No 50

The Day Formula

Amazingly there is one formula that can be used to calculate on which day of the week any given date will fall. Here it is:

Let's do the calculations for March 13th 2000. In this case m=3 since March is the 3rd month, d=13 and y=2000. The square brackets [.] indicate that when you have calculated what is inside the brackets then ignore any fractional value after the decimal point. So here is the calculation inside the largest brackets:

7+13+4+2000+500-20+5-2=2507

mod 7 asks for the remainder when 2507 is divided by 7. Check that this gives you 1 (since 2507=7x358+1). The value 1 from the formula gives Monday: Sunday=0, Monday=1, Tuesday=2 etc.

On which day of the week were you born? On which day of the week is your next birthday? Will April Fool's day land on a school day this year? Use the formula to find out.

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E-mail us at madrascollege.maths@fife.gov.uk

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