Required Mathematical Intelligence

Chapter 85 The tricky theft case
One morning, people found that the safe of a store had been broken, and the old man who guarded the store at night was killed and thrown into the river.After the body was recovered, a policeman found a high-end pocket watch with very accurate travel time in the pocket of the deceased, but it had stopped working.Undoubtedly, the time indicated by the hands is a very important clue.However, the policeman forgot the rules to protect the scene, and fiddled with the hands of his pocket watch several times.The detective chief asked him if he remembered the hour indicated by the front hour hand?The policeman reported: "I didn't look at the exact time, but I was very impressed by one thing, that is, the hour and minute hands overlapped, while the second hand stayed at a spot." The detective looked at the pocket watch, and there were spots on the surface. The place is 49 seconds.He immediately took out the paper and calculated, and quickly determined the exact time when the body was thrown into the river, thus narrowing down the scope of the case and quickly catching the murderer.Do you know when the pocket watch hands stop?

[Answer: The hands of the pocket watch stop at 4:21:49.This is because: within 12 hours, there are 11 opportunities for the hour and minute hands to coincide.The speed of the hour hand is 1/12 of the minute hand. Therefore, after the last overlap, the two hands will overlap again every 1 hour and 5 minutes.After midnight, the time when the two needles coincide is:
(1) 1 hour 5 minutes 27311 seconds;
(2) 2 hour 10 minutes 54611 seconds;
(3) 3 hour 16 minutes 21911 seconds;
(4) 4:21:49111.

And the police saw that the second hand stopped at the spot where it was exactly 49 seconds. ]
(End of this chapter)