Eddington's Zoo

I took some nephews and nieces to the Zoo, and we halted at a cage marked

      Tovus Slithius, male and female.
    Beregovus Mimsius, male and female.
       Rathus Momus, male and female.
  Jabberwockius Vulgaris, male and female.

 The eight animals were asleep in a row, and the children began to guess
 which was which.  "That one at the end is Mr Tove."  "No, no!  It's Mrs
 Jabberwock," and so on.  I suggested that they should each write down
 the names in order from left to right, and offered a prize to the one
 who got most names right.

 As the four species were easily distinguished, no mistake would arise in
 pairing the animals; naturally a child who identified one animal as Mr
 Tove identified the other animal of the same species as Mrs Tove.

 The keeper, who consented to judge the lists, scrutinised them carefully.
 "Here's a queer thing.  I take two of the lists, say, John's and Mary's.
 The animal which John supposes to be the animal which Mary supposes to be
 Mr Tove is the animal which Mary supposes to be the animal which John
 supposes to be Mrs Tove.  It is just the same for every pair of lists,
 and for all four species.

 "Curiouser and curiouser!  Each boy supposes Mr Tove to be the animal
 which he supposes to be Mr Tove; but each girl supposes Mr Tove to be
 the animal which she supposes to be Mrs Tove.  And similarly for the oth-
 er animals.  I mean, for instance, that the animal Mary calls Mr Tove
 is really Mrs Rathe, but the animal she calls Mrs Rathe is really Mrs
 Tove."

 "It seems a little involved," I said, "but I suppose it is a remarkable
 coincidence."

 "Very remarkable," replied Mr Dodgson (whom I had supposed to be the
 keeper) "and it could not have happened if you had brought any more
 children."

 How many nephews and nieces were there?  Was the winner a boy or a girl?
 And how many names did the winner get right? [by Sir Arthur Eddington]