# Blue and Red Maze

In this maze, you must alternate going through blue and red doors – in other words, you cannot go through two blue doors in a row or two red doors in a row.

Entering through the blue door in the top left, can you find your way through the maze and exit through the red door in the top right?

#### Solution

Yes! The most direct route is shown in magenta below:

Here is one way of figuring out the solution without using trial-and-error:

• The exit is red, so to successfully exit, you need to enter the room containing the exit using a blue door.
• There are two blue doors to the exit room, but we can rule out the one on the right. In order to pass through the blue door on the right, we must have entered that room using a red door, all of which come from the exit room—but if you were in the exit room and could go through a red door, you would just exit.
• So now we know the solution must pass through the left blue door from the room with the entrance.
• The entrance room has two red doors, but it has to be the one at the bottom because the one at the top leads to the exit room (again, if you’re in the exit room and could go through a red door, you would just exit).
• From there, we’re pretty much done, because there’s only one door of the correct color in each room after that.