How do you know the answer to this? Is there any AI/Computer-based reasoning system that could work out the answer? Is there any neuroscientific theory that explains how a mathematician's brain makes it possible to work out the answer?
The answer to the above question seems to require the following reasoning steps.
(a) Making a ring from a block of stone can be done simply by removing parts of
the stone without ever reattaching removed parts, and without ever bending or
otherwise deforming parts of the stone not yet removed.
(b)
If you start with two disconnected blocks of stone and remove material from each
you will always have two disconnected remainders.
(c)
If the remainders are rings, and the rings are disconnected they cannot come to
be connected (as in a chain) unless either parts are removed and then replaced,
or the material of one ring is made to pass through the material of the other
ring, which is impossible for two pieces of solid stone.
Making this argument water-tight is left as an exercise for the reader. As far as I know, no current artificial mathematical reasoner can produce or understand the sort of reasoning used here. Yet the impossibility of linking solid rings is so obvious to most people that stage conjurers can impress audiences by apparently linking and unlinking rings or closed loops made of impenetrable material, illustrated in these videos: