Weekday

The day of the week $W$ (numbered according to $W=0$ for Sunday, $W=1$ for Monday, etc.) for a given day of the month $D$, month $M$, and year $Y$ can be determined from the simple equation

$$W\equiv D+\left\lfloor{2.6m-0.2}\right\rfloor +y+\left\lfloo... ...1\over 4}}c}\right\rfloor -2c\ \left({{\rm mod\ } {7}}\right),$$

where $\left\lfloor{x}\right\rfloor$ is the Floor Function, months are numbered beginning with March and dates in January and February considered to be the 11th and 12 months of the previous year (Uspensky and Heaslet 1939, Vardi 1991).

A more complicated form is given by

$$W\equiv D+M+C+Y\ \left({{\rm mod\ } {7}}\right),$$

where $W=1$ for Sunday, $W=2$ for Monday, etc. and the numbers assigned to months, centuries, and years are given in the tables below (Kraitchik 1942, pp. 110-111).

Month	$M$
January	1
February	4
March	3
April	6
May	1
June	4
July	6
August	2
September	5
October	0
November	3
December	5

Gregorian
Century	$C$
15, 19, 23	1
16, 20, 24	0
17, 21, 25	5
18, 22, 26	3

Julian
Century	$C$
00, 07, 14	5
01, 08, 15	4
02, 09, 16	3
03, 10, 17	2
04, 11, 18	1
05, 12, 19	0
06, 13, 20	6

Year								Y
00	06		17	23	28	34		45	0
01	07	12	18		29	35	40	46	1
02		13	19	24	30		41	47	2
03	08	14		25	31	36	42		3
	09	15	20	26		37	43	48	4
04	10		21	27	32	38		49	5
05	11	16	22		33	39	44	50	6
51	56	62		73	79	84	90		0
	57	63	68	74		85	91	96	1
52	58		69	75	80	86		97	2
53	59	64	70		81	87	92	98	3
54		65	71	76	82		93	99	4
55	60	66		77	83	88	94		5
	61	67	72	78		89	95		6

See also Friday the Thirteenth

References

Kraitchik, M. ``The Calendar.'' Ch. 5 in Mathematical Recreations. New York: W. W. Norton, pp. 109-116, 1942.

Uspensky, J. V. and Heaslet, M. A. Elementary Number Theory. New York: McGraw-Hill, pp. 206-211, 1939.

Vardi, I. Computational Recreations in Mathematica. Reading, MA: Addison-Wesley, pp. 237-238, 1991.