We assume the numbers are corresponding with each day of the week as follows (Note the definition is different from that for equation (1).)

We define a prime symbol ( ) operator of 7-surplus by

We need to memorize the number of each month such that

The variable *M* will has the one of those numbers
in the following discussion.

Let us practice for the century of 1900's. Magic number of this century is 5 (we will discuss the magic number in the different section.) We can obtain the day of the week for each year of this century. Let

where *Y* is the year (1990 has 90 with no exception, thus
the definition of *Y* here is different from that in (1).)
We can obtain the day of the week for the new year day of the year 1900+*Y* by

Using the above definitions (3) and (4),
we can obtain the day of the week for
the month *M*, the day *D*, the year 1900+*Y* by