At a boarding school, in the evening, 9 students always take walks in groups of 3. How can the groups be arranged so that each person walks in a group with every other person exactly once in 4 days?

I would like to know whether there is a trick to these type of questions. My workings are students numbered 1-9 and I did 123 124 125 126 127 128 129. And I would also like to know whether my answer could be correct, 9 students, 3 spots is 27 different combinations?