"questions 10 year olds ask"
a friends 10 year old son asked me to adjust the date on his watch (analog with a non-self adjusting date)
i set the date for him and said "you have to do this every time there are less than 31 days in a month, otherwise it will never be accurate"
he thought for about 4.7852 secs, gave me 'the look' and said, "it will, just not as often" did i mention he's 'clever'?
well, i went home, sat there scribbling for about 5 minutes, reached the conclusion that 17 years can't be right and gave up 
the question:
if the date is correct on the 1st of january 2000 -not a leap year- and you don't adjust it on the 1st of march -the date showing is the 29th- when will the watch show the correct date again?
jonah
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General discussion
here's one for our logic/math people, or
Discussion is locked
17 Posts
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It's going to gain 3 days every 4 years. It's going to need to gain a full 365 days to be accurate again. Some quick math tells me the battery will die by then. When you put the new one in, you have to reset it. It will then be right. 
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It's going to turn over the date 12 X 31 times or 372 days per year. That means it will be slowed by 27 days every four years.
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It would be slow 6 days at the end of 2000. (February 2 days - leap year, April, June, September, November are 1)
It would slow another 7 in 2001 to toal 13. (same as above but Feb is 3 days now)
Then another 7 in 2002 for a total of 20.
It would be behind another 7 at the end of 2003, totaling 27.
And the final four would come in 2004 from 2 days in Feb (leap year again), and 1 each in April and June. So by July 1, 2004, the watch would be behind by exactly 31 days, causing it to be in sync again.
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contrary to what the calendar says. So if 2000 is not a leap year, you have a 7 day difference in 2000, and so on.
2000 not a leap year
2001 not a leap year
2002 not a leap year
2003 a leap year
so Dec 31 2003 there are 27 days difference, i.e. 4 days of mismatch remaining. January is 31 days, so no gain there. Feb. is 28 days, you are down to 1 day mismatch, March you remain the same, and April you catch up, thus May 1 you are even again.
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2000 was a leap year, but you said -not a leap year- so I assumed you wanted us to ignore that 2000 was a leap year. If we ignore that 2000 was aleap year, May 1 2004 is the next date when the watch will align with the calendar. If we were to take 2000 as a leap year, the next alignment will me July 1 2004.
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double "00" -1900- is, but if it divides by 500 -2000-, it isn't
*and i thought "the matrix" was complicated*
jonah
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the rule is years divisible by 100 are not, except in the case of years also divisible by 400.
1800 and 1900 were not, but 2000 is
2100, 2200, 2300 will not, but 2400 will be
http://aa.usno.navy.mil/faq/docs/leap_years.html
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Leap year rules
In order to get a closer approximation, it was decided to have a leap day 97 years out of 400 rather than once every four years. This would be implemented by making a leap year every year divisible by 4 unless that year is divisible by 100. If it is divisible by 100 it would only be a leap year if that year was also divisible by 400.[2][3] So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300, 2500, 2600, 2700, 2900 and 3000 will not be leap years, but 2400 and 2800 will be. The years that are divisible by 100 but not 400 are known as "exceptional common years". By this rule, the average number of days per year will be 365 + 1/4 - 1/100 + 1/400 = 365.2425.
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when will the watch show the correct date again?
the 2nd of January, 2000?
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"and you don't adjust it on the 1st of march -the date showing is the 29th- when will the watch show the correct date again?"
Which means that the asked-for date will occur after March 1, 2000.
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