2014 AMC 12B Problems/Problem 8
Problem
In the addition shown below , , , and are distinct digits. How many different values are possible for ?
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
2014 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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