One of our colleagues used to have a digital alarm clock - well, this was in the days before everyone started using their phones as alarm clocks! In spite of being "steam-age" technology it worked very well; let's face it alarm clocks have only one purpose, and so it either wakes you or it doesn't.
There was one little oddity about it - setting the time after a power cut. If it lost power it displayed 00:00, flashing to draw your attention to it. There were two button to alter the time, one went forward and the other went back. And here is the thing - the forward button advanced the time by ten minutes every second, but the back button decreased the time by one minute every second.
The design was clearly intended to allow you to move quickly to just past the correct time, and then move slowly back to the correct time.
However, you know the type of people who set quizzes and puzzles, always curious and thinking about things! There must be a time of day when it's quicker to just go backwards to the correct time, rather than go forwards and then back.
Obviously if the current time is 23;59 it is far, far quicker to click back one minute than to go forwards and then back. But where is the break even point? At what time of day does it become quicker to go back to the time, rather than forwards?
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Answer at 9.00 on Monday
By my count:
Go forwards for 00:01 – 21:40
Go backwards for 21:41 – 24:00
A day has 1440 minutes. Going forward is 10x as fast as going backwards. This means we can split the day in 10+1=11 parts;
1440/11=130,9 minutes = 02:10 to 02:11 is the breaking point;
At 02:10, going backwards takes 130/1=130 seconds, and going forwards takes (1440-130)/10=131 seconds.
At 02:11, going backwards takes 131/1=131 seconds, and going forwards takes (1440-131)/10=130,9 seconds.