Portfolio Management interview preparation

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September 2026

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1. 080There are n cars on a circular track and between them just enough petrol to complete one lap. Show that one car can finish the lap by collecting petrol from the others.BrainteasersHardtechnicalMillennium ManagementInvestments · London · 2024

   Say this

   Yes, and there is always such a starting car. Track the running fuel balance around the loop from any start point, find the position where that balance is at its minimum, and the car immediately after that point can complete the lap.

   Then walk it

   1. Set it up: let each car i have fuel f sub i and let d sub i be the fuel needed to reach the next car. Total fuel equals total requirement, so the sum of f minus d over all cars is exactly zero.
   2. Pick any car and walk the circle, keeping a running total of f minus d. Because the total is zero, the walk returns to where it started, so the running total has a well-defined minimum at some position.
   3. Start at the car immediately after that minimum. From there, every partial sum is the original partial sum minus the minimum, which is non-negative by construction. So the tank never goes negative and the lap completes.
   4. The intuition is that the minimum point is the worst moment in the journey, so you arrange to arrive there last, with everything already collected, rather than hitting it while your tank is nearly empty.
   5. Sanity check with two cars: one has all the fuel for the lap, the other has none. Starting at the full one works, starting at the empty one fails immediately, and the argument picks the right one.
   6. The finance version of this argument is worth saying out loud, because it is why this gets asked in an investment interview: the feasibility of a cash flow plan depends on the minimum cumulative balance, not the total. A fund with enough total liquidity over a year can still fail in month three. That is the same theorem, and it is how you size a liquidity buffer or a collateral waterfall.

   Where candidates lose it

   Trying specific examples and asserting it works, or getting lost in the case analysis. The whole problem is one idea: the cumulative sum returns to zero, so start just after its minimum. State that in one sentence, then verify it, then connect it to cumulative cash flow, because the interviewer is testing whether you can reduce a problem to an invariant.

   Expect next

   • How would you find that starting car algorithmically?
   • What if total fuel exceeds what is needed?
   • Where does the same argument appear in liquidity management?

   Reported by candidates at Millennium Management (Investments, London, 2024). Source: Wall Street Oasis.

Firm tags come from public, anonymous candidate reports on Wall Street Oasis: strong signal, not sworn testimony. Firms are named as the places a question was reported, not as partners of Fin Maverick. Answers are written for this page to show how to think out loud; they are not scripts to recite.