Find the number of trapeziums that it can be formed with the vertices of a regular polygon of n sides.
(In reply to
Generalized Solution by Brian Smith)
Amazing solution.
I was able to solve the odd case in a simpler way:
The are (n-1)/2 parallel chords in each of n directions. Choosing any two parallel chord gives a unique trapezoid.
[(n-1)/2 * ((n-1)/2 - 1)]/2 * n = n(n-1)(n-3)/8
I just couldn't figure out how to separate the rectangles from the trapezoids to avoid overcounting in the even case. Your diameters idea was great.
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Posted by Jer
on 2021-02-20 12:24:23 |
re: Generalized Solution
