Both in ancient and in modern times the number nine has been considered
to possess peculiarly mystic qualities. We know, for instance, that there
were nine Muses, nine rivers of Hades, and that Vulcan was nine days
falling down from heaven. Then it has been confidently held that nine
tailors make a man; while we know that there are nine planets, nine days'
wonders, and that a cat has nine lives--and sometimes nine tails.
Most people are acquainted with some of the curious properties of the
number nine in ordinary arithmetic. For example, write down a number
containing as many figures as you like, add these figures together, and
deduct the sum from the first number. Now, the sum of the figures in this
new number will always be a multiple of nine.
There was once a worthy man at Athens who was not only a cranky
arithmetician, but also a mystic. He was deeply convinced of the magic
properties of the number nine, and 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.