Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem B. 4802. (May 2016)

B. 4802. The inscribed sphere of a right circular cone \(\displaystyle \mathcal{K}\) is \(\displaystyle \mathcal{G}\). The centres of the spheres \(\displaystyle g_1, g_2, \dots, g_n\) of radius \(\displaystyle r\) form a regular \(\displaystyle n\)-gon of side \(\displaystyle 2r\). Furthermore, each sphere \(\displaystyle g_i\) is tangent to both the lateral surface and the base of \(\displaystyle \mathcal{K}\), and also tangent to \(\displaystyle \mathcal{G}\). What may be the value of \(\displaystyle n\)?

Competition problem from the Soviet Union

(6 pont)

Deadline expired on June 10, 2016.


Statistics:

39 students sent a solution.
6 points:Andó Angelika, Borbényi Márton, Cseh Kristóf, Gáspár Attila, Horváth András János, Imolay András, Klász Viktória, Kocsis Júlia, Kővári Péter Viktor, Lajkó Kálmán, Matolcsi Dávid, Nagy Dávid Paszkál, Sudár Ákos, Tóth Viktor, Török Zsombor Áron, Váli Benedek, Várkonyi Dorka, Zólomy Kristóf.
5 points:Bukva Balázs, Döbröntei Dávid Bence, Fuisz Gábor, Kondákor Márk, Kosztolányi Kata, Losonczy Richárd, Márton Dénes, Páli Petra, Szabó Kristóf, Szakály Marcell, Szemerédi Levente.
4 points:1 student.
3 points:7 students.
1 point:2 students.

Problems in Mathematics of KöMaL, May 2016