On 1st Jan, 2005 Saturday falls. What day of the week was it on 1st Jan, 2006?

The year 1985 is an ordinary year. So, it has 1 odd day.
So, the day on 19th June, 1985 will be 1 day after the day on 19th June, 1984.
But, 19th June,1984 is Monday
S0, 19th June, 1985 is Tuesday.