calendars problem using zellers formulae

Question

i've solved most of the day finding problems using zellers formulae $$ Z= K + \frac{13M -1}{5} + D +\frac{D}{4} + \frac{C}{4} - 2C $$ where

• $K$ = given
• $M$ = given month no. ( but here month count starts from march )
• $D$ = last 2 digits of the given year ( but $D = D-1$ if given month is Jan or Feb )
• $C$ = first 2 digits of the given year.

but it is not working for the find the day 01,march,2014?

Answer 1

As posted, there is a typo and you forgot the floor operations.

For the Gregorian calendar, Zeller's original congruence formula is $$Z= K + \lfloor \frac{13M +1}{5}\rfloor + D + \lfloor \frac{D}{4}\rfloor + \lfloor\frac{C}{4}\rfloor - 2C~~~~~~\mod7$$ Applying it to $1^{st}$ $\text {march}$ $2014$ gives $Z=-7$ that is to say $0$ which means a saturday, which is correct.

Do not forget the floor functions.