Question

In a certain year, there were exactly four Fridays and exactly four Mondays in May. On what day of the week did the 21st of May fall that year?

Answer 1

The 1st, 8th, 15th, 22nd, and 29th days of any month are the same say of the week. Since January has 31 days, if the month starts on a given day, there will be five of those days, and also five of the next two days of the week. Hence January could not have started on Saturday, Sunday or Monday (Otherwise there would be five Fridays). Hence January 1 was a Tuesday, and it is not difficult to see that January 20th was a Sunday.