[N. B.: This revision uses the constant 94 and 0=Sun, and adds
       further parameters to cover all valid Gregorian dates. Please
       post comments, if any, via Usenet or via ccnet.  Thanks.]

      HOW TO CALCULATE THE DAY OF THE WEEK FOR DATES AS OF 15.x.1582
 based on Hans' No-Sweat 1-Off 2-Fold 3-Step 4-Function Calculator Method  

     This is a more involved method to calculate the day of the week
     for Gregorian calendar dates from 15.x.1582 and as far into the
     future as workable using standard four-function calculators and
     certain mobile phones via a generalised formula requiring fewer
     key-clicks than any previous method not using tables.

Given:

Day.Month.Year as a Date on the Gregorian calendar as of
 15.octob.1582
   &
 YLJLD as the 'Year in which the Last Julian Leap Day occurred' prior to
 the given Date as if for a Julian Calendar whose years begin on 1.jan.
   &
 Century as a nominal "age" for each hundred of years as of 1.march.XY00
 (only one lag Offset thereby required for an entire Gregorian Century)
 so that if YLJLD = XYQR, then Century = XY (starting with Century 15)
   &
 delta = Year - YLJLD
   &
 yljld as the last two digits of XYQR, such that yljld = QR 
   &
 under as the number of years that Century is less than the next highest
 multiple of 4;

one can convert the given Date into a day of the week after completing
 the 3 steps below--with 33 key-clicks or less, without any mental
 multiplication or division.


STEP 0. Calculate the lag Offset:

        under * 2

  Remember the result or store it in memory.


STEP 1. Calculate the given Date's MonthIndex:

        Month * 2.56 + 94

  and then drop the fraction, and the hundreds digit, if any,
  to get an integer less than 100, e.g. 124.72 becomes 24;
  remember the result for use in Step 2.


STEP 2. Apply the generalised date conversion formula:

      (yljld/.8 + delta + MonthIndex + Day + Offset) / 7


STEP 3. Apply Hans' keypad mapping:

  Take the first digit after the decimal point (if none, use 0)   
  and map that to a day using the following patterns:

  +-----+-----+-----+                    +-----+-----+-----+
  | Fri | Sat |     |                    |  1  |  2  |  3  |
  |  7  |  8  |  9  |                    | Mon | Tue |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Wed | Thu |     |                    |  4  |  5  |  6  |
  |  4  |  5  |  6  |                    | Wed | Thu |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Mon | Tue |     |                    |  7  |  8  |  9  |
  |  1  |  2  |  3  |                    | Fri | Sat |     |
  +-----+-----+-----+                    +-----+-----+-----+
  | Sun |                                      |  0  |
  |  0  |                                      | Sun |
  +-----+                                      +-----+

(This is equivalent to assigning days to remainders of divisions by 7
 as for:  Sun=0  Mon=1  Tue=2  Wed=3  Thu=4  Fri=5  Sat=6.)


 Lag is the number of days that a Gregorian date to be converted falls before
 the same Julian date. It was zero for Century 02, during which the Gregorian
 Calendar, if already implemented beforehand, would have been the same as the
 Julian--thus leading to Hans' Julian Step 2 formula. It must be decreased by
 1 for every March 1st preceded by February 29th in the Julian but not in the
 Gregorian calendar. Lag is now -13 and will be -14 as of 1.iii.MMC to start
 off Century 21 when Hans' shorter Julian formula applies again to Gregorian
 dates, the last time being in Centuries 11 & 12 when it was -7 in both. In
 Century 00 as of 1.iii.IV, it was +2.


EXAMPLE Z.  29.Feb.1904  Century = 19  yljld = 00  delta = 4  under = 1

  1 * 2 = 2
  2 * 2.56 + 94 =  99.12 (MonthIndex = 99)
  00/.8 + 4 + 99 + 29 + 2    
  Divide by 7 = 19.142857...
  first decimal =  1   Day of Week = Mon


EXAMPLE A.  31.Dec.2100  Century = 21  yljld = 00  delta = 0  under = 3

  3 * 2 = 6
  12 * 2.56 + 94 = 124.72 (MonthIndex = 24)
  00/.8 + 0 + 24 + 31 + 6
  Divide by 7 =  8.714285...
  first decimal =  7  Day of Week = Fri


EXAMPLE B.  29.Feb.2000  Century = 19  yljld = 96  delta = 4  under = 1

  1 * 2 = 2
  2 * 2.56 + 94 =  99.12  (MonthIndex = 99)
  96/.8 + 4 + 99 + 29 + 2
  Divide by 7 = 36.285714...
  first decimal =  2  Day of Week = Tue


EXAMPLE C.  1.Mar.2000  Century = 20  yljld = 00  delta = 0  under = 4

  4 * 2 = 8
  3 * 2.56 + 94 = 101.28 (MonthIndex = 1)
  00/.8 + 0 + 1 + 1 + 8
  Divide by 7 = 1.428571...
  first decimal = 4  Day of Week = Wed 


 The Examples above are for a standard (running total) calculator;
 those for RPN or algebraic calculators are left as an exercise.

(Hint: re-order Steps and streamline operations.)

--

REFERENCES:     http://oz.ccnet.us/dayofweek/

http://groups.google.com/group/sci.math/msg/a716e5ca3af3ed28