What was the day of the week on 7 January 2013 ?

\(\frac{Date + Month code + Century code + Century upper year + \frac{Upper year}{4}}{7}\)

⇒ \(\frac{7 + 0 + 6 + 13+ 3}{7}\) 

= \(\frac{29}{7}\) = Remainder 2

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.