Mathematical and Physical Journal
for High Schools
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Problem B. 4780. (March 2016)

B. 4780. For what natural numbers \(\displaystyle n\) is it true that whenever the midpoints of the sides of a convex \(\displaystyle n\)-sided polygon \(\displaystyle \mathcal{K}_n\) form a regular \(\displaystyle n\)-gon, then \(\displaystyle \mathcal{K}_n\) itself is also a regular \(\displaystyle n\)-gon?

(4 pont)

Deadline expired on April 11, 2016.


Statistics:

68 students sent a solution.
4 points:Baran Zsuzsanna, Bindics Boldizsár, Borbényi Márton, Cseh Kristóf, Csiszár Zoltán, Döbröntei Dávid Bence, Fajszi Bulcsú, Fuisz Gábor, Fülöp Anna Tácia, Gáspár Attila, Glasznova Maja, Hansel Soma, Hornák Bence, Imolay András, Janzer Orsolya Lili, Kerekes Anna, Klász Viktória, Kocsis Júlia, Kovács 246 Benedek, Matolcsi Dávid, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Nagy Kartal, Németh 123 Balázs, Németh 417 Tamás, Radnai Bálint, Sal Kristóf, Schrettner Bálint, Schrettner Jakab, Szabó 417 Dávid, Szemerédi Levente, Váli Benedek, Varsányi András.
3 points:20 students.
2 points:9 students.
1 point:4 students.
0 point:2 students.

Problems in Mathematics of KöMaL, March 2016