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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.

enter image description here

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  • $\begingroup$ Can we go through one twice? ALso can we reverse our direction? $\endgroup$ – Sid Mar 25 '17 at 14:28
  • $\begingroup$ Yes. I will clarify that. $\endgroup$ – Nikolay Kostov Mar 25 '17 at 14:28
  • $\begingroup$ Do you need to go through all circles? $\endgroup$ – Beastly Gerbil Mar 25 '17 at 14:34
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    $\begingroup$ 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". $\endgroup$ – Rubio Mar 25 '17 at 20:11
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    $\begingroup$ @Rubio How is this question any different to this question? $\endgroup$ – boboquack Mar 25 '17 at 20:57
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enter image description here

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

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    $\begingroup$ you can go straight to exit from the second last yellow $\endgroup$ – JonMark Perry Mar 25 '17 at 14:43
  • $\begingroup$ Ah, Yes. That is also an option. I am too lazy now to edit that. :P $\endgroup$ – Sid Mar 25 '17 at 14:44
  • $\begingroup$ This is one of the correct answers. Great job! $\endgroup$ – Nikolay Kostov Mar 25 '17 at 14:57
  • $\begingroup$ 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. $\endgroup$ – Gerhard Mar 25 '17 at 17:15
  • $\begingroup$ @Gerhard; i quite like going round in infinite loops myself, for example right, up, left, down, and do it again! $\endgroup$ – JonMark Perry Mar 25 '17 at 17:19
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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. labyrinth with letters 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 ...

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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

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  • $\begingroup$ 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! $\endgroup$ – user21682 Mar 26 '17 at 1:21
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    $\begingroup$ If this is the intended answer then imgs.xkcd.com/comics/words_that_end_in_gry.png applies $\endgroup$ – Rubio Mar 26 '17 at 1:26

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