Posted: 12/4/2011 6:54:09 PM EDT
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How often and for how long (total minutes) are the numbers 0 thru 9 displayed in 24 hours on a digital clock? Go. |
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Assuming a 12-hour display format, which does not display a 0 in the first digit, the duration each digit appears, in minutes, is: 0 - 504 1 - 984 2 - 624 3 - 504 4 - 504 5 - 504 6 - 264 7 - 264 8 - 264 9 - 264 Frequency isn't really meaningful, as they don't appear at regular intervals. ETA: fixed my retarded arithmetic error just after DsrtEgl50 posted the correct answer below. If there's a monkey (or other, lesser prize) to be awarded, it's his. ETA2: My answer is more righterer than his (984 minutes for the number '1'). The monkey shall be mine! ETA3: ...unless simultaneous appearance of the same digit isn't counted more than once (e.g., '11:11' counts as 1 minute for the number '1'), in which case I'm far too drunk to figure it out. |
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Assuming HH:MM, 12-hour, no leading 0
Least significant digit, minute - 6 one minute displays/hr per digit over 24hrs = 144 minutes each for digits 0 through 9 MSD,M - 1 ten minute display/hr per digit over 24hrs = 240 minutes for 0 through 5 LSD,H - 2 one hour displays per 24 hours = 120 minutes for 0 through 9 LSD,H - 2 one hour displays per 24 hours = 120 minutes additional for 1 and 2 MSD,H - 2 two three hour displays per 24 hours = 240 360 minutes for 1 Aggregate for all instances of each digit: 0 = 504 minutes/day 1 = 864 984 minutes/day 2 = 624 minutes/day 3, 4 and 5 = 504 minutes/day 6, 7, 8 and 9 = 264 minutes/day I did already take my ambien for the night, so I'll double check my math tomorrow... Edited to fix my count on most significant digit, hour, which agrees with Holden_McRoyne. 
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Quoted:
ETA: fixed my retarded arithmetic error just after DsrtEgl50 posted the correct answer below. If there's a monkey (or other, lesser prize) to be awarded, it's his. I noticed some of your values were from 12 hour periods. Some were not, though, and I was trying to figure out where your offsets from 12/24 counts would've come from.
Edited to fix quote. |
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Quoted: Quoted: ETA: fixed my retarded arithmetic error just after DsrtEgl50 posted the correct answer below. If there's a monkey (or other, lesser prize) to be awarded, it's his. I noticed some of your values were from 12 hour periods. Some were not, though, and I was trying to figure out where your offsets from 12/24 counts would've come from. Edited to fix quote. I did the fourth digit wrong initially––I had 12 minutes for each, instead of 144. |
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OK, cancelling out overlaps, so that ANY minute in which a 1 is displayed only counts as one minute, etc., I get this: 0 - 450 1 - 780 2 - 600 3 - 450 4 - 450 5 - 450 6 - 252 7 - 252 8 - 252 9 - 252 Example: the number '6' appears in the fourth digit for six minutes every hour, for a total of 144 minutes in 24 hours. '6' appears in the second digit twice in 24 hours, for an hour at a time, giving a total of 120 minutes. However, 12 of these minutes are already accounted for, where '6' appears in the last digit, so the total duration during which a '6' appears is 252 minutes, not 264. ETA: This post brought to you by 3 liters of Asahi (I dunno, it sounded good with Chinese food). Do not use these calculations for missile guidance, Mars expeditions, life support equipment, etc. |