Problem:
If and are different digits, then the largest possible -digit sum for
has the form
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since the sum must be only three digits, it follows that because would give a four-digit sum. Thus the largest value for must be . Then, to obtain the largest sum, . This yields
Thus, the largest sum has the form .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions