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Omni-MATH / The points (0,0),(1,2),(2,1),(2,2) in the plane are colored red while the points (1,0),(2,0),(0,1),(0,2) are colored blue. Four segments are drawn such that each one connects a red…

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problem

The points (0,0),(1,2),(2,1),(2,2)(0,0),(1,2),(2,1),(2,2) in the plane are colored red while the points (1,0),(2,0),(0,1),(0,2)(1,0),(2,0),(0,1),(0,2) are colored blue. Four segments are drawn such that each one connects a red point to a blue point and each colored point is the endpoint of some segment. The smallest possible sum of the lengths of the segments can be expressed as a+ba+\sqrt{b}, where a,ba, b are positive integers. Compute 100a+b100a+b.
Plain-text mathematical notation (without MathML)
The points (0,0),(1,2),(2,1),(2,2) in the plane are colored red while the points (1,0),(2,0),(0,1),(0,2) are colored blue. Four segments are drawn such that each one connects a red point to a blue point and each colored point is the endpoint of some segment. The smallest possible sum of the lengths of the segments can be expressed as a+√(b), where a,b are positive integers. Compute 100a+b.
Original LaTeX notation
The points $(0,0),(1,2),(2,1),(2,2)$ in the plane are colored red while the points $(1,0),(2,0),(0,1),(0,2)$ are colored blue. Four segments are drawn such that each one connects a red point to a blue point and each colored point is the endpoint of some segment. The smallest possible sum of the lengths of the segments can be expressed as $a+\sqrt{b}$, where $a, b$ are positive integers. Compute $100a+b$.

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Source and history

task_id
535cca25-1768-5331-b6a7-a9d3e3084215
task_key
test--535cca25-1768-5331-b6a7-a9d3e3084215
task_revision_id
1
config / split
/ test

Official source

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