There is a simple pattern which shows that
some specific dates (day and month) in a year
ALWAYS fall on the same weekday, nicknamed D-day.
For 2016, D-day is Monday.
(1) The days 04/04, 06/06, 08/08, 10/10 and 12/12
all fall on the same week day — D-day.
(2) The days 05/09, 09,05, 07/11 and 11/07
also fall on D-day. This can be remembered
by the mnemonic “He had a 9 to 5 job at 7/11”
Because of leap years January and February
are slightly more complicated:
(3) The last day of February (mathematically known as 0 March)
falls on D-Day.
(4) In leap years (divisible by 4) the 4th of Jan falls on D-Day;
in non-leap years the 3th of Jan falls on D-Day.
(1) occurs because the difference in days is always two months
and two days, and of these two consecutive months
it is always true that one has 30 days and the other 31.
So the difference is always 30+31+2 = 63 days, a multiple
This rule was discovered by John Horton Conway and is described in
Richard Guy, John Horton Conway, Elwyn Berlekamp :
“Winning Ways: For Your Mathematical Plays, Volume. 2: Games in Particular”,
It is also possible to compute the D-day for
every year of the century, but I find it too
difficult to remember.