......BTW....SOD IS A HEBREW WORD FOR SECRET!

A dialog between two mathematicians:


Ted: I have two numbers x and y, where x + y = z. The sum of the digits of x is 43 and the sum of the digits of y is 68.
Can you tell me the sum of the digits of z?

Fred: I need more information. When you added x and y how many times did you have to carry?

Ted: Let’s see. … It was five times.
Fred: Then the sum of the digits of z is 66.

Ted: That’s right! How did you know?



How did he know?

Credit: USC mathematician Solomon W. Golomb

The digital root of the sum x+y equals the sum of the digital roots of a and y.  In fact the sum of the digits will be the same unless there are carries in the addition.  Each carry will reduce this sum by 9.  

Posted by Jer on 2021-08-26 09:11:31