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. Which number did Yunji leave out?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To find the number that Yunji left out, we need to find the sum of the integers from to and find its difference with the largest perfect square below the sum. We can calculate the sum of the integers from to as follows:
The largest perfect square less than would be and .
Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions