The riddle is given, together with its answer, in the Deipnosophistae of Athenaeus of Naucratis:

And a similar [riddle] is that of Panarces, mentioned by Clearchus, in his Essay on Griphi [riddles], that
“A man who is not a man, with a stone which was not a stone, struck a bird which was not a bird, sitting
on a tree which was not a tree.” For the things alluded to here are a eunuch, a piece of pumice-stone, a
bat, and a narthex¹. And Plato, in the fifth book of his Laws², alludes to this riddle, where he says, that those
philosophers who occupy themselves about minute arts, are like those who, at banquets, doubt what to eat,
and resemble too the boys’ riddle about the stone thrown by the eunuch, and about the bat, and about the
place from which they say that the eunuch struck down the bat, and the engine with which he did it.

¹ “Νἀρθηξ, a tall umbelliferous plant, (Lat. ferula) with a slight knotted pithy stalk, in which 
Prometheus conveyed the spark of fire from heaven to earth.” — L. & S. Gr. Eng. Lex. in voc. νἀρθηξ.

² This is a mistake of Athenaeus. The passage referred to occurs in the fifth book of the De Republica.

_{Athenaeus of Naucratis, Deipnosophistae X.76. Prose translation and notes by C. D. Yonge (1854), 
The Deipnosophists: or, Banquet of the learned, of Athenaeus, London: Bohn, p. 714.}

Athenaeus was writing in the 3rd century CE; Clearchus of Soli was a pupil of Aristotle who wrote a treatise
Περὶ γρίφων (On Riddles), now lost, in the 3rd century BCE.

The bat riddle has philosophical content. The first two elements expose a problem with definition by properties: if you
define ‘man’ by a list of properties including ‘possesses testicles’ then this goes wrong for eunuchs; if you define
‘stone’ by a list of properties including ‘sinks in water’ then this goes wrong for pumice. Plato’s attempt at a solu-
tion to this problem was the theory of forms. The last two elements of the riddle expose a problem in classification of
living things by their shared characteristics: the class of ‘winged vertebrates’ is unsatisfactory because it includes
bats as well as birds; the class of ‘tall plants’ is unsatisfactory because it includes giant fennel as well as trees. This
problem is solved by the theory of evolution, which distinguishes homologies (shared characteristics resulting from
common descent) from analogies (shared characteristics resulting from independent adaptation to similar environments).