Final answer:
Importuning someone typically relates to an urgent need that requires persistent and pressing request, which is more appropriate than the other scenarios listed.
Step-by-step explanation:
One is most likely to importune someone for an urgent need. The word importune means to ask someone persistently or pressingly, often seen as to the point of annoyance. An urgent need is a situation requiring immediate attention or action, which may lead someone to persistently request assistance. In contrast, requesting an alternative phone number, an answer to a riddle, or a toothpick does not typically require the persistent and pressing manner that the word importune implies, making these options less likely scenarios for importuning someone.