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Omni-MATH / Consider an equilateral triangular grid G with 20 points on a side, where each row consists of points spaced 1 unit apart. More specifically, there is a single point in the first r…

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problem

Consider an equilateral triangular grid GG with 20 points on a side, where each row consists of points spaced 1 unit apart. More specifically, there is a single point in the first row, two points in the second row, ..., and 20 points in the last row, for a total of 210 points. Let SS be a closed non-selfintersecting polygon which has 210 vertices, using each point in GG exactly once. Find the sum of all possible values of the area of SS.
Plain-text mathematical notation (without MathML)
Consider an equilateral triangular grid G with 20 points on a side, where each row consists of points spaced 1 unit apart. More specifically, there is a single point in the first row, two points in the second row, ..., and 20 points in the last row, for a total of 210 points. Let S be a closed non-selfintersecting polygon which has 210 vertices, using each point in G exactly once. Find the sum of all possible values of the area of S.
Original LaTeX notation
Consider an equilateral triangular grid $G$ with 20 points on a side, where each row consists of points spaced 1 unit apart. More specifically, there is a single point in the first row, two points in the second row, ..., and 20 points in the last row, for a total of 210 points. Let $S$ be a closed non-selfintersecting polygon which has 210 vertices, using each point in $G$ exactly once. Find the sum of all possible values of the area of $S$.

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Source and history

task_id
2c80136b-9ea2-56cc-b235-915dbfe3b9a7
task_key
test--2c80136b-9ea2-56cc-b235-915dbfe3b9a7
task_revision_id
1
config / split
/ test

Official source

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