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For a competition, I need to choose a maze puzzle, only one. There are tons of mazes, but most of them are not clever, i.e. they are just solved by trial and error.
Few days ago I saw A blue, white and red maze. It's a clever puzzle: when you approach it with trial and error, you can easily fail and conclude that it doesn't have a solution, but it does. I liked it a lot. A problem with it? It is too simple, as I think most of the people can solve it eventually.

So, I need a maze, which:

  • has a solution;
  • is clever, i.e. not a usual maze where you just walk in all possible ways until you find an exit. In this puzzle, you should be required first to find an idea how to approach it, only then to try different paths;
  • hard, i.e. the idea should not be trivial and most of the people who try to solve the maze should feel like there is no solution.
  • relatively small, with rules, which are easy to understand. Let's say it should fit to a piece of squared paper of size about 15 by 15 cells;

Could you help me to find such a puzzle?

P.S. Looking at Near-impossible puzzle for Christmas, I suppose this is not off-topic.

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klm123
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  • We typically don't help with competitions as it would be unfair to the others involved in them. – dcfyj Jan 11 '17 at 15:36
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    @dcfyj, unfair? why? I'm not asking to help me to solve a puzzle from a competition, where I'm participant. I'm asking to help me to Find a puzzle for a competition, where I'm Organazer. – klm123 Jan 11 '17 at 15:37
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    Oh ok, I misunderstood. Carry on :P – dcfyj Jan 11 '17 at 15:38
  • This had a maze that was very interesting, a 4x4 version would likely be more difficult, while being 16x16. – Sconibulus Jan 11 '17 at 15:43
  • @Sconibulus, do you mean "megamaze"? But it is just a 4D maze, which, I would imagine, is solved just like usual 2D mazes, or what is the idea behind it? – klm123 Jan 11 '17 at 15:49
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    @klm123 The odd geometry will probably mess with some people, and certain isolated boxes can be eliminated as useless very easily restricting the number of plausible paths more so than an ordinary maze (at least in my opinion) – Sconibulus Jan 11 '17 at 15:51
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    There are some unconventional mazes here. (One of them was featured in a "reverse puzzling" puzzle on this site a while ago.) – Gareth McCaughan Jan 11 '17 at 15:51
  • @GarethMcCaughan I love that site! A lot of the mazes are dynamic, however, meaning they couldn't be emulated very well on paper. – TheGreatEscaper Jan 11 '17 at 15:53
  • If you're willing to look at video games, I suggest looking up one-screen puzzles in Super Mario Maker. People have created some very difficult maze-like puzzles in that game! – Kevin Jan 11 '17 at 18:51
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    Here's a famous one: Theseus and the Minotaur – Cort Ammon Jan 12 '17 at 01:54

5 Answers5

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Here's a maze of mine.

Start at the top left square. End at the bottom right.

RULES: You must stay on a color for exactly THREE squares. You may not do a U-turn (return to the square you just came from) at any time.

enter image description here

Like most mazes, it's easier to solve working backwards. But it's definitely very difficult going forwards.

EDIT: will continue to update this post when more mazes come to mind.

Here is a maze by Hiroshi Yamamoto. You must jump 1 square in a single direction, 2 squares in a single direction, then 3 squares in a single direction, then repeat. You must always land on a square after each turn, and you may not turn while jumping. This one is very lovely!

(Clarification: Every move starts on an unshaded square, ends on an unshaded square, and does not turn, and does not pass over any shaded areas)

enter image description here

TheGreatEscaper
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    Gonna post these as puzzles? They're great regardless of difficulty. (Suggest adding stipple patterns to help distinguish colors, though. Some of my favorite solvers see textures more distinctly than hues. Oops just noticed, outlines are all that matter in the first one.) – humn Jan 11 '17 at 16:00
  • Unless I'm mistaken you can't finish your puzzle without making a u-turn. Working back from the finish line will end up in a u-turn either at the left-most red parts or at the middle yellow. Correct me if i'm wrong :) – Piotr Pytlik Jan 11 '17 at 16:43
  • can you jump over "walls" in Yamamoto's maze? – klm123 Jan 11 '17 at 16:50
  • What are the movement rules in the first (colorful) maze? Can you also move to diagonally adjacent squares? Does the "You must stay on a color for exactly THREE squares" rule also apply to the final move? – Gamow Jan 11 '17 at 17:10
  • @Gamow only orthogonal moves allowed. The rule does not apply to the final square, obviously. – TheGreatEscaper Jan 11 '17 at 23:08
  • @klm123 you may not jump over walls. – TheGreatEscaper Jan 11 '17 at 23:08
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    @PiotrPytlik there is no U turn in the solution. – TheGreatEscaper Jan 11 '17 at 23:08
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    What is your definition of a UTurn? Right, Left or Right, Down, Left? Are both of these banned, or just one? – Rob Jan 12 '17 at 04:06
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    Right, Left. Perhaps I should phrase it as 'You cannot return to the square you just came from.' – TheGreatEscaper Jan 12 '17 at 05:18
  • @TheGreatEscaper I have (independently) come up with a maze which has mechanics identical to the 123 maze (except with different numbers) :( all the good ideas have been taken. – Wen1now Jan 12 '17 at 06:17
  • if you may not jump over walls this is huge. Looks unsolvable :D So I must be sure I understand you correctly. First of all, walls - are shaded squares. What do you mean then by "You must always land on a square after each turn", this supposes that you may not land on square before the end of turn. What does it mean if you may not be above a wall before turn is finished anyway? Also, is it correct that if you jump 1 square down, 2 square down and 3 square up you end up at the starting position? – klm123 Jan 12 '17 at 07:01
  • Every move starts on an unshaded square, and ends on an unshaded square, sorry if my explanation was a bit ambiguous. Yes, your set of starting moves is valid. – TheGreatEscaper Jan 12 '17 at 07:03
  • @TheGreatEscaper, so you may jump over shaded squares? – klm123 Jan 12 '17 at 07:04
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    No. Every move starts on an unshaded square, ends on an unshaded square, and does not pass over any unshaded squares. I'll clarify this in my answer. – TheGreatEscaper Jan 12 '17 at 07:06
  • @TheGreatEscaper ok, if a u-turn means literally going back to the previous square, but going for instance up - right - down is legal, then its possible :) – Piotr Pytlik Jan 12 '17 at 07:53
  • Do the start and end squares count as part of the three you must stay on? – nzaman Jan 12 '17 at 13:20
  • The start square yes. The end square obviously must be moved onto as the first of a set of three, but it doesn't matter since its the last square. – TheGreatEscaper Jan 12 '17 at 13:25
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A maze that sounds perfect for your problem is one called a recursive or fractal maze.

The actual map that is required to be drawn is quite small but it leads to a much much bigger map :-)

There is a good example here...

Alice and the Fractal Hedge Maze

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Fogmeister
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    The examples may be a bit large, but the idea of fractal maze is new for me and indeed, I don't know how to approach it! Thanks a lot! – klm123 Jan 11 '17 at 20:40
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    @klm123 Not sure if you saw all the examples at the bottom of the post, but this one in particular is quite small while still being tricky. – Mike Earnest Jan 11 '17 at 21:23
  • @MikeEarnest what do the + and - do in these ones? I saw a few but didn't understand that mechanic? – Fogmeister Jan 11 '17 at 21:31
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    Right, forgot to mention that! Those are the start and goal places. Start at + and get to -. You have to get to the - on the same level you started on. – Mike Earnest Jan 11 '17 at 21:34
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Okay, not sure if this deserves an answer, but I found this fun but complex puzzle on Wolfram:

          enter image description here

The rules:

  • Put two coins at the center of the maze;
  • Pick an arrow under either coin;
  • Move the other coin in that direction;
  • Only move one tile per turn;
  • Get both coins back to the center.

Here's a quick animation for a $3*3$ maze (warning: the initial condition is different, the coins are placed in opposite corners here):

                                                        enter image description here

This puzzle is... pretty hard, because some solutions requires a great number of moves.

Edit: I stumbled across this website, which is a small collection of small but complex mazes.

IAmInPLS
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Here is a clever puzzle that requires logic and thinking outside the box!

Zen Labryinth It's tricky, but can be solved using logic, go from top to bottom through all of the yellow boxes, the lines may not cross over each other or go in the same place as where another line is (2 lines in the same corridor). You cannot turn around, or have 2 lines in a yellow square.

I did not actually create this puzzle myself, it was created by Dave Phillips, who is an excellent puzzle maker, who also happened to make the blue, white, and red puzzle that you linked to. It is in his "The Zen of the Labyrinth" book.

Since I do not actually own the book (although I am now very tempted to buy it!), I found this sample on his website, and had to reverse engineer it to find the rules and solutions, so it may be different from what was intended. I have checked my answer though, and the puzzle is solvable.

Techniques I used to solve this puzzle:

I started with the yellow boxes that were connected to two corridors, I added lines and extended them along the corridors until I came to a junction, this allowed me to immediately start to fill in the grid. From here I tried out different possibilities and used elimination to get a few more lines. Then I used logic to finish off the puzzles, making sure to go through all the boxes. A few things to keep in mind are that the line cannot go in a loop, and also one line cannot go past another in a T shape. This may seem obvious but it is very useful to think about when doing logic.

Melkor
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  • About 2nd puzzle. How thick is the line should be? Can I enter a yellow box from below then make a circle inside of the box and exit down-ward, just 1 micrometer from the place I've entered? – klm123 Jan 19 '17 at 11:26
  • @klm123 No you cannot turn around, or have 2 lines in a yellow square. – Melkor Jan 19 '17 at 16:19
  • So what exactly means "lines may not cross over each other"? Can I go twice in the same corridor? – klm123 Jan 20 '17 at 08:46
  • Is this the answer? https://i.stack.imgur.com/aCYia.gif – klm123 Jan 20 '17 at 08:50
  • @klm123 you are sooo close. Just slightly rearange the bit where you have 2 lines down the same corridor, as you cannot do that. – Melkor Jan 20 '17 at 16:21
  • Here we go: https://i.stack.imgur.com/rp2rw.gif But i've found it with try and error, could you please explain the idea, which makes this maze easy? – klm123 Jan 20 '17 at 16:51
  • Perfect, good job! I solved this with a tiny amount of trial and error, but mostly with logic. I will add to my answer the techniques I used to solve the puzzle (in a spoiler) – Melkor Jan 20 '17 at 16:54
  • Nice! Indeed, if you solve it localy, then there are only 2 options to check, every other connection is stricly determened. – klm123 Jan 20 '17 at 18:40
  • Glad I could help :) – Melkor Jan 23 '17 at 21:26
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I came up with this idea:

1212arrows_game1

You start at the top left. You travel 1 or 2 steps in the direction of the arrow you are on. Continue until you reach the bottom right.

Only there's a 'twist' - when you leave an arrow, it rotates 90$^\circ$ clockwise.

There could be any number of solutions - I don't even know if this particular puzzle has even one - I just made it up!

Other variations on the rules might work as well.

Beastly Gerbil
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