2024 AMC 8 Problems/Problem 4
Problem
When Yunji added all the integers from to , she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?
Solution 1
The sum of the numbers from to is Denote the number left out when adding to be . Thus, is a perfect square. We could rigorously solve the values of such that is a perfect square. However, since this is the AMC 8, we can simply try each option. When , we see that , a perfect square. Therefore, our answer is .
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