‘DIGITAL’ ROOTS 45

(a) The sum of all the digits from 1 to g inclusive is 45
and thus has the root of g. Similarly the root of the total of
any nine consecutive natural numbers is always g.

(b) Take any number and reverse the digits. If the number
thus obtained is deducted from the original number, the root
of the difference is always g. This is self-evident since the root
of the original number must be the same as the reversed
number and the difference between their individual roots
must therefore be o.

(¢c) If the separate digits of a number are added together
to form a total and this total is deducted from the original
number, then the difference will again be a multiple of 9.
This follows from the previous example.

(d) Take any number. Reverse its digits to form another
number. Square both numbers and subtract the smaller
square from the larger. The difference will be a multiple of g.

Thus:

622—262=3168 =9 X 352
This is because the root of 62 is the same as the root of 26
and therefore the root of 622 must be the same as the root
of 262

T

i R

R0

R,

RN R

o0

sy
gt

w‘\ B

i

&
=5
2
=

{}

.
SRS A AR B0