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Omni-MATH / Eight points are chosen on the circumference of a circle, labelled P₁,P₂,…,P₈ in clockwise order. A route is a sequence of at least two points P_(a₁),P_(a₂),…,P_(a_(n)) such that i…

Problem

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problem

Eight points are chosen on the circumference of a circle, labelled P1,P2,…,P8P_{1}, P_{2}, \ldots, P_{8} in clockwise order. A route is a sequence of at least two points Pa1,Pa2,…,PanP_{a_{1}}, P_{a_{2}}, \ldots, P_{a_{n}} such that if an ant were to visit these points in their given order, starting at Pa1P_{a_{1}} and ending at PanP_{a_{n}}, by following n−1n-1 straight line segments (each connecting each PaiP_{a_{i}} and Pai+1P_{a_{i+1}} ), it would never visit a point twice or cross its own path. Find the number of routes.
Plain-text mathematical notation (without MathML)
Eight points are chosen on the circumference of a circle, labelled P₁,P₂,…,P₈ in clockwise order. A route is a sequence of at least two points P_(a₁),P_(a₂),…,P_(a_(n)) such that if an ant were to visit these points in their given order, starting at P_(a₁) and ending at P_(a_(n)), by following n−1 straight line segments (each connecting each P_(a_(i)) and P_(a_(i+1)) ), it would never visit a point twice or cross its own path. Find the number of routes.
Original LaTeX notation
Eight points are chosen on the circumference of a circle, labelled $P_{1}, P_{2}, \ldots, P_{8}$ in clockwise order. A route is a sequence of at least two points $P_{a_{1}}, P_{a_{2}}, \ldots, P_{a_{n}}$ such that if an ant were to visit these points in their given order, starting at $P_{a_{1}}$ and ending at $P_{a_{n}}$, by following $n-1$ straight line segments (each connecting each $P_{a_{i}}$ and $P_{a_{i+1}}$ ), it would never visit a point twice or cross its own path. Find the number of routes.

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Source and history

task_id
f30dbf6c-8473-58e9-b51e-9d0a6130423a
task_key
test--f30dbf6c-8473-58e9-b51e-9d0a6130423a
task_revision_id
1
config / split
/ test

Official source

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