Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 477. (November 2015)

K. 477. Johnny is trying to learn how to eat with chopsticks. To practice, he needs to lift a ball of diameter 4 cm with the chopsticks, as shown in the diagram. (A ball can be lifted if its centre lies in the plane of the two sticks.) The two chopsticks in Johnny's hand enclose an angle of 60 degrees. Find the distance of the crossing point of the two sticks from the closest point of the ball during this operation.

(6 pont)

Deadline expired on December 10, 2015.

### Statistics:

 109 students sent a solution. 6 points: Aradi Sára Katalin, Barta Ákos, Bertók Zsanett, Cseke Tibor, Csikós-Nagy Máté, Csóka Zoárd, Csontos Lilla Ágnes, Czeba Zsolt, Dékány Barnabás, Dobák Dániel, Farkas Norbert, Földvári Ádám, Gárdonyi Csilla Dóra, Giorgos Nikiforakis, Hegedüs Péter, Hoffmann Balázs, Horváth Balázs Máté, Kertész Ferenc, Kiss 468 Péter, Kluèka Vivien, Kovács 161 Márton Soma, Kovács Levente András, Kozma Bianka, Köpenczei Csenge, Lapu Kolos, Marshall Tamás, Máté 446 Dávid, Mester Gyöngyvér, Miskolczi Abigél, Nagy Csaba Jenő, Nemes Balázs Boldizsár, Németh 728 Ágnes Sára, Pálvölgyi Szilveszter, Piller Ádám, Pinke Jakab Zoltán, Rubovszky Cecília , Sal Dávid, Simon Dóra, Szalai Regina, Szöllősi Brigitta, Veress Luca, Zentai Flóra, Zsótér Laura. 5 points: 26 students. 4 points: 21 students. 3 points: 6 students. 2 points: 5 students. 1 point: 4 students. 0 point: 2 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, November 2015