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Omni-MATH / Determine the greatest positive integer n such that in three-dimensional space, there exist n points P₁,P₂,⋯,P_(n), among n points no three points are collinear, and for arbitary …

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problem

Determine the greatest positive integer n n such that in three-dimensional space, there exist n points P1,P2,⋯,Pn, P_{1},P_{2},\cdots,P_{n}, among n n points no three points are collinear, and for arbitary 1≤i<j<k≤n 1\leq i < j < k\leq n, PiPjPk P_{i}P_{j}P_{k} isn't obtuse triangle.
Plain-text mathematical notation (without MathML)
Determine the greatest positive integer n such that in three-dimensional space, there exist n points P₁,P₂,⋯,P_(n), among n points no three points are collinear, and for arbitary 1≤i<j<k≤n, P_(i)P_(j)P_(k) isn't obtuse triangle.
Original LaTeX notation
Determine the greatest positive integer $ n$ such that in three-dimensional space, there exist n points $ P_{1},P_{2},\cdots,P_{n},$ among $ n$ points no three points are collinear, and for arbitary $ 1\leq i < j < k\leq n$, $ P_{i}P_{j}P_{k}$ isn't obtuse triangle.

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Source and history

task_id
0b09e5a0-b76f-5b8d-8254-c27fdc106000
task_key
test--0b09e5a0-b76f-5b8d-8254-c27fdc106000
task_revision_id
1
config / split
/ test

Official source

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