When I was in grade school my father told me about a method of checking my addition when I added columns of numbers. I hold degrees in mechanical engineering but none of my math courses ever broached this subject as it is pretty much useless for engineering type problems. 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.