"As dull as arithmetic" is a phrase that is familiar to almost every schoolboy, and is a figure of comparison that is frequently evoked by those sages who hold down empty cracker-boxes in rural general stores. The fact is, however, that arithmetic is not always half so dull as it looks. Like some of those persons who earn a livelihood by teaching it to the young, it has a dry humor and a few 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.