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It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

Question

It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?

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Solution

To find out the day of the week for Jan 1, 2010, we can follow these steps:

  1. Count the number of years between 2006 and 2010, which is 4 years.
  2. Determine the number of leap years in this period. 2008 is the only leap year between 2006 and 2010.
  3. Each normal year has 1 odd day (365 % 7 = 1) and each leap year has 2 odd days (366 % 7 = 2).
  4. So, the total number of odd days in these 4 years is 3 normal years (31 = 3 odd days) + 1 leap year (12 = 2 odd days) = 5 odd days.
  5. Since it was Sunday on Jan 1, 2006, we add the total number of odd days to Sunday.
  6. 5 odd days after Sunday is Friday.

So, the day of the week on Jan 1, 2010 was Friday.

This problem has been solved

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