Problem:
In the addition shown below A,B,C, and D are distinct digits. How many different values are possible for D?
ABBCB+BCADADBDDD​​
Answer Choices:
A. 2
B. 4
C. 7
D. 8
E. 9
Solution:
As indicated by the leftmost column A+B≤9. Then both the second and fourth columns show that C=0. Because A,B, and C are distinct digits, D must be at least 3. The following values for (A,B,C,D) show that D may be any of the (C)7​ digits that are at least 3:(1,2,0,3),(1,3,0,4),(2,3,0,5), (2,4,0,6),(2,5,0,7),(2,6,0,8),(2,7,0,9).
The problems on this page are the property of the MAA's American Mathematics Competitions