Determination of the day of the week day of the week begins by starting from an ‘anchor date’: a known pair (such as January 1, 1800 as a Wednesday), determining the number of days between the known day and the day that you are trying to determine, and using arithmetic modulo 7 to find a new numerical day of the week. One standard approach is to look up (or calculate, using a known rule) the value of the first day of the week of a given century, look up (or calculate, using a method of congruence) an adjustment for the month, calculate the number of leap years
Determination of the day of the week January 1, 2000. (year − 1 for January) formula_3 formula_4 Note: The first is only for a 00 leap year and the second is for any 00 years. The term mod 7 gives the values of months: The term mod 7 gives the values of years: The term mod 7 gives the values of centuries: Now from the general formula: formula_5; January 1, 2000 can be recalculated as follows: formula_6 formula_7 Kraitchik proposed two methods for calculating the day of the week. One is a graphical method. The other uses a formula that he credits to Gauss on p. 110: