Which of the following assumptions on preferences leads to an interior solution to the consumer choice problem (i.e., one in which the optimal consumption choice involves some of each good)? Classify each case as:

Definitely YES (an interior solution is certain)

Definitely NO (an interior solution is impossible)

or

Possible (an interior solution might happen)

1. perfect substitutes
2. strictly concave preferences
3. convex preferences
4. a good and a bad
5. concave preferences
6. discrete goods
7. strictly convex preferences
8. perfect complements