If it was Monday on 18 December, 1812. Then, what was the day of the on 16 September 1917?

Wednesday

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

\(\frac{18+5+2+12+3}{7}\)

\(\frac{40}{7}\) =  Remainder 5 means Friday but here Monday is given i.e. 4 days before.

We have to find out 16/09/1917

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

\(\frac{16+5+0+17+4}{7}\)

\(\frac{42}{7}\) =  Remainder 0 means Sunday

Therefore, 4 days before Sunday is Wednesday which is the correct answer.

Note:

Code for   

Mon – 1       Tues – 2       Wed – 3        Thurs – 4     Fri – 5         Sat ­­–6          Sun – 0

Code for    

Jan – 0         Feb – 3        Mar – 3

Apr – 6        May – 1       June – 4

July – 6        Aug – 2       Sep – 5

Oct – 0         Nov – 3       Dec – 5

Code for         1800 is 2

                    1900 is 0

                    2000 is 6

                    2100 is 4

                    2200 is 2

                    2300 is 0

                    2400 is 6

                    2500 is 4   and  Likewise