Figuring out first day of a month

[MrGillig]

Hey guys!

Say I have a date. Let's just take todays date 05/04/2009.

And say I have numbers 0 - 6 corresponding to each day of the week ie. Sunday is 0, Monday is 1 etc.

From just knowing the day of the date, in this case 5, and that today is a Sunday, is it possible to calculate what the first day of the month was? By using the numbers that correspond to each day, of course.

So, I'll reiterate: from just knowing that its the 5th and that it's a Sunday (0), is it possible to figure out what the first day of the month was?

 

[qntty]

Let today be the d^th day of the month, and the day of the week be w. The weekday of the first day of the month is the least residue of $$w-(d-1)$$ mod 7 and in general, the weekday of the k^th day is the least residue of $$w-(d-k)$$ mod 7.

 

[MrGillig]

I'm confused. If I were to plug the values in for today would they then be "0 - (5+1) % 7". When I calculate this I seem to get -6, which isn't Wednesday. Did I mess up the calculation somewhere?

EDIT: Just read your edit sorry. Gonna try again.

 

[MrGillig]

Sorry man but I'm still confused. If I plug in the values for today, for instance, I get -4. Should I be counting from 1 instead of 0 for the days of the week ie. Sunday is 1, Monday is 2 etc?

 

[CRGreathouse]

Sorry man but I'm still confused. If I plug in the values for today, for instance, I get -4. Should I be counting from 1 instead of 0 for the days of the week ie. Sunday is 1, Monday is 2 etc?

-4 = 3 (mod 7).

 

[MrGillig]

Ah I realize now how to equate it to correspond to the day of the week. If it happens to be below 0, I add 7 and get the result for the number corresponding to the first day of the month.

Thanks for the help!