## Reshuffling cars brainteaser

By David Shaw, 13 October 2021

**Difficulty: Extreme!**

Terri wants the cars moved around – can you help her do it?

Terri runs a car showroom. It has 3 roads to park cars on, which all meet in the middle of the showroom. Terri can fit 3 cars on each road. If she tries to park a fourth, it blocks the intersection in the middle.

At the moment, there are 2 Audis on one road, 2 BMWs on the second, and 2 Citroëns on the third. Terri wants to move them all around, putting the Audis where the BMWs are, the BMWs where the Citroëns are, and the Citroëns where the Audis are.

Terri isn’t sure she can do it. Can you explain a way to move the cars to the correct location?

**Scroll down or click for a hint, or the answer!**

## Brainteaser hint

This activity is a lot easier if you make a model. You can draw the roads on a piece of paper and use toy cars or cut up pieces of paper as the cars!

## Brainteaser answer

There are lots of ways to solve the problem, but this method is quite fast:

- Start by moving one Audi over to the Citroëns. Eventually it needs to go where the BMWs are, but we need to move the BMWs out of the way first.
- Move the 2 BMWs to where the Audis started.
- Move an Audi and 2 Citroëns into the empty road. That Audi has now reached its goal.
- Move the BMWs and the other Audi into the empty road. The BMWs are at their goal, and you’ve just made space for the Citroëns.
- Put the Citroëns on the empty road, which is their goal.
- Finally, put the last Audi in its place too!

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