To determine how many times all six digits on a digital clock (hours, minutes, and seconds) change simultaneously within a 24-hour period, let's break it down:
Hours: The hours on a digital clock range from 00 to 23, which is a total of 24 possible values.
Minutes: The minutes on a digital clock range from 00 to 59, which is a total of 60 possible values.
Seconds: The seconds on a digital clock also range from 00 to 59, giving us another 60 possible values.
To find the number of times all six digits change simultaneously, we need to calculate the number of common combinations between hours, minutes, and seconds.
The total number of possible combinations is obtained by multiplying the number of options for each digit:
Total Combinations = (Number of hours) × (Number of minutes) × (Number of seconds) Total Combinations = 24 × 60 × 60 Total Combinations = 86,400
Therefore, within a 24-hour period, all six digits on a digital clock change simultaneously 86,400 times.