Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 695. (April 2017)

A. 695. We are given \(\displaystyle 2k\) lines, \(\displaystyle e_1, \ldots, e_{2k}\) in a plane \(\displaystyle S\), further given a line \(\displaystyle g\) which has an angle \(\displaystyle \alpha\) with \(\displaystyle S\). Show that the sum of the pairwise angles between the lines \(\displaystyle e_1, \ldots,e_{2k}, g\) is at most

\(\displaystyle (k^2+k)\cdot \dfrac \pi 2 + k\alpha. \)

(5 pont)

Deadline expired on May 10, 2017.


9 students sent a solution.
5 points:Baran Zsuzsanna, Gáspár Attila, Imolay András, Matolcsi Dávid, Szabó Kristóf, Williams Kada.
4 points:Schrettner Jakab.
3 points:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, April 2017