3. Before you is a segment-digit. For displaying time on electronic clocks, each digit uses seven segments, each of which can be lit or not; the lit segments form the digit as shown in the figure

## 8723456789

That is, to display zero, six segments are used, to display one - two segments, and so on. On electronic clocks, only hours and minutes are displayed. How many minutes in a day does it take to display a time that uses more lit segments than the time one minute later? (The day starts at 00:00 and ends at 23:59) (20 points)
Solution: Let's write down the number of segments required to display each digit:

\section*{8723456789

$$
\begin{array}{llllllllll}
6 & 2 & 5 & 5 & 4 & 5 & 6 & 3 & 7 & 6
\end{array}
$$

Consider several types of displayed time:

1) The last digit of the minutes is not 9. Then the next displayed time differs by only the last digit. To reduce the number of segments, the last digit of the minutes at this moment should be 0, 3, 6, or 8. In total, such time is displayed for $24 \cdot 6 \cdot 4 = 576$ minutes in a day.
2) The last digit of the minutes is 9, but the number of minutes is not 59. Then in the next minute, the last digit will become zero, and the number of segments for its display will not change, meaning this number should decrease in the tens of minutes. That is, the digit in the tens of minutes can only be 0 or 3. In total, such time is displayed for $24 \cdot 2 = 48$ minutes in a day.
3) The number of minutes is 59, and the number of hours does not end in 9. Then in the next minute, the number of minutes will be zero, which means the number of segments for displaying the minutes will increase by 1. Therefore, the number of segments for displaying the last digit of the hours should decrease by at least 2, meaning the last digit of the hours can only be 0 or 6. In total, such time is displayed for 5 minutes in a day.
4) The number of minutes is 59, and the number of hours ends in 9. Then in the next minute, one of the times 10:00, 20:00 will be displayed - only the time 09:59 fits.

In total, suitable time is displayed for $576 + 48 + 5 + 1 = 630$ minutes in a day.

## Answer: 630 minutes