Difference between revisions of "2024 AIME II Problems/Problem 11"

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==Problem==
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Find the number of triples of nonnegative integers \((a,b,c)\) satisfying \(a + b + c = 300\) and
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\begin{equation*}
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a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000.
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\end{equation*}
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==See also==
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{{AIME box|year=2024|num-b=10|num-a=12|n=II}}
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[[Category:]]
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{{MAA Notice}}

Revision as of 09:35, 9 February 2024

Problem

Find the number of triples of nonnegative integers \((a,b,c)\) satisfying \(a + b + c = 300\) and \begin{equation*} a^2b + a^2c + b^2a + b^2c + c^2a + c^2b = 6,000,000. \end{equation*}

See also

2024 AIME II (ProblemsAnswer KeyResources)
Preceded by
Problem 10
Followed by
Problem 12
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
All AIME Problems and Solutions

[[Category:]] The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png