Goldman Sachs 4 Cars Puzzle: Answer 208 Miles [Solved]

The Goldman Sachs 4 cars puzzle answer is 208 miles. Four cars start with full tanks, each tank enough for 100 miles, and the cars can transfer fuel between them. Drive all four together, pool the fuel into three cars, then two, then one, and the last car reaches 208 miles and a third. The rest of this post shows every transfer, the maths behind it, and the traps that catch most candidates.

The Goldman Sachs 4 cars puzzle is a classic from the finance interview circuit. The answer is not 100 miles, and it is not 400 miles either. It sits in between, and the only way to find it is to treat the cars as fuel carriers, not as four separate journeys.

The Question

You have four cars. Each car starts with a full tank of fuel, and a full tank takes a car 100 miles. The cars can transfer fuel to each other at any point, and you can leave a car behind once its tank is empty. How far can you get one car?

Three rules are worth stating before you start. First, a car cannot hold more than one full tank, so you cannot pour all four tanks into one car at the start. Second, driving burns fuel. Third, only the distance of the furthest car counts. Driving four cars 100 miles each in different directions scores 100 miles, not 400.

The answer comes from one idea: drive the cars together in stages, and at each stage retire one car and give its fuel to the cars that keep going.

How to Solve the Goldman Sachs 4 Cars Puzzle

Stage 1: Four Cars Drive 25 Miles

Start with all four cars driving together. After 25 miles, each car has used a quarter of its tank, so each has three quarters left. Four cars times three quarters equals three full tanks, spread across four cars. Pour fuel from one car into the other three until they are full, then leave the empty car behind. You have three full cars, and you have travelled 25 miles.

Stage 2: Three Cars Drive 33 Miles and a Third

Drive the three full cars together for 100 divided by 3 miles. Each car uses a third of its tank, so each has two thirds left. Three cars times two thirds equals two full tanks. Pour fuel from one car into the other two until they are full, then leave the empty car behind. You have two full cars, and you have travelled 58 miles and a third.

Stage 3: Two Cars Drive 50 Miles

Drive the two full cars together for 50 miles. Each car uses half its tank, so each has half a tank left. Two cars times one half equals one full tank. Pour fuel from one car into the other until it is full, then leave the empty car behind. You have one full car, and you have travelled 108 miles and a third.

Stage 4: One Car Drives 100 Miles

The last car has a full tank and an open road. It drives 100 miles, then stops. Add the stages together: 25 plus 33 and a third plus 50 plus 100 equals 208 miles and a third.

Stage	Cars driving	Distance	Fuel left after the stage	Total distance
1	4	25 miles	3 full tanks	25 miles
2	3	33.33 miles	2 full tanks	58.33 miles
3	2	50 miles	1 full tank	108.33 miles
4	1	100 miles	Empty	208.33 miles

The pattern is neat: the four stages are 100 times one quarter, one third, one half and one. So the answer is 100 times (1/4 + 1/3 + 1/2 + 1), which is 100 times 25/12, which is 208.33 miles. Each stage burns exactly one tank, and the plan uses all four tanks, so no fuel goes to waste.

Why This Plan Cannot Be Beaten in the Goldman Sachs 4 Cars Puzzle

Every mile past 100 needs fuel another car carried there, and that helper car burned fuel to get there. The relay plan keeps the number of cars driving as small as possible at every distance: four cars only for the first 25 miles, three for the next 33, two for the next 50, and one for the final 100. Keeping an extra car driving longer only burns fuel moving that car.

Check the arithmetic another way. The four tanks hold 400 miles of driving in total, and the plan uses exactly that: four cars times 25 miles is 100, three cars times 33.33 miles is 100, two cars times 50 miles is 100, and one car times 100 miles is 100. The plan uses every drop of fuel, yet the furthest car ends at 208.33 miles, because some fuel went on carrying fuel forward. That is the whole puzzle in one sentence: fuel spent carrying fuel is fuel that cannot carry the car.

The Traps That Catch Candidates

The 100-mile answer. The most common answer is 100 miles: one car drives until its tank is empty. It ignores the other three cars entirely. The interviewer is testing whether you notice that the extra fuel exists and you can move it.

The 400-mile answer. The second most common answer is 400 miles: four tanks times 100 miles each. It ignores the tank-capacity rule. A car cannot hold four tanks of fuel at once, so you cannot load all the fuel into one car at the start. You have to carry it forward in stages, and carrying it costs fuel.

What the Interviewer Is Testing in the Goldman Sachs 4 Cars Puzzle

First, it tests whether you spot the hidden resource. The question hands you four cars, but the real resource is four tanks of fuel you can move around. Candidates who think of the cars as four separate journeys never get past 100 miles. Candidates who think of them as fuel carriers find the relay plan.

Second, it tests structured, staged thinking. The answer is not one clever move, it is four stages, and each stage follows the same rule: drive until the remaining fuel exactly fills one fewer car, then consolidate.

Third, it tests whether you check your own answer. The table above is the check: four stages, one tank burned per stage, 400 car-miles in total, nothing wasted. Strong candidates run that check out loud.

Follow-Up Variations Interviewers Ask Next

The 1,000-mile tanks. If each tank covered 1,000 miles instead of 100, the same plan gives 1,000 times (1/4 + 1/3 + 1/2 + 1), which is 2,083 miles and a third.

Three cars instead of four. With three cars, the plan has three stages, and the answer is 100 times (1/3 + 1/2 + 1), which is 183.33 miles.

Five cars instead of four. With five cars, the answer is 100 times (1/5 + 1/4 + 1/3 + 1/2 + 1), which is 228.33 miles. Notice the pattern: each extra car adds less than the last one. The fifth car adds only 20 miles, because you retire it after the first 20 miles and spread its fuel thin across the rest of the trip.

This is the same relay idea as the classic desert-crossing puzzle, where cars carry a traveller across a desert with no fuel stations. The mathsisfun version of cars across the desert uses the same stage-by-stage consolidation. The question setup is a classic finance interview brain teaser; the solution and walkthrough above are original.

Frequently Asked Questions

Why can the cars not just drive 400 miles?

Because a car cannot hold more than one tank of fuel. Four tanks hold 400 miles of driving in total, but you have to carry that fuel forward in stages, and carrying it burns fuel. The relay plan spends 400 car-miles to move one car 208.33 miles.

Where is this puzzle asked?

It appears in candidate-shared Goldman Sachs brain teaser lists and in Heard on the Street, the book of real Wall Street interview questions. The arithmetic is simple fractions, and the hard part is seeing that the cars are fuel carriers.

What should I say first in the interview room?

Say the plan before the number. Start with “I will drive all four cars together and pool the fuel in stages,” then walk through the four stages with the numbers. If you open with “208 miles” and stop, the interviewer has no idea how you got there. The reasoning is the answer.

Try This One Next

If you liked the Goldman Sachs 4 cars puzzle, try 8 Balls Puzzle: Find the Heavier Ball in 2 Weighings (Solved). It is the same kind of thinking in a different shape: a small number of moves, a strict limit, and one clean idea that makes the answer fall out.