Question 50
We started the Mathematical Olympiad punctually at 9:00, as I checked on my watch, which was working correctly at that moment. When I finished, at 13:00, I looked at the watch again and saw that the hands had come off their axis but kept the position they had when the watch was working. Curiously, the hour and minute hands appeared exactly superimposed, one on top of the other, forming a (non-zero) angle of less than $120^\circ$ with the second hand. At what time did the watch break? (Give the answer in hours, minutes and seconds with a maximum error of one second; assume that, while it was working, the hands of the watch moved continuously.)