The Mystical Number Nine.
The discovery of remarkable properties of the number 9 was accidentally made, more than forty years since, though, we believe, it is not generally known:
The component figures of the product made by the multiplication of every digit into the number 9, when added together, make NINE.
The order of these component figures is reversed, after the said number has been multiplied by 5.
The component figures of the amount of the multipliers (viz. 45), when added together, make NINE.
The amount of the several products, or multiples of 9 (viz. 405), when divided by 9, gives, for a quotient, 45; that is, 4+5=NINE.
The amount of the first product (viz. 9), when added to the other product, whose respective component figures make 9, is 81; which is the square of NINE.
The said number 81, when added to the above-mentioned amount of the several products, or multiples of 9 (viz. 405) makes 486; which, if divided by 9, gives, for a quotient, 54: that is, 5+4=NINE.
It is also observable, that the number of changes that may be rung on nine bells, is 362,880; which figures, added together, make 27; that is, 2+7=NINE.
And the quotient of 362,880, divided by 9, will be, 40,320; that is 4+0+3+2+0=NINE.
To add a figure to any given number, which shall render it divisible by Nine: Add the figures together in your mind, which compose the number named; and the figure which must be added to the sum produced, in order to render it divisible by 9, is the one required. Thus
Suppose the given number to be 7521:
Add those together, and 15 will be produced; now 15 requires 3 to render it divisible by 9; and that number, 3, being added to 7521, causes the same divisibility: 7521 plus 3 gives 7524, and, divided by 9, gives 836.
This exercise may be diversified by your specifying, before the sum is named, the particular place where the figure shall be inserted, to make the number divisible by 9; for it is exactly the same thing, whether the figure be put at the head of the number, or between any two of its digits.