To broaden participation, competitive programming contests may include beginner-level problems that do not require knowledge of advanced Computer Science concepts (e.g., algorithms and data structures). However, since most participants have easy access to AI code-generation tools, these problems often become trivial to solve. For beginner-friendly programming contests that do not prohibit the use of AI tools, we propose Probeable Problems: code writing tasks that provide (1) a problem specification that deliberately omits certain details, and (2) a mechanism to probe for these details by asking clarifying questions and receiving immediate feedback. To evaluate our proposal, we conducted a 2-hour programming contest for undergraduate Computer Science students from multiple institutions, where each student was an active member of their institution’s computing club. The contest comprised of six Probeable Problems for which a popular code-generation tool (GitHub Copilot) was unable to generate accurate solutions due to the absence of details. Students were permitted to work individually or in groups, and were free to use AI tools. We obtained consent from 26 groups (67 students) to use their submissions for research. We analyze the extent to which the code submitted by these groups identifies missing details and identify ways in which Probeable Problems can support learning in formal and informal CS educational contexts.