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jmc

algebra intermediate

Problem

In the game of Frood, dropping froods gives a score of the sum of the first positive integers. For example, dropping five froods scores points. Eating froods earns points. For example, eating five froods earns points. What is the least number of froods for which dropping them will earn more points than eating them?
Solution
Dropping Froods earns points. Eating Froods earns points. So we seek the least such that . Solving, we see that . Thus, is our desired answer.
Final answer
20