K23 on Monday?

On the CITS.net website they mention: Train 23
28 May, 2013 - 27 May, 2014: Every Tuesday Departure.
17 Jun, 2013 - 28 Oct, 2013: Every Monday Departure.
I want to go on monday 6th of January, is this possible? Because I got a confirmation from this website that is was ok, but it looks strange for me since on other website they say that the train doesn't go on mondays during this period.