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View Full Version : interesting question from USSR olympiad book

gumpzilla
02-01-2006, 11:01 AM
Does New Year's Day fall more frequently on Saturday, Sunday, or neither?
Marko Schmarko
02-01-2006, 02:13 PM
It seems like it must be neither, but I'm pretty sure I'm wrong.
jason1990
02-01-2006, 03:11 PM
I think the reason it is not neither is because every fourth year is not a leap year. Years ending in 00 are a leap year only when that year is divisible by 400. As a consequence, 1/1/2000 and 1/1/2400 are both Saturdays. According to Excel, there are 56 Saturday New Year's Days between 2000 and 2399. There are 58 Sundays. Since the days of the week repeat exactly every 400 years, Sunday occurs more often.
ADDboy
02-02-2006, 01:08 AM
A similar calculation shows that the 13th is a Friday more often than any other day of the week.