Digital Clock Digits

[Dr. Atul Nischal]

Hi,

Most of us have seen and used digital clocks. But, did you think that there is a lot of mathematics you can do with these clocks. Here is a nice problem that requires a bit of reading...but it is definitely very interesting.

Also, see if you can create your own digital clock problems :-)

 

Problem: Digital Clock Digits

My clock radio can display times from 12:00 to 11:59 using a four-digit display.Each digit is made up of seven LEDs (Light-Emitting Diodes) which are turned off or on depending on the digit to be displayed. The digit 2 has five of the seven lights on while the digit 8 has all seven lights on. All of the digits are shown below:

For times from 1:00 to 9:59 only three digits are displayed. The leftmost digit is completely off for these times. For times from 10:00 to 12:59 all four digits are used.

One night I was having difficulty sleeping so I counted the number of lights that were on to make each individual time from 10:00 PM to 12:59 AM. For example, when it was 11:11, I noted that a total of 8 of the LEDs were on.

During the time that I was awake from 10:00 PM to 12:59 AM, how many of the times had exactly 20 of the LEDs on?

Happy Thinking!