Do you know what day you were born?
month     day     year (range 1 ... 2400)
Saturday May 18th 2013 

Mondays child is fair of face
Tuesdays child is full of grace
Wednesdays child is full of woe
Thursdays child has far to go
Fridays child is loving and giving
Saturdays child works hard for his living
And the child that is born on the Sabbath day is bonny and blithe and good and gay.

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Tutorial:

How to calculate 'Day of the Week' in your head
Seven steps - detailed below
The year, month and date are used to find a total.
Adjustments are only necessary for certain centuries
and the days preceeding February 29th.
The total is divided by 7 but only the remainder used.
The day is where remainder 0=Sunday, 1=Monday, 2=Tuesday, etc.
Works for all centuries :

Step[#]Using:
year=13, month=05, day=18
ValueSub-total
1-1   if century is 2000 [1] -1 -1
2-1   if leap year and before Feb 29 0 -1
3+ year   (+ 13)
+ year   divided by 4 (+ 3)
    ignore remainder
1615
4+ month equal to '0336 1462 5035'
ie Jan=0, Feb=3, Mar=3, Apr=6, May=1
1 16
5+ day 18 34
6+ remainder of total divided by 7 6 6
7Solution:   Day of week where:
Sun=0, Mon=1, Tue=2, Wed=3, Thu=4, etc
Sat
Notes for above steps
#1 - Century adjustment:
0000,  0400,  0800,  1200,  1600,  2000   -1
0100,  0500,  0900,  1300,  1700,  2100   +4
0200,  0600,  1000,  1400,  1800,  2200   +2
0300,  0700,  1100,  1500,  1900,  2300   +0

May be simplified by using the following 3 rules:
-1   for centuries exactly divisible by 400 (Leap Century)
+2   for all other even centuries
+4   for centuries following a Leap Century
#2 - Leap Year adjustment::
if and only if a Leap Year
and the date is less than Februray 29th    -1
#3 - Years and quarter of years to be added
add last two digits of the year
also divide the last two year digits by 4
only add the remainder
#4 - Month numbers to be exchanged from following table:
Jan Feb Mar Apr    0 3 3 6
May Jun Jul Aug    1 4 6 2
Sep Oct Nov Dec    5 0 3 5
#5 - Days to be added to running total:
Add the day number to the total
#6 - Divide sub-total by 7:
Only use the remainder to find day of the week (see above).
#7 - Use remainder to find Day of Week from following table
0 = Sunday
1 = Monday
2 = Tuesdayday
3 = Wednesday
4 = Thursdayday
5 = Fridayday
6 = Saturday
Once the month table is learned the calculation is quite simple and gets easier with practise :)