Brain Teasers and Puzzles

Digital Sum of the Sum

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?



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.

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