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Omni-MATH / Two unit squares S₁ and S₂ have horizontal and vertical sides. Let x be the minimum distance between a point in S₁ and a point in S₂, and let y be the maximum distance between a po…

Problem

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problem

Two unit squares S1S_{1} and S2S_{2} have horizontal and vertical sides. Let xx be the minimum distance between a point in S1S_{1} and a point in S2S_{2}, and let yy be the maximum distance between a point in S1S_{1} and a point in S2S_{2}. Given that x=5x=5, the difference between the maximum and minimum possible values for yy can be written as a+bca+b \sqrt{c}, where a,ba, b, and cc are integers and cc is positive and square-free. Find 100a+10b+c100 a+10 b+c.
Plain-text mathematical notation (without MathML)
Two unit squares S₁ and S₂ have horizontal and vertical sides. Let x be the minimum distance between a point in S₁ and a point in S₂, and let y be the maximum distance between a point in S₁ and a point in S₂. Given that x=5, the difference between the maximum and minimum possible values for y can be written as a+b√(c), where a,b, and c are integers and c is positive and square-free. Find 100a+10b+c.
Original LaTeX notation
Two unit squares $S_{1}$ and $S_{2}$ have horizontal and vertical sides. Let $x$ be the minimum distance between a point in $S_{1}$ and a point in $S_{2}$, and let $y$ be the maximum distance between a point in $S_{1}$ and a point in $S_{2}$. Given that $x=5$, the difference between the maximum and minimum possible values for $y$ can be written as $a+b \sqrt{c}$, where $a, b$, and $c$ are integers and $c$ is positive and square-free. Find $100 a+10 b+c$.

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Source and history

task_id
00a63d8a-0368-5836-9647-12615900cadf
task_key
test--00a63d8a-0368-5836-9647-12615900cadf
task_revision_id
1
config / split
/ test

Official source

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