Question

in the addition problem on the right, each letter stands for a digit and different letters stand for different digits. What digits do the letters H,E, and A each represent?
H E
H E
H E
+ H E
____________
A E

Answers

  1. Answer:
    This problem is easy but I’ll demonstrate an approach for simplifying these kind of problems that can be applied to problems of higher complexity.
    Key: Notice that you can write AH as 10A + H and HEE as 100H + 10E+E, and thus
    AH +A = HEE
    10A + H + A = 100H + 10E +E
    11A + H = 100H + 11E
    11A = 99H + 11E
    A = 9H + E
    As H can not be 0 (it is the leading digit in HEE), A must be at least and therefore exactly 9 and the problem solves itself from there on.

    Reply
  2. Answer:
    This problem is easy but I’ll demonstrate an approach for simplifying these kind of problems that can be applied to problems of higher complexity.
    Key: Notice that you can write AH as 10A + H and HEE as 100H + 10E+E, and thus
    AH +A = HEE
    10A + H + A = 100H + 10E +E
    11A + H = 100H + 11E
    11A = 99H + 11E
    A = 9H + E
    As H can not be 0 (it is the leading digit in HEE), A must be at least and therefore exactly 9 and the problem solves itself from there on.
    Step-by-step explanation:

    Reply

Leave a Comment