Does finding the number of unique elements in a set actually require comparison of each element with everything else? Can't you use a hashtable? For every element, add it to the table (ignore if already exists), and finally, take a count of keys.
NASA knew that people new that planetariums existed, so they didn't paint a realistic sky because people would think they used a planetarium. Game theory!
But some random word in its response can trigger an idea in your mind. Getting an idea from a conversation is not always about getting it directly. It's already in you and you just wanted a trigger.