Desert Driving Puzzle

January 13, 2016 | Elizabeth Knowles

There are no gas stations in a desert and your car only holds enough for half a trip. You can access to as many drivers with the same cars as you want. Each car can transfer its gas to another car at any point. How many cars (including yours) are needed?

Will you make it across the desert?

Yes, I know that this question is full of hypotheticals and isn’t something you’ll ever want to calculate in real life, but let’s go ahead and figure it out for the fun of math!

Let’s start by thinking about a single car: It will make it halfway across the desert and run out of gas. So, you know you need help.

How about if you use two cars (you and one other driver)? Well that could work if the driver could teleport to the middle of the desert, but even in hypothetical questions like this one, that’s not allowed. So, you need at least three cars.

If you have three cars, in total, you have enough gas for 1½  trips (for a single car). This means that the total distance the two other cars travel has to be ½ a trip or less. But, a car transferring gas to you at the halfway point would have to be completely full in order to get you to the other side of the desert. So, three cars doesn’t work either.

SEE ALSO: Only 2% of People Can Solve Einstein’s Riddle

How about four cars? Travel ⅙ of the way with all four cars. Each car will now be ⅔ full. Have car A sacrifice itself and transfer all of its gas to cars B and C.

Keep driving to the ⅓ mark. Your car is now ⅓ full and cars B and C are ⅔ full. Have car B sacrifice itself and give all its gas to you.

Keep travelling to the halfway point. Car C will be ⅓ full and your car will be ⅔ full. If car C gives all of its gas to you, you will have enough to make it out!

On the other hand, you will have abandoned three drivers and their empty cars in the middle of the desert — don’t be too proud!

Puzzle from Math is Fun.

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