Let S1, S2, . . . , Sk be k different sequences whose elements have integer keys in the range [0,N − 1], for some parameter N ≥ 2. Describe an algorithm running in O(n+N) time for sorting all the sequences, where n denotes the total size of all the sequences.

Exactly right, as the whole point of this question (and all other assignments) is to test how much you have learned, and how much research you can do on your own. You could start by creating some of the mentioned sequences on paper and think about how you would go about sorting the numbers.

He just tells us to try on our own

Do I have to use radix sort?