We introduce a new type of construction set which can be used to build valence sphere models of any cage-like hydrocarbon, of general formula (CH)_2n. Using n linear five-bead chains, one can connect these building units into a three-dimension arrangement that stands for its valence sphere model through n cross-linkings. More interestingly, the assembly processes of certain symmetric molecules, such as three Platonic hydrocarbons, including tetrahedrane, cubane, and dodecahedrane, are similar to solving interlocking puzzles. Hence, a bead chain construction set can also be considered as a new type of take-apart put-together puzzles.