It's interesting how often fermi estimation problems are used as proxy's for "intelligence". Something like: 'let's assess how well "they can think" - how many golf balls fit in a baseball stadium?' etc.
Often, doing well in these kinds of problems can more than makeup for a lack of specific knowledge in something someone is interested in assessing!
There are about 13,500 taxi medallions.
I'm probably taking this more seriously than it was intended above, but the idea that this is some sort of proxy for "thinking" or "intelligence" feels off to me; doing the math given the size of something might be thinking or intelligence, but knowing roughly "how big" something is seems more like intuition.
The ability to estimate within an order of magnitude or within 2X is vastly more valuable, and beyond being able to have a sense of whether the "official" answer is likely accurate or off by orders of magnitude.
During most of the process of designing anything in or that touches the physical world, you are using rough figures.
Taking time to get the fully accurate and precise answer for every question is a waste of time as you don't need that many decimals of precision to move forward. Every decimal of precision in the answer takes more time and there are MANY of those questions, so being 100% accurate in every answer does not scale.
Of course, when it gets to the end of the process, the accuracy & precision requirements increase, but the emphasis needs to be placed where needed, not everywhere.
Plus, you are not going to find the "official" and accurate number of golf balls in the particular school bus you want to model. You'll find some vaguely similar answer or set of sub-answers, so sure, those will be fully accurate and precise, but THEN you must take those as inputs for your estimate, and we're back to the skill of estimating being most critical.
Being able to estimate and do sound back-of-the-envelope calculations is the far more critical skill, at least on any team I'm building.