# Go through the labyrinth by alternating yellow and green circles

Go through the labyrinth by alternating yellow and green circles. The entrance is the yellow circle on the left-bottom and the exit is the green circle in the middle-bottom (as shown with the arrows).

You can go through one circle more than once. If you touch the circle you must go through it.

• Can we go through one twice? ALso can we reverse our direction?
– Sid
Mar 25, 2017 at 14:28
• Yes. I will clarify that. Mar 25, 2017 at 14:28
• Do you need to go through all circles? Mar 25, 2017 at 14:34
• This seems very under-constrained, making it feel like there are going to be enough valid answers to nudge this over the line of being "too broad".
– Rubio
Mar 25, 2017 at 20:11
• @Rubio How is this question any different to this question? Mar 25, 2017 at 20:57

Here's the answer. I have followed all the rules, I hope.

• you can go straight to exit from the second last yellow
– JMP
Mar 25, 2017 at 14:43
• Ah, Yes. That is also an option. I am too lazy now to edit that. :P
– Sid
Mar 25, 2017 at 14:44
• This is one of the correct answers. Great job! Mar 25, 2017 at 14:57
• Defining each area between the circles to be a single waypoint, @JonMark Perry's suggestion seems to be the only solution avoiding turns or extra loops. Mar 25, 2017 at 17:15
• @Gerhard; i quite like going round in infinite loops myself, for example right, up, left, down, and do it again!
– JMP
Mar 25, 2017 at 17:19

You can find a solution using this systematic approach:

Define each area with crossroad between the circles to be a single waypoint A B C D E. Then list all possible ways through the labyrinth, avoid loops, so do not go to a waypoint/color combination you already have in your path.

• Start - Dy (D after yellow) - Eg - Cy - loop (only loop continuations; Eg is already in this path)
• Start - Dy - Ag - By - Bg - Ay - Dg - Ey - exit
• Start - Dy - Ag - By - Bg - Ay - Eg - Cy - loop
• Start - Dy - Ag - By - Bg - Cy - Eg - loop
• Start - Dy - Ag - By - Bg - Eg - Cy - loop

You can see, only the second try leads to the exit. So the only solution path is

Start - D - A - B - green Circle - A - D - E - exit

From this path you can derive any other solution by adding additional loops.
For instance Ey - Cg - Ey ...

Since the goal is to reach the end by exchanging Green - Yellow. Having said that and knowing that the "player" is standing on the original yellow circle, it follows that with each swap the Green Circle trades places with a Yellow Circle, and so does the "player".

In other words:

You don't need to alternate between yellow and green circles. You can only swap your current circle with a green circle (because you're always in yellow)

I have to put the image like this because I'm failing at conceiling it, Im sorry:

https://i.stack.imgur.com/LqThd.jpg

• I'm not sure that this is what the OP wanted, but it's technically correct and it's a creative answer (and also the first one I thought of). +1!
– user21682
Mar 26, 2017 at 1:21
• If this is the intended answer then imgs.xkcd.com/comics/words_that_end_in_gry.png applies
– Rubio
Mar 26, 2017 at 1:26