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jmc

number theory junior

Problem

In this addition problem, each letter stands for a different digit. If T = 7 and the letter O represents an even number, what is the only possible value for W?
(A)
(B)
(C)
(D)
Solution
Since both T's are 7, then O has to equal 4, because 7 + 7 = 14. Then, F has to equal 1. To get R, we do 4 + 4 (since O = 4) to get R = 8. The value for W then has to be a number less than 5, otherwise it will change the value of O, and can't be a number that has already been used, like 4 or 1. The only other possibilities are 2 and 3. 2 doesn't work because it makes U = 4, which is what O already equals. So, the only possible value of W is 3
Final answer
D