Discussion

What will be the day of the week 15th August, 2010?

Answer: A

Count the odd days up to the date.

2000 years. Complete centuries in multiples of 400 leave no odd days, so 2000 years contribute 0.

2001 to 2009. Nine years of which 2004 and 2008 are leap:

\[ 7(1) + 2(2) = 11 \equiv 4 \pmod 7 \]

1 January to 15 August 2010. 2010 is ordinary:

\[ 31 + 28 + 31 + 30 + 31 + 30 + 31 + 15 = 227 \equiv 227 - 224 = 3 \pmod 7 \]

\[ \text{total odd days} = 0 + 4 + 3 = 7 \equiv 0 \pmod 7 \]

Zero odd days corresponds to Sunday.

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