Discrete kinematic synthesis of discretely actuated hyper-redundant manipulators is a new practical problem in robotics. The problem concerns with determining the type of each manipulator module from among several specific types, so that the manipulator could reach several specified target frames with the lowest error. This paper suggests using a breadth-first search method and a workspace mean frame to solve this problem. To reduce errors, two heuristic ideas are proposed: two-by-two searching method and iteration. The effectiveness of the proposed method is verified through several numerical problems.