Make a market on the number of cars parked at a large suburban mall at 1 pm on Saturday: four levels of about 250 bays, occupancy somewhere between 70% and 90%. Then the interviewer sells to your bid three times in a row. How do you quote, and how do you update?

Open at 760 bid, 840 offer around a central estimate of 800 cars, then shade down about 20 per sell and widen after the third, to 690 at 790. Four levels of 250 bays at 80% gives 800; the ends of the ranges give 644 and 972, a standard deviation of about 69. Three sells at your bid say your number is probably high. You are long three at an average of 740.

Break it into pieces you can each defend, as you would guess the number of chairs in a cinema from rows times seats per row. Here cars equal levels times bays per level times occupancy, and each piece has its own range. The central case is 4 x 250 x 80%, which is 800. Take the low end of both ranges and you get 644; the high end gives 972. Say the pieces out loud: the interviewer can then challenge one of them, which is far better than challenging a single number you plucked from the air.

Width should reflect how unsure you are, scaled by how much you are willing to lose to a better-informed trader. Treat each range as even odds across it. Bays contribute about 4.6% relative uncertainty and occupancy about 7.2%, so together about 8.6% of 800, roughly 69 cars. A market of plus or minus 40 is a little over one standard deviation wide in total: tight enough that the interviewer will trade with you, wide enough that a single trade against you costs a known amount. The occupancy piece dominates, which tells you where to spend thinking time.

Each sell is a vote. A seller who thought the count was above 760 would have bought at 840 or done nothing. Repeated selling at your bid says your estimate is high, so a Fermi market is updated by the flow as well as by your reasoning. A simple rule is to shade the mid down by a quarter of the width, 20 cars, after each hit: 740 at 820, then 720 at 800. After the third, widen as well, to 690 at 790, because flow that keeps coming one way raises the chance that the seller has a sharper number, perhaps having thought harder about Saturday lunch at a mall whose peak is the evening show.

You bought at 760, 740 and 720, an average of 740, and your new mid is 740, so the position marks flat. If the true count is 700, the three contracts lose Rs 12,000 at Rs 100 a car, the price of being slow to listen. Say one more thing: the updated mid of 740 is still well inside the range your own reasoning produced, so the flow has not proved you wrong; it has told you which part of your range to lean on. If the sells kept coming below 700, you would ask what you had missed, such as a level closed for repairs.