PHONE NUMBER METHOD FOR DAY-OF-WEEK CALCULATION (1901 to 2099)
              by Hans Lachman, 12/13/2014

Here is a convenient method for determining the day of the week
for any date (1901 to 2099) using only a mobile phone with a
built-in calculator, or any calculator along with a phone keypad.

Each month is assigned a one-digit "phone number" as follows:

For month m, select the mth letter from the 12-letter mnemonic
"IRS FLU FOX IRA", and then find that letter on the phone keypad.
That key is that month's phone number.  (For example, December is
the 12th month, so select the mnemonic's 12th letter, "A", which
is found on phone button 2.)

Using that "phone number" in place of "#", follow these steps on
the phone's calculator ("YYYY.MM" is the 4-digit year followed by
a decimal point and the 2-digit month, and DD is the day):

YYYY.MM * 1.25 + 0.97 = (drop the fraction, integer part is ZZZZ)
ZZZZ + # + DD =
/ 7 =

The final step is really a "mod 7" which can be completed by
multiplying the fraction part of the last result above by 7.
But to avoid that multiplication step, this method suggests
looking at the first digit of the fraction part and using the
phone keypad to help visualize the result as follows:

.1=Mon .2=Tue .3=unused
.4=Wed .5=Thu .6=unused
.7=Fri .8=Sat .9=unused
       .0=Sun

Or, use the equivalent visualization on a calculator keypad:

.7=Fri .8=Sat .9=unused
.4=Wed .5=Thu .6=unused
.1=Mon .2=Tue .3=unused
.0=Sun

EXAMPLE: 15 APR 2000 (Tax Day in the U.S., used in this example
to help you remember that the mnemonic starts with "IRS")

2000.04 * 1.25 + 0.97 = 2501.02
2501 + F + 15 = 2519 ("F" is on phone button 3)
/ 7 = 359.857... (.8 = Sat)

The method can be expressed notationally as follows:

(INT[YYYY.MM * 1.25 + 0.97] + # + DD) mod 7

where # is the month's one-digit "phone number" (for month MM,
select the MMth letter from "IRS FLU FOX IRA" and find it on the
phone keypad).  Result of 0 = Sunday, 1 = Monday, etc.

To remember the mnemonic "IRS FLU FOX IRA", it may help to say,
"The IRS gave the FLU to the FOX, so he opened an IRA."  This is
rather U.S.-centric, and some may prefer to use a different but
equivalent mnemonic, like "GPS FLU DNA GPA" or "ISP DJU DOW IRC".

The constant "1.25" is used because every block of 4 years
advances the day-of-week calculation by 5 days (an advance of
1.25 days per year).  "0.97" effects a leap-day adjustment; this
constant might be more easily remembered if one knows that there
are 97 leap days per 400 years (but this is only coincidental).
The result of "1 = Monday", etc., is by design, to be consistent
with some other published methods, and because in some cultures
(e.g., Chinese), Monday is referred to as day number one.

This method was designed to be easy to remember and quick to use
in any situation where a calculator and a telephone keypad are
available and the date is within the target range (1901-2099).
Whether it meets those objectives better than other methods is,
of course, subjective; but it is probably at least competitive
in terms of minimizing number of steps, avoiding conditionals,
and allowing the user to not consider or know anything about when
leap days occur.  This method and the previously-published one,
"Method to Calculate the Day of the Week for All Dates 1905-2099"
(H. Lachman), can both be considered variations of the 9-step
"standard method" given in "sci.math FAQ: Day of Week"
<www.faqs.org/faqs/sci-math-faq/dayWeek/>.

Regards,
Hans Lachman

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      REFERENCE

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