Problem P. 3888. (April 2006)
P. 3888. A man is walking along a straight road from point A to point B with a uniform speed. Point O is on the perpendicular bisector of the line segment AB, and at O there is a man who is beating a drum. Another day another man is walking from A to B, with the same speed as the first man was walking, and plays the drum, while an observer listens at point O. In which case does the observer count more beats while the man moves from A to B? (The beating starts in both cases well before the man leaves A, and lasts at least until the man reaches B. The beating is uniform, its period is the same in both cases and much smaller than the time needed to walk from A to B.)
Deadline expired on May 11, 2006.
42 students sent a solution. 5 points: Almási 270 Gábor András, Balogh Máté, Blázsik Zoltán, Dombi András, Dudás János, Engedy Balázs, Englert Dávid, Farkas Ádám László, Fülöp Bálint, Gombos Gergely, Győri Tamás Noé, Hasznos László, Hotzi Bernadette, Konczer József, Kónya 495 Gábor, Megyeri Balázs, Molnár 811 Kristóf, Nagy 224 Csaba, Nagy 317 Péter, Nagy 555 Zoltán, Nyíri Dávid Ákos, Pásztor Attila, Schattmann 123 Péter, Széchenyi Gábor, Szilágyi Zsombor, Szirmai Péter, Szolnoki Lénárd, Takács 484 Marcell, Takátsy Balázs, Tüzes Dániel, Varga Bonbien, Vécsei Miklós, Werner Miklós. 2 points: 6 students. 1 point: 3 students.