2021 AIME I Problems/Problem 15

Problem

Let $S$ be the set of positive integers $k$ such that the two parabolas $y=x^2-k~~\text{and}~~x=2(y-20)^2-k$ intersect in four distinct points, and these four points lie on a circle with radius at most $21$ . Find the sum of the least element of $S$ and the greatest element of $S$ .

Solution

Solution 1

Using the computer science algorithm called binary search, you can narrow down the answer. Binary search takes 10 iterations because the range is 0 to 999 and log base 2 of 999 is 10.

You end up finding the bounds of 5 and 280. The sum is 285

~Lopkiloinm

2021 AIME I (Problems • Answer Key • Resources)
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2021 AIME I Problems/Problem 15

Contents

Problem

Solution

Solution 1

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