Mathematical and Physical Journal
for High Schools
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Problem B. 4756. (December 2015)

B. 4756. In the interior of a unit cube, there are some spheres with a total surface area of 2015. Show that

\(\displaystyle a)\) there exists a line that intersects at least 500 spheres,

\(\displaystyle b)\) there exists a plane that intersects at least 600 spheres.

Hungarian Mathematics Competition of Transylvania

(6 pont)

Deadline expired on January 11, 2016.


Statistics:

42 students sent a solution.
6 points:Andó Angelika, Baran Zsuzsanna, Bodolai Előd, Borbényi Márton, Bukva Balázs, Busa 423 Máté, Csertán András, Czirkos Angéla, Dobák Dávid, Döbröntei Dávid Bence, Gáspár Attila, Hansel Soma, Imolay András, Juhász 326 Dániel, Kasó Ferenc, Kerekes Anna, Keresztes László, Keresztfalvi Bálint, Klász Viktória, Kovács 246 Benedek, Kővári Péter Viktor, Matolcsi Dávid, Molnár-Sáska Zoltán, Nagy Dávid Paszkál, Németh 123 Balázs, Páli Petra, Schefler Barna, Somogyi Pál, Souly Alexandra, Sudár Ákos, Szabó 864 Blanka, Szabó 997 Balázs István, Tóth Viktor, Váli Benedek, Záhorský Ákos, Zsigri Bálint.
4 points:1 student.
3 points:3 students.
1 point:1 student.
0 point:1 student.

Problems in Mathematics of KöMaL, December 2015