This is a variation of the question [Can a tangle of arcs interlock?][1], asked by Joseph O'Rourke, and solved. I reproduce the question here: > Can a (finite) collection of disjoint circle arcs in $\mathbb{R}^3$ be > interlocked in the sense in that they cannot be separated, i.e. each > moved arbitrarily far from one another while remaining disjoint (or at > least never crossing) throughout? (Imagine the arcs are made of rigid > steel; but infinitely thin.) The arcs may have different radii; each > spans strictly less than $2 \pi$ in angle, so each has a positive > "gap" through which arcs may pass. My proposed variation is: > Can they interlock in $\mathbb R^2$? I posted [a comment][2] at the original question, claiming that three circle arcs can be locked. ![enter image description here][3] And two cannot ![enter image description here][4] I soon realized that the examples with three arcs can in fact be unlocked, and I think Joseph O'Rourke [did the same][5]. I reproduce here my solution to unlock them: ![enter image description here][6] So, the question is still open for two dimensions. [1]: http://mathoverflow.net/questions/139105/can-a-tangle-of-arcs-interlock [2]: http://mathoverflow.net/a/140555/10095 [3]: https://i.sstatic.net/j58z0.gif [4]: https://i.sstatic.net/gG7Ot.gif [5]: http://mathoverflow.net/a/140567/10095 [6]: https://i.sstatic.net/f5edL.gif