Difference between revisions of "2021 AIME I Problems/Problem 15"

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==Solution==
 
==Solution==
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===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.
 
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.
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You end up finding the bounds of 5 and 280. The sum is 285
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~Lopkiloinm
  
 
==See also==
 
==See also==
 
{{AIME box|year=2021|n=I|num-b=14|after=Last problem}}
 
{{AIME box|year=2021|n=I|num-b=14|after=Last problem}}
 
{{MAA Notice}}
 
{{MAA Notice}}

Revision as of 04:23, 12 March 2021

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

See also

2021 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Last problem
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

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