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Omni-MATH / Ten points are equally spaced on a circle. A graph is a set of segments…

Problem

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problem

Ten points are equally spaced on a circle. A graph is a set of segments (possibly empty) drawn between pairs of points, so that every two points are joined by either zero or one segments. Two graphs are considered the same if we can obtain one from the other by rearranging the points. Let NN denote the number of graphs with the property that for any two points, there exists a path from one to the other among the segments of the graph. Estimate the value of NN. If your answer is a positive integer AA, your score on this problem will be the larger of 0 and ⌊20−5|ln(A/N)|⌋\lfloor 20-5|\ln (A / N)|\rfloor. Otherwise, your score will be zero.
Plain-text mathematical notation (without MathML)
Ten points are equally spaced on a circle. A graph is a set of segments (possibly empty) drawn between pairs of points, so that every two points are joined by either zero or one segments. Two graphs are considered the same if we can obtain one from the other by rearranging the points. Let N denote the number of graphs with the property that for any two points, there exists a path from one to the other among the segments of the graph. Estimate the value of N. If your answer is a positive integer A, your score on this problem will be the larger of 0 and ⌊20−5|ln(A/N)|⌋. Otherwise, your score will be zero.
Original LaTeX notation
Ten points are equally spaced on a circle. A graph is a set of segments (possibly empty) drawn between pairs of points, so that every two points are joined by either zero or one segments. Two graphs are considered the same if we can obtain one from the other by rearranging the points. Let $N$ denote the number of graphs with the property that for any two points, there exists a path from one to the other among the segments of the graph. Estimate the value of $N$. If your answer is a positive integer $A$, your score on this problem will be the larger of 0 and $\lfloor 20-5|\ln (A / N)|\rfloor$. Otherwise, your score will be zero.

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Source and history

task_id
9833d2d9-44b7-5fc1-bcab-9b2ebe0d9bc8
task_key
test--9833d2d9-44b7-5fc1-bcab-9b2ebe0d9bc8
task_revision_id
1
config / split
/ test

Official source

initial import