### Vedic Math fun with Digit Sums

## >> Friday, December 18, 2015

**What is Digit Sum:**

The sum of all the digits in a number is

**Digit Sum**.

e.g. The digit sum of 125 is 1 + 2 + 5 = 8

The digit sum of 1357 is 1 + 3 + 5 + 7 = 16

**Some fun with Digit Sums:**

Let's add a 2 digit number with the number generated by reversing its digits.

For Example, for 28, we have to add 28 + 82 = 110

Let's see few more examples:

16 + 61 = 77

13 + 31 = 44

38 + 83 = 121

27 + 72 = 99

The result is in a pattern. You can see, all the numbers are divisible by 11.

Let's derive an equation out of the above calculation.

We have a number xy. The number with reversed digits will be yx.

So, xy + yx = 10x + y + 10y + x = 11x + 11y = 11 * (x + y)

So the conclusion is "When we add a 2 digit number with another number resulting from reversing the digits, the result will be

**".**

__11 times their Digit Sum__To verify this, let's take above examples again.

28 + 82 = 110 = 11 * (2 + 8)

16 + 61 = 77 = 11 * (1 + 6)

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