What was the day of the week on 16 June 1999?

16 June 1999 was a Wednesday.

Odd days from 1600 years = 0 and from the next 300 years = 1.

Years 1901 to 1998 have 24 leap and 74 ordinary years = 48 + 74 = 122, i.e. 3 odd days.

Days to 16 June = 31 + 28 + 31 + 30 + 31 + 16 = 167, leaving 6 on division by 7.

Total odd days = 1 + 3 + 6 = 10, i.e. 3, which counts to Wednesday.