This is a more involved method to calculate the day of the week
     for Gregorian calendar dates from 15.oct.1582 & as far into the
     future as workable using standard four-function calculators &
     certain mobile phones via a modified 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
   &
 SPQR as the 'Year of the last Julian Leap Day' prior to the given
 Date (as if for a Julian Calendar whose years begin on 1.jan.)
   &
 SP as a nominal 'century' for the hundred years as of 1.march.SP00
 (only one Lag offset thereby required for such a Gregorian century,
  starting with century 15)
   &
 QR as the two-digit 'Year of the last Julian Leap Day'
   &
 delta = Year - SPQR
   &
 under as the amount that SP is less than the next higher multiple
 of 4;

a standard four-function calculator 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 by the user.


STEP 0. Calculate the effective Offset due to Lag and delta:

        under + under + delta

  Remember the result or store it in memory.


STEP 1. Apply Lachman's Congruence:

        Month * 2.56 + 94

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


STEP 2. Apply the modified date conversion formula:

      (QR/.8 + 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 behind
 the same Julian date. It was zero for century 02, during which the Gregorian
 Calendar, if already implemented beforehand, would have coincided with 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 would have been -7.
 In century 00 as of 1.iii.IV, it would have been +2.


EXAMPLE Z.  29.feb.1904  SP = 19  QR = 00  delta = 4  under = 1

  1 + 1 + 4 = 6
  2 * 2.56 + 94 =  99.12 (MonthIndex = 99)
  00/.8 + 99 + 29 + 6
  Divide by 7 = 19.142857...
  first decimal =  1   Day of Week = Mon


EXAMPLE A.  31.dec.2100  SP = 21  QR = 00  delta = 0  under = 3

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


EXAMPLE B.  29.feb.2000  SP = 19  QR = 96  delta = 4  under = 1

  1 + 1 + 4 = 6
  2 * 2.56 + 94 =  99.12  (MonthIndex = 99)
  96/.8 + 99 + 29 + 6
  Divide by 7 = 36.285714...
  first decimal =  2  Day of Week = Tue


EXAMPLE C.   1.mar.2000  SP = 20  QR = 00  delta = 0  under = 4

  4 + 4 + 0 = 8
  3 * 2.56 + 94 = 101.28 (MonthIndex = 1)
  00/.8 + 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.)

--

       REFERENCE

gopher://gopherite.org/0/users/retroburrowers/TemporalRetrology/cc/jg