice of favoring efficiency over exhaustiveness, justified empirically: in a few seconds, with satisfying success rates, we generate complex contact plans for various scenarios and robots, namely HRP-2, HyQ, and a dexterous hand.