Hint. It is not the case that New Year's Day falls on each day of the week with equal probability. The Gregorian calendar cycles exactly every 400 years, so look at any 400-year period. Every year a multiple of 4 is a leap year except multiples of 100 that are not multiples of 400 (1700, 1800, and 1900 were not leap years, but 2000 was). Go through an entire 400-year cycle in 28-year mini cycles. Or just bite the bullet and write a Python program, a whole lot easier but not available in days past and not as revealing of calendar facts.