To determine how many times all four digits change simultaneously on a digital clock displaying hours and minutes, we need to consider the possible combinations of digits for hours and minutes.
On a digital clock, the hours can range from 00 to 23, and the minutes can range from 00 to 59.
For the hours:
- There are 24 possible values for the first digit (0 to 2).
- There are 10 possible values for the second digit (0 to 9).
For the minutes:
- There are 6 possible values for the first digit (0 to 5).
- There are 10 possible values for the second digit (0 to 9).
To calculate the total number of times all four digits change simultaneously, we multiply the possibilities for hours by the possibilities for minutes:
24 (hours) * 10 (hours) * 6 (minutes) * 10 (minutes) = 14,400
Therefore, all four digits change simultaneously 14,400 times in a 24-hour period on a digital clock.