Appendix A: Chain of Thought Implementation Details Due to context limits of gpt-4-0314, it is not suitable for the chain-of-thought prompting with 100 ideas. We investigated its 32,000 token sibling model gpt-4-32k-0314, however we found that it struggled to follow the prompt. Hence, we used gpt4-1106-preview which boasts a much larger context window of 128,000. To compensate for its completion limit of 4095 tokens, we sent multiple requests for one generation while preserving the context window. To ensure that any findings in performance differences are not merely due to a different model, we also ran all using gpt4-0314 on smaller pools with 30 ideas each. In addition, we also ran tests with our base prompt and chain of thought using gpt4-1106-preview. Appendix B: Most Common Ideas One might ask what the most common ideas are that GPT-4 comes up with? We ran a pairwise comparison on a subset of all our pools containing around 1200 ideas due to the computational complexity. Further analysis suggests that these ideas often occur early in a completion request and hence running longer, more exhaustive, requests could be beneficial. This is likely due to the initial entropy being lower than after a few completed tokens. Idea Count Collapsible Laundry Hamper: The Collapsible Laundry Hamper is a space-saving, portable laundry hamper designed for college students living in dorm rooms or small apartments. The hamper is made from durable, lightweight materials and can be easily collapsed and stored when not in use. The Collapsible Laundry Hamper also features built- in handles for easy transportation to and from the laundry room. 30 / 1200 Portable Smoothie Maker: The Portable Smoothie Maker is a compact, battery-operated blender designed for college students who want to maintain a healthy diet on a busy schedule. With its small size and easy-to-use design, students can quickly make and enjoy smoothies, protein shakes, or other blended drinks in their dorm room or apartment. The Portable Smoothie Maker comes with a reusable, dishwasher-safe blending cup and lid, making clean-up a breeze. 30 / 1200 Bedside Caddy: The Bedside Caddy is a convenient storage solution for college students who need to keep their essential items close at hand while in bed. This caddy features 25 / 1200