The rapid advancement of Large Language Models (LLMs) like ChatGPT has raised concerns among computer science educators about how programming assignments should be adapted. This paper explores the capabilities of LLMs (GPT-3.5, GPT-4, and Claude Sonnet) in solving complete, multi-part CS homework assignments from the SIGCSE Nifty Assignments list. Through qualitative and quantitative analysis, we found that LLM performance varied significantly across different assignments and models, with Claude Sonnet consistently outperforming the others. The presence of starter code and test cases improved performance for advanced LLMs, while certain assignments, particularly those involving visual elements, proved challenging for all models. LLMs often disregarded assignment requirements, produced subtly incorrect code, and struggled with context-specific tasks. Based on these findings, we propose strategies for designing LLM-resistant assignments. Our work provides insights for instructors to evaluate and adapt their assignments in the age of AI, balancing the potential benefits of LLMs as learning tools with the need to ensure genuine student engagement and learning.