Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 490. (January 2016)

K. 490. Anthony is training ants. The performance starts with 99 ants sleeping on a 1-metre long straight rod. When a whistle is blown, they all wake up at the same time, and start crawling towards an end of the rod, at a speed of 1 cm/s. If an ant reaches the end of the rod, it will leave the rod. If two ants meet, they will turn back immediately, and start crawling in the opposite direction. The performance ends when the last ant has left the rod. What is the maximum possible duration of the performance?

(6 pont)

Deadline expired on February 10, 2016.

### Statistics:

 54 students sent a solution. 6 points: Barta Ákos, Csáfordi József, Csóka Zoárd, Debreczeni Tibor, Dékány Barnabás, Fekete Barnabás, Gárdonyi Csilla Dóra, Gilicze Márton, Hoffmann Balázs, Kertész Ferenc, Kiss 468 Péter, Kovács 576 Kristóf, Marshall Tamás, Mészáros 916 Márton, Mónos Péter, Nagy Csaba Jenő, Nyitrai Boglárka, Póta Balázs, Rubovszky Cecília , Szántó Julianna, Varga 294 Ákos. 5 points: Hegedűs András, Keltai Dóra, Máté 446 Dávid. 4 points: 3 students. 3 points: 2 students. 2 points: 2 students. 1 point: 1 student. 0 point: 20 students. Unfair, not evaluated: 2 solutions.

Problems in Mathematics of KöMaL, January 2016