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I had to calculate the number of odd days in 1600 years. I have read the answer to be equal to 0. But I don't get it to equal to 0.

This is the way I am calculating the number of odd days in 1600 years :

1600 years = 24 x 16 = 384 leap years   (100 years = 24 leap years) (because 100 years have 24 leap years) 1 leap year = 2 odd days (52 weeks + 2 odd days) 384 leap years = 384 x 2 = 768 odd days --(A) 1600 years = 1600 - 384 = 1216 ordinary years 1 ordinary year = 1 odd day (52 weeks + 1 odd day) 1216 ordinary years = 1216 x 1 = 1216 odd days--(B)  Total number of odd days = (A) + (B) = 768 + 1216 = 1984 odd days in 1600 years  and 1984 is not divisible by 7 ! 

Am I making a mistake ? If yes,what is it ?

  • 13
    what is an odd day?2012-08-05
  • 1
    @Khromonkey In a year there a 365 days. It means 52 weeks + 1 odd day2012-08-05
  • 2
    Is today an "odd day", for example? Why/why not?2012-08-05
  • 0
    @HenningMakholm I guess I had the incorrect knowledge.I knew odd day as 52 weeks + 1 .2012-08-05
  • 1
    My attempt at making sense is that an "odd day" is a day of the week that occurs an odd number of times. In a non-leap year with 52weeks+1day, six of the seven days of the week occur 52 times (an even number), while one of them occurs 53 times (an odd number). So the number of "odd days" in a year is the number of {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday} that occur an odd number (53) of times. [I haven't thought about 1752 when the Gregorian change happened. :-)]2012-08-05

7 Answers 7