Great idea for a quiz, but perhaps use a different source? There is no way Princeton is the "best" university in the country as a whole; Harvard and MIT (and possibly Stanford) are almost certainly "better" colleges. Despite being a very good college, it also does not make sense to put Columbia at the same rank as the aforementioned Bostonian ones. Furthermore, I don't why UWash @ St. Louis is ranked even higher than colleges like Cornell and CMU.
This is far and away the generally accepted list for the "best" schools. Individual schools' prestige might be higher. The reason columbia is so low is because they used to be #2, but it turns out they were tricking the ranking comittee by reporting false stats, so they were put this low as a "punishment" https://www.washingtonpost.com/education/2022/09/09/columbia-usnews-college-ranking/