Question about closing a chain of elastic bands -- and hatching eggs

[Timothy Y. Chow]

Aaron Sloman wrote:
> Question: is it possible to turn such a *chain* of rubber bands into a 
> *ring* of rubber bands by linking the band at one end of the chain to 
> the band at the other end, in the same way as new bands are linked to an 
> existing end band?

The standard approach is to find a link invariant that distinguishes the 
two configurations.

https://en.wikipedia.org/wiki/Knot_invariant

I don't know offhand a specific invariant that will work for your problem 
but it seems likely that many of the standard invariants will fit the 
bill.

Tim