Digital Clock LightsDate: 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 Check out our web site! http://mathforum.org/dr.math/ |
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