ew vagaries of its own.

One of these vagaries has to do with the figure 9, and it is thus
described by William Walsh in his "Handy Book of Literary Curiosities":

It is a most romantic number, and a most persistent,
self-willed, and obstinate one. You cannot multiply it away
or get rid of it anyhow. Whatever you do, it is sure to turn
up again, as did the body of Eugene Aram's victim.

A mathematician named Green, who died in 1794, is said to
have first called attention to the fact that all through the
multiplication table the product of nine comes to nine.
Multiply by any figure you like, and the sum of the
resultant digits will invariably add up as nine. Thus, twice
9 is 18; add the digits together, and 1 and 8 make 9. Three
times 9 is 27; and 2 and 7 is 9. So it goes on up to 11
times 9, which gives 99. Very good. Add the digits together;
9 and 9 is 18, and 8 and 1 is 9.

Go on to any extent, and you will find it impossible to get
away from the figure 9. Take an example at random: 9 times
339 is 3,051; add the digits together, and they make 9. Or
again, 9 times 2,127 is 19,143; add the digits together,
they make 18, and 8 and 1 is 9. Or still again, 9 times
5,071 is 45,639; the sum of these digits is 27, and 2 and 7
is 9.

This seems startling enough. Yet there are other queer
examples of the same form of persistence. It was M. de
Maivan who discovered that if you take any row of figures,
and, reversing their order, make a subtraction sum of
obverse and reverse, the final result of adding up the
digits of the answer will always be 9 As, for example:

2941
Reverse, 1492
----
1449

Now. 1 + 4 + 4 + 9 = 18; and 1 + 8 = 9.

The same result is obtained if you raise the numbers so
changed to their squares or cubes. Start anew, for example,
with 62; reversing it, you get 26. Now, 62 - 26 = 36, and 3
+ 6 = 9. The squares of 26 and 62 are, respectively, 676 and
3844. Subtract one from the other, and you get 3168 = 18,
and 1 + 8 = 9.

So with the cubes of 26 and 62, which are 17,576 and
238,328. Subtracting, the result is 220,752 = 18, and 1 + 8
= 9.

Again, you are confronted with the same puzzling peculiarity in another
form. Write down any number, as, for example, 7,549,132, subtract
therefrom the sum of its digits, and, no matter