was perpetually strolling out to the
groves of Academia to bother poor old Plato with his nonsensical ideas
about what he called his "lucky number." But Plato devised a way of
getting rid of him. When the seer one day proposed to inflict on him a
lengthy disquisition on his favourite topic, the philosopher cut him
short with the remark, "Look here, old chappie" (that is the nearest
translation of the original Greek term of familiarity): "when you can
bring me the solution of this little mystery of the three nines I shall
be happy to listen to your treatise, and, in fact, record it on my
phonograph for the benefit of posterity."

[Illustration]

Plato then showed, in the manner depicted in our illustration, that three
nines may be arranged so as to represent the number eleven, by putting
them into the form of a fraction. The puzzle he then propounded was so to
arrange the three nines that they will represent the number twenty.

It is recorded of the old crank that, after working hard at the problem
for nine years, he one day, at nine o'clock on the morning of the ninth
day of the ninth month, fell down nine steps, knocked out nine teeth,
and expired in nine minutes. It will be remembered that nine was his
lucky number. It was evidently also Plato's.

In solving the above little puzzle, only the most elementary arithmetical
signs are necessary. Though the answer is absurdly simple when you see
it, many readers will have no little difficulty in discovering it. Take
your pencil and see if you can arrange the three nines to represent
twenty.

109.--_Noughts and Crosses._

Every child knows how to play this game. You make a square of nine cells,
and each of the two players, playing alternately, puts his mark (a nought
or a cross, as the case may be) in a cell with the object of getting
three in a line. Whichever player first gets three in a line wins with
the exulting cry:--

"Tit, tat, toe,
My last go;
Three jolly butcher boys
All in a row."

It is a very ancient game. But if the two players have a perfect
knowledge of it, one of three things must always happen. (1) The first
player should win; (2) the first player should lose; or (3) the game
should always be drawn. Which is correct?

110.--_Ovid's Game._

Having examined "Noughts and Crosses," we will now consider an extension
of the game that is distinctly mentioned in the works of Ovid. It is, in
fact, the parent of "Nine Men's