Problem:
In this addition problem, each letter stands for a different digit.
+F​TTO​WWU​OOR​​
If T=7 and the letter O represents an even number, what is the only possible value for W?
Answer Choices:
A. 0
B. 1
C. 2
D. 3
E. 4
Solution:
As given, T=7. This implies that F=1 and that O equals either 4 or 5. Since O is even, O=4. Therefore, R=8. Replacing letters with numerals gives
+1​774​WWU​448​​
W+W must be less than 10; otherwise, a 1 would be carried to the next column, and O would be 5. So W<5. Wî€ =0 because Wî€ =U,Wî€ =1 because F=1, Wî€ =2 because if W=2 then U=4=O, and Wî€ =4 because O=4. So W=3.
The addition problem is
+1​774​336​448​​
Answer: D​.
The problems on this page are the property of the MAA's American Mathematics Competitions