If it was a Monday on 1 January 2018, what was the day of the week on…

\(\frac{Date + Month\;code + Century\;code + Century\;upper\;year + Quotient\;of\;\frac{upper\;year}{4}}{7}\)

\(\frac{1 + 0 + 6 + 18 + 4}{7}\) = \(\frac{29}{7}\) = Remainder 1

so, remainder is 1

The day for Code 1 is monday. So, it is the same day which is given

therefore,

The day for 31 december 2018 was :

\(\frac{Date + Month\;code + Century\;code + Century\;upper\;year + Quotient\;of\;\frac{upper\;year}{4}}{7}\) 

\(\frac{31 + 5 + 6 + 18 + 4}{7}\) = \(\frac{64}{7}\) = Remainder 1

The day for Code 1 is monday. 

Note:     

Code for      Mon – 1      Tues – 2      Wed – 3      Thurs – 4

                   Fri – 5         Sat ­­– 6        Sun – 0

Code for      Jan – 0        Apr – 6       July – 6       Oct – 0

                   Feb – 3       May – 1      Aug – 2       Nov – 3

                   Mar – 3       June – 4      Sep – 5       Dec – 5

Code for     

1900 is 0

2000 is 6

2100 is 4

2200 is 2

2300 is 0

2400 is 6

2500 is 4   and  Likewise