Expert: Ahmed Salami - 10/22/2004

Question
January 1, 2000 was a Saturday, and 2000 was a leap year.  What day of the week will January 1, 2050 be.

Answer
Hi Craig,
A leap year occurs once in every 4 years. From January 1, 2000 to December 31, 2003 we have a complete 4 year period of a total of 366 + 3(365) = 1461 days
From January 1, 2000 to December 31, 2047 we would have completed 12 series of a similar 4 year period amounting to a total of 1462(12)days = 17532 days
The year 2048 would also be a leap year and 2049 an ordinary year with a combined number of days of 366 + 365 = 731 days
Therefore, between January 1, 2000 and December 31, 2049 we have 17532 + 731 = 18263 days
January 1, 2050 would therefore be exactly 18263 days after January 1, 2000. But exactly any number of 7 days after January 1, 2000 we would have a saturday.
18263/7 = 2609
So we have it that January 1, 2050 is exactly 2609 weeks after January 1, 2000 and is therefore a saturday.
I hope you understand it.
Regards.