- #1

- 1,198

- 5

Suppose you added three numbers, say 389+248+730. Adding correctly one gets 1367. Now let's add the digits of each number.

3+8+9=20

2+4+8=14

7+3+0=10

Now let's add the two digits of each of the previous sums.

2+0=2

1+4=5

1+0=1

Adding the result one gets

2+5+1=8

Going back to the original sum of 1367 and adding digits one gets

1+3+6+7=17

Adding the remaining two digits one gets

1+7=8

The fact that all this addition of digits produces the same final digit is a necessary condition that the addition was performed correctly.

Can someone please explain to me why this is so.

It works for any amount of numbers.