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Digital Clock Lights

Date: 07/29/98 at 04:26:31
From: Rasheed O
Subject: Digital Clock Lights

A photographer's darkroom has no natural light. If the only light 
source in the room is a digital alarm clock (red LEDs, of course), at 
what time is the room the darkest? At what time is the room the 
lightest?  (Assume A.M. or P.M. makes no difference.)

Date: 07/30/98 at 16:15:54
From: Doctor Floor
Subject: Re: Digital Clock Lights

Hi Rasheed,

Thank you for sending your question to Dr. Math. 

For each digit we can count how many LEDs are lit:

   digit        number of LEDs
     0                6
     1                2
     2                5
     3                5
     4                4
     5                5
     6                6
     7                4
     8                7
     9                6

Each time consists of a number between 0 and 23, followed by : , and 
then a number between 00 and 59 (always two digits). Here I assume we 
can choose times between 0:00 and 23:59, rather than use A.M./P.M.

For the first number, between 0 and 23, the darkest choice is 1 and 
the lightest choice is 20. For the second number the darkest choice is 
11 and the lightest choice is 08. Here we are just looking at the 
possible combinations of the digits (left column) whose corresponding 
right column digits sum to the smallest possible number and largest 
possible number. 

So the lightest time is 20:08 and the lightest is 1:11.

Best regards,

- Doctor Floor, The Math Forum
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