The digital sum of a number is just the sum of the individual digits. E.g., the digital sum of 123 is 1 + 2 + 3 = 6.

- The digital sum of
*x*is 42 - The digital sum of
*y*is 67 - When
*x*and*y*are added, you have to “carry the 1” exactly five times (e.g., if you add 8 and 9, you “carry the 1” once to get a “1” in the tens digit, thereby getting 17)

What is the digital sum of *z* = *x* + *y*?

#### Solution

64

If *x* and *y* could be added without needing to “carry the 1” at all, then the digital sum of *z* would be equal to sum of the digital sums of *x* and *y* (e.g. 12 + 34 = 46 gives you digital sums of 3 + 7 = 10).

Starting from there, every time you carry the 1 in a summation, you reduce the digital sum by 9, because you essentially subtract 10 from the smaller digit and add 1 to the greater digit. So if you “carry the 1” five times, you reduce the digital sum by 45, so the digital sum of *z* is 42 + 67 – 45 = 64.