Ruda received an alarm clock for his birthday. He was happy about it and set it according to the exact time. Since then, every morning when he got up (Saturdays, Sundays, and holidays included), he pressed the button that lights up the display for exactly 4 seconds. He noticed that during the time the button was pressed, the time on the alarm clock was stopped. Otherwise, the alarm clock neither slowed down nor sped up. On the afternoon of December 11th, Ruda looked at his alarm clock and found that it was exactly 3 minutes behind the correct time.

When did Ruda receive this alarm clock?

(M. Petrová)

Hint. How many times did Ruda press the button?
First, we will determine how many times Ruda pressed the button that lights up the display: He held the button for 4 seconds each time, and the total delay of the alarm clock was eventually 3 minutes, or 180 seconds. Ruda therefore pressed the button a total of 45 times $(180: 4=45)$.

Every day, he pressed the button in the morning after waking up. Now we will determine which day he pressed it for the first time by counting back 45 days from December 11: In December (from the 11th to the 1st), it is 11 days, and November (from the 30th to the 1st) has 30 days, which totals 41 days. We need to count back 4 more days in October: 31st, 30th, 29th, 28th.

Ruda pressed the lighting button for the first time on October 28. He received the alarm clock one day earlier, i.e., on October 27.