Goldman Sachs Interview Puzzle: 4 Cars 1000 Miles Question (Solved)

The Question

Suppose you have 4 cars, each fueled so that they can drive for 1000 miles. What is the maximum distance you can get with the cars if you can transfer petrol in the middle of the journey?

This is a real brain teaser reported from Goldman Sachs interviews. It tests whether you can think in stages and optimize under constraints, exactly the kind of structured problem-solving investment banks look for.

The Answer

2,083.33 miles (2,083 and 1/3 miles).

That is more than double what any single car could do alone. Here is how.

Step-by-Step Solution

The trick is to drive the cars together, then sacrifice them one by one, transferring their remaining fuel to the survivors at each stage.

Stage 1: All 4 cars drive 250 miles

Each car uses 250 miles of fuel and has 750 left. Take all 750 from car 4 and split it among cars 1, 2, and 3 (250 each). Cars 1-3 now have a full 1,000 miles of fuel each. Abandon car 4.

Distance so far: 250 miles

Stage 2: 3 cars drive 333.33 miles

Each car uses 333.33 miles of fuel and has 666.67 left. Take all 666.67 from car 3 and split it between cars 1 and 2 (333.33 each). Cars 1-2 now have a full 1,000 miles of fuel each. Abandon car 3.

Distance so far: 583.33 miles

Stage 3: 2 cars drive 500 miles

Each car uses 500 miles of fuel and has 500 left. Transfer car 2’s remaining 500 to car 1. Car 1 now has a full 1,000 miles of fuel. Abandon car 2.

Distance so far: 1,083.33 miles

Stage 4: 1 car drives 1,000 miles

The last car drives its full 1,000 miles on the consolidated fuel.

Total distance: 250 + 333.33 + 500 + 1,000 = 2,083.33 miles

Why This Works

At each stage, you are converting the fuel of a sacrificed car into extra range for the survivors. The key insight is that the transfer points are not arbitrary: each stage length equals the remaining fuel divided by the number of surviving cars. This keeps every survivor exactly full after each consolidation.

The general pattern for n cars each with range R: the maximum distance is R x (1 + 1/2 + 1/3 + … + 1/n). For 4 cars: 1000 x (1 + 1/2 + 1/3 + 1/4) = 1000 x 2.0833 = 2,083.33 miles.

What the Interviewer Is Testing

• Structured thinking: Can you break a complex problem into stages instead of guessing?
• Optimization instinct: Do you look for the transfer points that maximize range, or settle for the first idea?
• Comfort with abstraction: The harmonic series pattern (1 + 1/2 + 1/3 + 1/4) separates candidates who see the math from those who only see cars.
• Communication: Can you walk through your reasoning clearly under pressure?

You do not need the perfect answer immediately. Interviewers care more about hearing your thought process: start with a simple strategy, then refine it. Saying “let me think about when to transfer fuel to maximize range” is already a strong start.

More Interview Brain Teasers

Preparing for investment banking or consulting interviews? These puzzles test the same skills:

• How many golf balls fit in a school bus? (Coming soon)
• 8 balls, one heavier: find it in 2 weighings (Coming soon)
• Why are manhole covers round? (Coming soon)