Path: utzoo!mnetor!uunet!husc6!mit-eddie!uw-beaver!uw-june!uw-entropy!dataio!suvax1!hirayama
From: hirayama@suvax1.UUCP (Pat Hirayama)
Newsgroups: comp.sys.ibm.pc
Subject: Re: day of week
Message-ID: <961@suvax1.UUCP>
Date: 3 Feb 88 16:46:35 GMT
References: <141900013@occrsh.ATT.COM>
Organization: Seattle University, Seattle, WA.
Lines: 64

In article <141900013@occrsh.ATT.COM>, fubar@squid.UUCP writes:
> ***
> *** PLEASE send replies to ihnp4!occrsh!squid!david
> 
> >   Here's a formula given in the book An Introduction to the Theory of Numbers,
> >by Niven and Zuckerman.
> >   Let M be the number of the month, defined so that Jan = 11, Feb = 12,
> >Mar = 1, Apr = 2, ..., Dec = 10.  Let N be the number of the day within the
> >month.  Let C be the hundreds in the year, and let Y be the rest of the year.
> >Let L be 1 for a leap year and 0 for a non-leap year.
> >
> >
> >(N + [2.6M - 0.2] + Y + [Y / 4] + [C / 4] - 2C - (1 + L)[M / 11]) mod 7
> >yields 0 for Sunday, 1 for Monday, ..., 6 for Saturday.
> >
> >(Square brackets denote the greatest integer function.)
    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 
> Thursday, Jan 28, 1988, should yield 4:
> 
>  N = 28   (number of day within month)
>  M = 11   (Jan = 11)
>  C = 19   (Hundreds w/in year)
>  Y = 88   (rest of year??)
>  L = 1    (1988 is leap year)
> 
>  = (N  + [2.6M - 0.2]  +  Y +  [Y/4] +  [C/4] -   2C   -  (1+L)[M/11])  mod 7
>  = (28 + (2.6*11)-0.2] + 88 + [88/4] + [19/4] - (2*19) - (1+1)*[11/11]) mod 7
>  = (28 +    [28.4]     + 88 +  [22]  + [4.75] -   38   -      2)        mod 7
>  = (28 +      29       + 88 +   22   +   5    -   38   -      2)        mod 7
>  = 6 ??
> 
> What is the correct formula for this?

David,

You are ignoring the underlined statement indicated above.  If you consider
this, you will realize the following:

Given, your initial data values given above.

Let X=Number you are seeking...

 
X  = (N  + [2.6M - 0.2]  +  Y +  [Y/4] +  [C/4] -   2C   -  (1+L)[M/11])  mod 7
   = (28 + (2.6*11)-0.2] + 88 + [88/4] + [19/4] - (2*19) - (1+1)*[11/11]) mod 7
   = (28 +    [28.4]     + 88 +  [22]  + [4.75] -   38   -      2)        mod 7
   = (28 +      28   	 + 88 +   22   +   4  	-   38	 -	2)	  mod 7
   = 4

Which is Thursday and the answer that you expect to get.


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 Pat Hirayama		UUCP:    ...!uw-entropy!dataio!suvax1!hirayama
 Seattle University	USNail:  28625-47th Pl S, Auburn, WA 98001-1140
 Class of 1988		Phone:	 (206) 946-0833

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