2009 AIME II Problem 4

A group of children held a grape-eating contest. When the contest was over, the winner had eaten n grapes, and the child in k-th place had eaten n+2-2k grapes. The total number of grapes eaten in the contest was 2009. Find the smallest possible value of n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.