# The Amazing Number 9

If you multiply nine by any whole number (except zero), and repeatedly add the digits of the answer until it’s just one digit, you will end up with nine:

2 × 9 = 18 (1 + 8 = 9)

3 × 9 = 27 (2 + 7 = 9)

9 × 9 = 81 (8 + 1 = 9)

121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 9)

234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)

578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27 (2 + 7 = 9))

482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45 (4 + 5 = 9))

(Exception) 0 x 9 = 0 (0 is not equal to 9)

It is easy to work out whether a number is exactly divisible by 9. This is the same as asking whether a number is in the “9 times table”. All you have to do is add up its digits. If the answer is more than one digit long, you add up the digits again, and go on doing this, until you are left with a single digit. If this single digit is 9 then the original number was divisible by 9.

For example, is 781236 divisible by 9? Adding up its digits 7 + 8 + 1 + 2 + 3 + 6 = 27, and adding again 2 + 7 = 9. And because the answer is 9, the original number must be divisible by 9.

The formula for determining the sum of interior angles of a polygon is n-2(180). n= number of sides. The sum of all angles of any polygon will always equal 9. A 9-sided polygon is 9-2(180) or 7(180) or 1260. 1+2+6+0 = 9. Try it with any sided polygon.

Any random number (e.g 35967930) when arranged with its integers in a descending order (i.e. 99765330) and subtracted from it the reverse number with rearranged integers in an ascending order ( i.e 03356799) the resulting subtraction (i.e. 96408531) individual integers when added (i.e 36) leads to a multiple of number 9.

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