OK thank you guys, finally got it working. Had some problems with the whole idea (what to do in which class etc). Post my solution here if it may help someone else.
In class Person:
//implements Comparable
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public int compareTo(Object next) {
String bLastN = ((Person)next.getLastName();
int comp = ((Person)this).getLastName().compareTo(bLastN);
if (comp == 0) return 0; //guess this is the only return statement that is
if (comp < 0) return -1; //needed, but the 2 other doesn't seem to do
else return 1; //any harm either
}
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In class CardIndex:
public void sortItorScrewIt(){
Collections.sort(cInd);
}