A home has 3 clocks: Clock A keeps perfect time, clock B loses a minute every 24 hours and clock C gains a minute every 24 hours.
On Jan 1 2022, (midnight of Dec 31 2021) all three show the correct time.
Assuming they were to continue at the same speed,
when will all of them again show the correct time at the same moment?
I'll assume all three clocks are ordinary 12-hour clocks that make no distinction between AM and PM. After exactly 720 days (half of the 1440 minutes in a day) the two inaccurate clocks will again show the right time. We'll assume there are no leap seconds intervening that would affect the outcome by a second or two.
720 days after Jan. 1, 2022 is Dec. 22, 2023.
The answer is thus the midnight shared by Dec. 21, 2023 and Dec.22, 2023, coincidentally the start of the day that I turn 79.
The date was calculated by a program I wrote "ages" ago for Apple ][+, in Applesoft basic, now converted to QuickBasic (with a lot of GWBASIC aka BASICA still in the code) and run under DOSBox in Windows. Too much spaghetti code to show here.
However, current verification can be found at
https://www.alarmdaddy.com/calculators/date/count/720-days-after-01-jan-2022
(found with a Google search
January 1 2022 + 720 days)
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Posted by Charlie
on 2022-07-10 09:53:53 |
solution
