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On What Day Did it Happen?

Stage: 1, 2 and 3
Article by NRICH team

Published February 2011.

There is a mathematical method for working out what day of the week each particular date fell on back as far as 1700. I wonder what day it was on Christmas Day in 1801. Neil Armstrong stepped onto the moon on July 21st 1969 - what day of the week was it? What day of the week were you born on? Test your parents' memory! You can also go into the future. What day will your birthday be on in ten years?

You need to know the year, month and day of the month. You need the special numbers listed below. And you need to follow the steps.

Month Numbers Century Numbers Day Numbers
January 1
February 4
March 4
April 0
May 2
June 5
July 0
August 3
September 6
October 1
November 4
December 6

If it's a leap year,

January is 0 and

February is 3

Dates from 1700 to Sept 16th 1742 Add 4
Dates from 1800 to 1899 Add 2
Dates from 1900 to 1999 Add 0
Dates from 2000 to 2099 Add 6
Dates from 2100 to 2199 Add 4
Sunday 1
Monday 2
Tuesday 3
Wednesday 4
Thursday 5
Friday 6
Saturday 7

Here are the steps, with an example to test it out.

I know my daughter was born on Wednesday October 1st 1986.

Steps Example
Step 1: Take the last two digits of the year (1986) 86
Step 2: Divide this by 4 and ignore any remainder (86/4 = 21 rem 2) 21
Step 3: Find the month number (October)  1
Step 4: Add the day number (1st) to the numbers found in Steps 1 to 3. 1 + 86 + 21 + 1 = 109
Step 5: Divide the answer by 7. If the remainder is 0, use 7 for the remainder number 109/7 = 15 rem 4
Step 6: Find the century number 0
Step 7: Add the remainder number from Step 5 to the century number 4 + 0 = 4
Step 8: Match this number to a day on the Day Number chart It's Wednesday!

Mmmmmm . I wonder how it all works?