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1. What will be the day of the week 15th August, 2010?
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days ≡ 4 odd days.
Jan. Feb. March April Mayb June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
∴ 227 days = (32 weeks + 3 days) ≡ 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 ≡ 0 odd days.
Given day is Sunday.
Solution:
15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days ≡ 4 odd days.
Jan. Feb. March April Mayb June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
∴ 227 days = (32 weeks + 3 days) ≡ 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 ≡ 0 odd days.
Given day is Sunday.