Problem:
In the addition problem, each digit has been replaced
Answer Choices:
A.
B.
C.
D.
E.
Solution:
For the sum to be in the hundreds' place, since gives numbers too small and makes the sum too large. If then , since and or would be too large for the ones' place and and would not be enough to carry a from the tens' to the hundreds' place. Thus, if and and in the ones' place, then .
Since the second column carry is . The first column carry is also since the sum of and is less than or equal to and . In the second column, this makes (first column carry) , so . Then from the first column , so .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions