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Number Theory Level 2

What day of the week was 15th August 1947 ?

Saturday Friday Monday Thursday Sunday Tuesday Wednesday

Manish Dash by Manish Dash , 22, India

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1 solution

Vineet Singh
Jul 18, 2015

Required Day = Saturday - {(366 * 17 + 365 * 51 - 28)mod7} = Saturday - 1 = Friday

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Can you please elaborate the solution?

Simran Kaur - 5 years, 10 months ago

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Simran, I basically found out the remainder of the total number of days between 15 Aug 1947 to 18 July 2015, Saturday (the day when i solved the question) with 7 as there are 7 days in a week.

So, we should see the number of leap years and non leap years between those two dates.

Non leap years is given by [(2015-1947)/4] = 17, while non-leap years are the remaining 51 years.

Also, 15 Aug of any year is 28 days ahead of 18 July. Hence we need to substract 28 from 366 * 17 + 365 * 51.

Since the overall remainder is -1 wrt 7 or a remainder of 6 wrt 7 and we are looking at it with Saturday as the reference (the day when i wrote the solution :-), the required day must have been one less than or 6 more than a Saturday => Friday.

Hope this helps!

Vineet Singh - 5 years, 10 months ago

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