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
