Browse · harp
Printsmc
number theory senior
Problem
In the addition shown below , , , and are distinct digits. How many different values are possible for ?
(A)
(B)
(C)
(D)
Solution
From the first column, we see because it yields a single digit answer. From the fourth column, we see that equals and therefore . We know that . Therefore, the number of values can take is equal to the number of possible sums less than that can be formed by adding two distinct natural numbers. Letting , and letting , we have
Final answer
C