Question

What day of the week was 20${}^{th}$ June 1837?

Answer 1

20${}^{th}$ June 1837 means 1836 complete years + first 5 months of the year 1837 + 20 days of June.

1600 years give no odd days.

200 years give 3 odd days.

36 years give (27+9) or 3 odd days.

1836 years give 6 odd days.

From 1${}^{st}$ January to 20${}^{th}$ June there are 3 odd days.

Odd days :

January :3

February :0

March :3

April :2

May :3

June :6

--------

17

Therefore, the total number of odd days = (6+3) or 2 odd days.

This means that the 20${}^{th}$ of June fell on the 2${}^{nd}$ day commencing from Monday. Therefore, the required day was Tuesday.