# A blue, white and red maze

First, let's give to Caesar what belongs to Caesar: this maze comes from the mind of Dave Phillips, a brilliant maze designer 1.

So, for the maze. It is a fairly easy one:

Your goal is to exit by the blue tile on top left, after having entered the maze by the red tile at the bottom right. And here are the rules:

• Keep to the path;
• Do not turn around (the same path may be used twice);
• Alternate between red and blue tiles (i.e. don't pass over two red/blue tiles in a row, including the exit tile).

1 Check his website!

If going over the same path twice is allowed, this is a probable solution. I just started at the end and worked my way backwards to the start since there is only one possibility for the second-last tile (the other red tile would have resulted in an infinite loop)

The line colour is the colour of the last tile passed through

The solution posted by KritixiLithos, re-posted by Hermansh, and re-re-posted by myself here [below] does indeed work but it is not the only solution.

In this particular maze it's possible to traverse through every single square on a single run before reaching the end. You can even traverse through every single square an arbitrary number of times before reaching the end.

Below the standard solution you'll find a second solution that passes through many more more squares. I change the color the line several times to make it more readable.

No matter what you do, your must at a minimum pass through the squares passed through in the simple (first) solution.

• The fact that you change colors in the middle of your lines is a bit... unreadable. Commented Dec 28, 2016 at 12:54
• There's only one line. Commented Dec 28, 2016 at 14:37
• Yes, with multiple colors, I got it, but it is still visually hurting my eyes :-). Commented Dec 28, 2016 at 14:40
• I tried creating a single line for comparison and it's completely unreadable. Sorry about your eyes. :) Commented Dec 28, 2016 at 14:42

Another working version. Though more of a similar to another answer but a unique one

• The other answer takes a left after first blue, but this one goes straight. As I said, a slightly different. Commented Dec 28, 2016 at 12:22
• You're right, even if it is very slightly different :-) Commented Dec 28, 2016 at 12:25
• Glad you got it ;) And yes i have m +1 for the other answer. Commented Dec 28, 2016 at 12:30

I haven't got a new answer, but I do have a way to find it more systematically.

Note that the maze can be split into four contiguous sections, which subdivide into eight unique states depending on the color last encountered.

Then the maze can be simplified and solved as follows. Note for the simplified version, the interior color of the circle is the region that the line is currently in, and the border is the last encountered red/blue square.