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Omni-MATH / 2014 points are placed on a circumference. On each of the segments with end points on two of the 2014 points is written a non-negative real number. For any convex polygon with vert…

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problem

20142014 points are placed on a circumference. On each of the segments with end points on two of the 20142014 points is written a non-negative real number. For any convex polygon with vertices on some of the 20142014 points, the sum of the numbers written on their sides is less or equal than 11. Find the maximum possible value for the sum of all the written numbers.
Plain-text mathematical notation (without MathML)
2014 points are placed on a circumference. On each of the segments with end points on two of the 2014 points is written a non-negative real number. For any convex polygon with vertices on some of the 2014 points, the sum of the numbers written on their sides is less or equal than 1. Find the maximum possible value for the sum of all the written numbers.
Original LaTeX notation
$2014$ points are placed on a circumference. On each of the segments with end points on two of the $2014$ points is written a non-negative real number. For any convex polygon with vertices on some of the $2014$ points, the sum of the numbers written on their sides is less or equal than $1$. Find the maximum possible value for the sum of all the written numbers.

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Source and history

task_id
03951613-32e7-5ca2-8f6f-7b966158573f
task_key
test--03951613-32e7-5ca2-8f6f-7b966158573f
task_revision_id
1
config / split
/ test

Official source

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