Unstructured Cases 2026: The L.E.K. Airplane Prompt

An unstructured case prompt with no business inside it

L.E.K. publishes three prompts on its interview preparation page at lek.com, checked 30 September 2026. The first is labeled "A Brainteaser" and reads: "Airplanes are taking off from JFK and LAX airports every hour on the hour continuously, flying identical New York-Los Angeles routes. The flight takes five hours. You are leaving New York at 12:00 PM EST and flying to Los Angeles (because it's sunny and the beaches are great). How many airplanes flying the opposite route will you pass on the way there".

There is no revenue, no client and no model answer. The firm publishes five approach questions underneath instead, and two of them exist only because the prompt is open: "What logical traps might you want to avoid?" and "What information really matters and what is superfluous?"

That second question is doing real work here. The prompt hands you a departure city, a departure time, a reason involving beaches, and a flight duration. Only two of those matter. Sorting the load-bearing facts from the decorative ones is the first visible act, and on an open prompt it is most of the grade, because there is no framework to hide inside.

The prompt also hands you a trap that a framework would never catch. Read it quickly and you count departures during your flight, which gives six. That answer ignores every plane already in the air when you leave, and there are several.

Counting the airplanes you pass

Put every time on one clock. Los Angeles sits a whole number of hours behind New York, so departures on the hour stay on the hour whichever clock you pick. Use Eastern time and the arithmetic stops being about time zones.

You are airborne from 12:00 to 17:00. An eastbound airplane that leaves Los Angeles at hour t is airborne from t to t plus 5. You share sky with it when its window overlaps yours.

1. It must still be flying when you take off. So t plus 5 is later than 12:00, which means t is later than 07:00.
2. It must already be flying before you land. So t is earlier than 17:00.
3. Departures are hourly. So t runs over 08:00, 09:00 and so on to 16:00.

Count that list: 08:00 through 16:00 inclusive is nine airplanes.

Now check it a second way, which is the move that turns a guess into an answer. You and an eastbound airplane close on each other at twice the speed either of you flies, so you cover the five hour route in two and a half hours of relative time. Eastbound airplanes are spread one flight hour apart along the route. Meetings therefore arrive every thirty minutes of your flight.

Your flight lasts five hours, which is 300 minutes. Meetings at 0, 30, 60 and so on to 300 minutes give eleven moments. Strip the two that land exactly on your departure and your arrival and nine remain, which matches the list above.

The convention that changes the count

The two boundary meetings are the whole difference between the two answers, and they are worth naming out loud.

The first is the airplane that left Los Angeles at 07:00 and touches down at Kennedy at 12:00, the instant you push back. The second left Los Angeles at 17:00 as your own wheels touch the runway. Both encounters happen at an airport rather than in the air.

The prompt says "on the way there". Read strictly, neither boundary airplane is passed on the way, and the answer is nine. Read loosely, both count and the answer is eleven. L.E.K. publishes no answer, so we are not correcting a firm here; we are showing that the number follows from a convention the candidate sets.

The third row is the failure, and it is the one a hurried candidate produces. The interviewer cannot tell a convention from a mistake unless you say which you picked, so say it in one sentence before you give the number. That habit costs four seconds and it converts a wrong-looking answer into a defensible one.

Two firms disagree on stalling in an unstructured case

Open prompts produce stalls, and the published instructions for that moment conflict.

Kearney writes: "Acknowledge that you are stuck, seek more information, or pursue a different logical path." That is written permission to stop, at kearney.com, read through a text proxy because the site refuses direct requests. Oliver Wyman writes the opposite instruction under its analysis step: "If you're stumped, take a creative leap."

One firm tells you to halt and re-ask. The other tells you to jump. Both are their own words about their own interviews, and a candidate cannot obey both at once.

The resolution is to ask what kind of stall you are in. If the missing piece is a fact, Kearney's instruction is the right one, because a leap over a fact is a fabrication. If the missing piece is an idea, Oliver Wyman's is right, because no amount of asking will produce it. On the airplane prompt the stall is an idea, which is why the closing speed argument is the leap that unlocks it.

Say which stall you are in, then act. That sentence does the job of both instructions: "I have the facts I need and I am short an approach, so let me try something."

Building a tree for an unstructured case with no named shape

The airplane prompt has no business content. Most unstructured cases do, and they still refuse the named shapes. L.E.K.'s second published prompt is one: two brewers, "reporting similar revenues over the last five years showing steady growth", one with steady profits and one whose profits "have fluctuated significantly". The firm asks why, and what the volatile one's chief executive should do.

No framework covers profit volatility. An equation does. Profit equals revenue minus variable cost minus fixed cost, so the swing in profit for a given swing in revenue depends on how much of the cost base moves with revenue.

Here is that idea with numbers, all of them ours, since L.E.K. publishes none.

Both brewers make 500 million dollars of revenue and 50 million dollars of profit. Cheapo runs variable costs at 70 percent of revenue, so 350 million dollars, and fixed costs of 100 million. Bourgeois runs variable costs at 40 percent, so 200 million dollars, and fixed costs of 250 million. Check both: 500 minus 350 minus 100 is 50, and 500 minus 200 minus 250 is 50.

Now drop revenue by 10 percent, to 450 million dollars.

The same 10 percent revenue move costs Cheapo 30 percent of profit and Bourgeois 60 percent. The ratio is exactly two, and it is the ratio of their contribution margins, 60 percent against 30 percent. That is the answer to the firm's question, and the structure that produced it came from an equation rather than a named shape.

What the scale rewards on an open prompt

The weights below are ours, read from the grading code in src/lib/grading. No consulting firm publishes a marking scheme, and that absence holds across every research file we keep.

Drilling unstructured case prompts that refuse to fit

Open prompts are practicable alone, because the answer is checkable by a second method.

1. Change one parameter and redo it. Make the flight three hours instead of five. Meetings arrive every thirty minutes still, over 180 minutes, so seven moments including both boundaries and five strictly in flight. Check with the window rule: t later than 09:00 and earlier than 15:00 gives 10:00 through 14:00, which is five.
2. Solve for the parameter. Ask what flight time produces exactly 15 strict meetings. Fifteen strict meetings need 16 intervals of thirty minutes, so eight hours.
3. Force a second method. Never accept an open answer you reached one way. Two methods that agree are the only proof available when no model answer exists.

Use the structuring drill for the opening move on prompts that supply no shape, and the math drill for the arithmetic above. Both are free and need no account. Neither will invent the second method for you.

For prompts that do hand you an equation, see structured thinking. For the two questions worth asking before you draw anything, see clarifying questions. For the named shapes and what each one assumes, see case interview frameworks.