Dear Sir,
I suppose you want to know about thrayodashi (13th tithi of krishna paksham maargazhi) and not trithyai.
Because, for krishna paksham thrithyai there is no problem at all. it falls on margazhi 20th. Jan 4th 2018.
But if you are looking for thrayodashi krishna paksham of margazhi, then you should consider thai 1st for anushtaanam.
if you are using vakya(pambu) panchangam, you can check, the same has been mentioned at the bottom of the page in margazhi month.
Please double check with aathu vadhyar.
Sarvam Krishnaarpanam.
Venkat.