Does 17 January ever fall on Monday?

Answer 1

Yes it does. All dates fall on all days of the week, at some point or another. Taking just the 20th and 21st centuries, the 17th of January is on a Monday in the following years:

1910, 1916, 1921, 1927, 1938, 1944, 1949, 1955, 1966, 1972, 1977, 1983, 1994, 2000, 2005, 2011, 2022, 2028, 2033, 2039, 2050, 2056, 2061, 2067, 2078, 2084, 2089 and 2095.

Answer 2

Yes, exactly 14% of all Jan. 17ths are Mondays. The next time it falls on a Monday is in 2022.