In this work we explore the kinematics of structures made out of interlocked puzzle blocks, like this chair. The slightly loose joints between blocks cause the structure to flex. Our work is able to quickly approximate extreme configurations of large structures through linear programming, by using linearized distance constraints. One potential application is making structures more rigid by adding blocks. Another application is analyzing the needed tightness of joints. We can also plan motions for swarms. Or find motions that disassemble a puzzle-like structure.