You own a 12-hour LED clock. There are two digits available for the hour, a colon (which is always illuminated) and two digits for the minute. Each LED digit is composed of seven separate segments. Assuming that it takes the same amount to energy to illuminate each LED segment, at what time will the clock consume the most power, and the least power?

* Although two digits are available for the hour, the clock does not display leading zeroes. For example, four o’clock is displayed as 4:00, not 04:00.
* Six LED segments are used to display the numerals “9″ and “6″.

Solution

While its intuitive to know that 8 uses the most power, and 1 the least; it is still useful to jot down the power consumption of each digit.

1 = 2 segments
7 = 3 segments
4 = 4 segments
2,3,5,6,9 = 5 segments
0 = 6 segments
8 = 7 segments

It is important to realize that the set of valid digits for hours differs from that of minutes.

HH = {1,2,3,4,5,6,7,8,9,10,11,12}

MM = {01,02,03,…,10,11,12,…,57,58,59}

You could do the work and go through each combination… or use some intuition!

The most power

We know 8′s use the most power so we should try to use as many of them as possible.

88:88 would be the easy answer but there is no such time!

So we know it is likely something like: _8:_8

Inserting the next highest valid digit from our table above we get 8:08.

Instinctively, we know we should be using both digits of the hour component.

Sure enough 10 uses more electricity than 8!

Answer: 10:08

The least power

Using a similar strategy we want to use as many 1′s as possible: 11:11

Although this is a valid time, we know instinctively that we can drop the first digit.

Answer: 1:11

I think 10:08 must be an inside engineering joke or something. You will often see that as the time in print ads and what not. Keep you eye out!