The analogy compares relationships: "teeth" belong to "hen" as "nest" belongs to "mare." Just as hens have teeth in a figurative sense (as in the term "hen's teeth," which are rare), mares (female horses) have "nests" in the form of their foals or the areas where they give birth. Therefore, "mare" is the answer because it completes the relationship in the same way.
The answer is "mare".The expression "as scarce as hen's teeth" means that it doesn't exist (because they don't). The original meaning of "mare's nest" is something illusory--or doesn't exist.In addition to the parallel meaning between the two expressions or idioms, there is also a parallel construction, with a possessive in each case: hen's teeth; mare's nest.This is important in an analogy question, which requires an exact parallel for the answer to be correct (A is to B as X is to Y).The parallel construction provides the test against which other "possible" answers to this analogy can be tried. There are plenty of things that don't exist, for example, but only one expression or idiom that shares with "hen's teeth" both meaning and the possessive construction.
The answer is "gums".
Mare
If it has eggs in the nest.
Mare's Nest
nest?
They sit in the hen house on eggs, on the roost or in a nest.
she\well\take\to\the\nest
Mare's Nest - 2004 was released on: USA: 3 October 2004 (New York International Independent Film and Video Festival)
hen's teeth
Air. Beaks dont have teeth
Example sentence - She had to move the hen off the nest in order to pick up the eggs.