So that they don't fall down the hole.
As for the recursive factorial problem, that's the very first example that they give in computer textbooks, when they introduce recursion. I'd be amazed if that tripped up anyone who's taken, and passed, a computer course.
The factorial problem is more efficiently solved with a loop. I'd be more inclined to pose a problem that is easiest to solve using recursion, but don't tell them that you expect them to use recursion. Then see if they figure it out on their own. One example that I can think of is generating all of the combinations or permutations of r digits out of a set of n. In math notation: nCr or nPr. For example, the list of combinations of 5 digits from a set of 8 is:
12345, 12346, 12347, 12348, 12356, 12357, 12358, 12367, 12368, 12378, 12456, 12457, 12458, 12467, 12468, 12478, 12567, 12568, 12578, 12678, 13456, 13457, 13458, 13467, 13468, 13478, 13567, 13568, 13578, 13678, 14567, 14568, 14578, 14678, 15678, 23456, 23457, 23458, 23467, 23468, 23478, 23567, 23568, 23578, 23678, 24567, 24568, 24578, 24678, 25678, 34567, 34568, 34578, 34678, 35678, 45678.
Doing this using loops is messy, but is almost trivial using recursion.