Path of Exile - Labyrinth: guide and tips for passing. How to find a way out of the labyrinth Finding a way out of the bizarre labyrinths of fate

One of the simplest rules for passing the maze is the "one hand" rule: moving through the maze, you must touch the wall with your right or left hand all the time. This algorithm was probably known to the ancient Greeks. You will have to go a long way, going into all dead ends, but in the end the goal will be achieved. Although this rule has one drawback, we will talk about it later.

Let's try to describe a robot acting according to the "right-hand" rule.

At the beginning of its work, the robot must find a wall along which it will follow. To do this, he can simply move forward until he hits an obstacle.

After the robot hits an obstacle, it begins to move according to the "right hand" rule.

Moving along the wall, the robot monitors if there is a passage to the right. If there is a passage, the robot must follow it in order not to break away from the wall to the right.

If there is no passage - there is a wall in front - the robot turns left. If there is no passage again, it turns left again, thus turning 180 degrees, and goes in the opposite direction.

The block diagram of the algorithm for a robot working according to the "right hand" rule is shown in the figure.

Let's try to check the operation of this algorithm and write a program for it. For this purpose, let's turn to the programming environment. This environment is a convenient tool for simulating various algorithms related to robot control. It features a turtle performer who is essentially nothing more than a real robot. The turtle has a very convenient set of commands - forward, right, left, back. In addition, there is a sensor in the center of the turtle, which takes a value from 0 to 100, depending on the tone of the surface on which it is located.

The dialect of the Logo language we'll be using is very simple and similar to Basic. You can get acquainted with the commands of the language. A free download of the GameLogo programming environment -. The size of the distribution kit is small - only 1 Mb.

In the archive with GameLogo there are maze backgrounds, one of which we will use.

At the very beginning of the program, we will give a command to the turtle to pick up the feather (by default, the turtle leaves a trail after itself).

The size of the field is 800 by 600 points. The original position for the turtle is at coordinates 115, 545 (white square).

The color of the labyrinth paths is light, on them the sensor will take values ​​greater than 50. The color of the labyrinth walls is dark, the sensor value will be less than 50. The exit from the maze is represented by a black square, the sensor value above which will be equal to 0.

We will declare a flag variable with which we will control whether the exit from the maze is reached.

Let's write a program and run it using the big red button labeled Run.

Variable flag background = maze1.gif raise pen to place 115, 545 "search for the first wall repeat until sensor> 50 (forward 12) "right hand rule repeat until flag = 0 (right 90 forward 12 if sensor = 0 then flag = 1 otherwise if sensor

If it is known that the labyrinth has no separate walls, that is, there are no closed routes along which one can return to the starting point, then such a labyrinth is called simply connected and it can always be completely bypassed by applying the "one hand" rule.

If the labyrinth contains free-standing walls, then, applying the "one hand" rule, it is not always possible to go through all the corridors and dead ends. Labyrinths with free standing walls and with closed routes are called multiply connected. In this case, multiply connected labyrinths can be divided into two groups: without a "loop" around the target (the closed route does not go around the target) and with a closed "loop" around the target (the target can be bypassed along a closed route).

In the multiply connected labyrinths of the second group, the "one hand" rule does not work and, applying it, it is impossible to achieve the goal. But even these labyrinths can be traversed by relying on an exact algorithm.

The solution to the problem of such labyrinths belongs to a relatively late time, and the beginning was laid by Leonard Euler. Euler, not without reason, believed that a way out of any labyrinth could be found, and, moreover, in a relatively simple way.

A universal algorithm for passing any labyrinth was described only a century later in the book of the French mathematician E. Luc "Recreations matematiques", published in 1882. It is interesting that Lucas, when describing the algorithm, pointed to the primacy of another French mathematician M. Tremo. Thus, the algorithm became known as Lucas-Tremaud algorithm.

Tremo offers the following rules: leaving any point of the maze, you need to make a mark on its wall (cross) and move in an arbitrary direction to a dead end or intersection; in the first case, go back, put a second cross, indicating that the path has been traveled twice - back and forth, and go in a direction that has not been traveled even once, or passed once; in the second - go in an arbitrary direction, marking each intersection at the entrance and exit with one cross; if there is already one cross at the cross, then you should follow a new path, if not, then the traveled path, marking it with a second cross.

Knowing the Tremot algorithm, you can correct the behavior of the legendary Theseus. Inspired by the gift of his beloved Ariadne, he confidently walks through the maze. Suddenly, a move appears in front of him, along which a thread has already been stretched ... What to do? In no case should you cross it, but return along the already known path, doubling the thread until you find another uncompleted move.

Using a variant of Tremaud's algorithm, the father of information theory, Claude Elwood Shannon, built one of the first self-learning robots. Shannon gave him the sonorous name "Theseus", but in history "Theseus" became better known as "Shannon's mouse". The "mouse" first examined the entire maze, and then (for the second time) traveled all the way much faster, avoiding the sections passed twice.

Nowadays, robots passing the maze are participants in one of the most interesting thinking machine competitions, which takes place in several countries around the world. These competitions bear a common name and, by their technical innovations, belong to the leaders of robotic sports.

At the first Russian Olympiad of Robots, competitions were held, the purpose of which was to pass a kind of labyrinth: in the shortest time, moving through the "open doors" in the walls, the robot had to get from the start to the finish. The robot could control its movement along the black lines drawn on the floor of the maze.

This picture is now roaming all over the Internet. This is often accompanied by the following text: " The Israeli military intelligence has a special unit, which serves young men and women suffering from various autism spectrum disorders. Autistic people are mainly involved in analyzing maps and aerial photographs that appear on computer screens. Due to the peculiarities of their thinking, they pay attention to the smallest details, the consideration of which in the preparation of military operations on the ground makes it possible to prevent possible losses of personnel. This is how autistic scouts save the lives of soldiers. "

Have you tried this maze?

Let's find out more about this issue ..

even at the mention of this labyrinth, it is specified that " An autistic person is able to process visual and textual information several times faster than a person without autism spectrum disorders. This feature turned out to be indispensable in high-tech. At Danish technology consulting company Specialisterne, 75 percent of employees are autistic and people diagnosed with Asperger's syndrome, also on the autism spectrum. They differ from ordinary workers with incredible attention to detail, superhuman concentration, and the ability to quickly process huge amounts of information. These skills are especially useful for software testers. The quality of work of autistic people doing this work is several times higher than the quality of work of ordinary people. Autistic people can check 4,000 pages of technical documentation 10 times faster than ordinary people and never miss a single mistake. "

But let's leave the autistic aside and find out in the end how you can get through this maze! That's how...

The task is unsolvable! We have 3 rooms with an odd number of doors (analogy with drawings "without lifting a pencil"). In order for the problem to have a solution, it is necessary that there are no more than 2 points (in our case, rooms) with an odd number of lines (in our case, passes)

If we build the graph of this labyrinth, then we will see that this is an Euler path, since it has 3 vertices with an odd number of edges (doors), and there can be only two of them to fulfill the test conditions.

The problem of the seven bridges of Königsberg or Königsberg bridges problem(it. Königsberger Brückenproblem) is an old mathematical problem that asked how you can walk across all seven bridges in Königsberg without walking across any of them twice. It was first solved in 1736 by the German and Russian mathematician Leonard Euler.

For a long time, such a riddle has been widespread among the inhabitants of Königsberg: how to get across all the bridges (across the Pregolya River) without going through any of them twice. Many Königsberg residents tried to solve this problem both theoretically and practically, during walks. However, no one could prove or disprove the possibility of such a route.

In 1736, the problem of seven bridges interested the outstanding mathematician, a member of the St. Petersburg Academy of Sciences Leonard Euler, about which he wrote in a letter to the Italian mathematician and engineer Marioni dated March 13, 1736. In this letter, Euler writes that he was able to find a rule, using which, it is easy to determine whether it is possible to cross all the bridges without crossing any of them twice. The answer was "no".

On a simplified diagram of a part of a city (graph), bridges correspond to lines (arcs of a graph), and parts of a city correspond to points of connection of lines (vertices of a graph). In the course of reasoning, Euler came to the following conclusions:

• The number of odd vertices (vertices to which an odd number of edges lead) of the graph must be even. There cannot exist a graph with an odd number of odd vertices.


• If all the vertices of the graph are even, then you can draw the graph without lifting the pencil from the paper, and you can start from any vertex of the graph and end it at the same vertex.


• A graph with more than two odd vertices cannot be drawn with a single stroke.

The graph of Koenigsberg bridges had four (blue) odd peaks (that is, all), therefore, it is impossible to walk over all the bridges without passing through any of them twice.

The theory of graphs created by Euler has found a very wide application in transport and communication systems (for example, for studying the systems themselves, drawing up optimal routes for the delivery of goods or routing data on the Internet).

In 1905, the Imperial Bridge was built, which was later destroyed in a bombing raid during World War II. There is a legend that this bridge was built by order of the Kaiser himself, who could not solve the problem of Koenigsberg bridges and became the victim of a joke played with him by the scientists who attended a social reception (if you add the eighth bridge, then the problem becomes solvable). In 2005, the Jubilee Bridge was built on the pillars of the Imperial Bridge. At the moment, there are seven bridges in Kaliningrad, and the graph, built on the basis of the islands and bridges of Kaliningrad, still does not have an Eulerian path

Here is another solution suggested by xlazex

Let's look at picture1: we will surround each separate part with squares, exclude the "extra" points, i.e. those points, the use of which would increase the possible number of paths, and the exclusion of which will not affect the number of doors traversed by the line and the closedness of the contour. For the beginning of the path, take, for example, the point 2 .
Let's look at picture 2: on it, I depicted the same contour, but so that the connections of the initial point with subsequent ones were more visible. The image clearly shows that the blue part of the contour cannot be closed once, i.e. even if this part of the contour was the only one, then there would be no paths along which a closed line could be built.
Bottom line: the problem has no solution in a two-dimensional coordinate system.

But there is a solution in 3D :-)

Okay, joke, joke ...

Good day, dear community.

Background

One fine day, walking the vastness of the Internet, a maze was found. It became interesting to find out its passage and after walking on the network, I still did not find a working software implementation, a solution to the maze.

Here is he actually:

The working day was boring, the mood was excellent. The goal, the means and the desire are there. The conclusion is obvious, we will go through.

History

For a convenient solution, it is necessary to convert the existing image of the maze to the type of a two-dimensional array. Each element of which can take one of 3 values:

Const WALL = -1; BLANK = -2; DEADBLOCK = -3;

Beforehand, I want to show the functions for scanning the maze image with the subsequent writing of data to the array, and the function of generating a new image based on the data from the array:

Scanning an image:

Var N: integer = 600; LABIRINT: array of integer; ... var bit: TBitmap; i, j: integer; begin bit: = TBitmap.Create; If OpenDialog1.Execute then begin bit.LoadFromFile (OpenDialog1.FileName); for i: = 0 to N do for j: = 0 to N do if bit.Canvas.Pixels = clWhite then LABIRINT: = BLANK else LABIRINT: = WALL; bit.Free; ... end; end; ...

Image generation:

Var N: integer = 600; LABIRINT: array of integer; ... procedure genBitmap; var bit: TBitmap; i, j: Integer; begin bit: = TBitmap.Create; bit.Width: = N + 1; bit.Height: = N + 1; for i: = 0 to N do for j: = 0 to N do begin if LABIRINT = BLANK then bit.Canvas.Pixels: = clWhite // else if LABIRINT = WALL then bit.Canvas.Pixels: = clBlack else bit.Canvas .Pixels: = clRed; end; bit.SaveToFile ("tmp.bmp"); bit.Free; end; ...

First, you need to resave the image as a monochrome bmp, in order to have 2 colors white or black. If you look closely at the maze, it has a wall 2 pixels thick and a road 4 pixels thick. It would be ideal to make the wall and road thickness 1 pixel. To do this, you need to rebuild the image, divide the image by 3, that is, remove every 2nd and 3rd, row and column of pixels from the picture (this will not affect the correctness and passability of the maze).

Prepared drawing:

Image width and height: 1802 pixels.

1. We use the function of scanning the image.
2. Rebuild the image:

Var N: integer = 1801; LABIRINT: array of integer; ... procedure rebuildArr2; var i, j: integer; begin for i: = 0 to ((N div 3)) do for j: = 0 to ((N div 3)) do LABIRINT: = LABIRINT; N: = N div 3; end; ...

3. Generate the rearranged image.

The result of the procedure:

Image width and height: 601 pixels.

And so, we have an image of a labyrinth of the desired type, now the most interesting thing is the search for all options for passing the labyrinth. What do we have? An array with the recorded values ​​WALL - wall and BLANK - road.

There was one unsuccessful attempt to find the passage of the maze using the wave algorithm. Why unsuccessful, in all attempts this algorithm led to the error "Stack Overflow". I'm 100% sure that using it, you can find a passage, but there was a fuse to come up with something more interesting.

The idea did not come immediately, there were several realizations of the passage, which took about 3 minutes to complete, after which an insight came: “what if we look not for paths of passage, but paths that do not lead to the passage of the maze and mark them as dead-end?"

The algorithm is as follows:
Execute a recursive function along all road points in the maze:
1. If we stand on the road and there are 3 walls around us, mark the place where we stand as a dead end, otherwise we exit the function;
2. Go to a place that is not a wall from point # 1, and repeat point # 1;

Software implementation:

Var N: integer = 600; LABIRINT: array of integer; ... procedure setBlankAsDeadblockRec (x, y: integer); var k: integer; begin k: = 0; if LABIRINT = blank then begin if LABIRINT<><><><>BLANK then k: = k + 1; if k = 4 then LABIRINT: = DEADBLOCK; if k = 3 then begin LABIRINT: = DEADBLOCK; if LABIRINT = BLANK then setBlankAsDeadblockRec (x-1, y); if LABIRINT = BLANK then setBlankAsDeadblockRec (x, y-1); if LABIRINT = BLANK then setBlankAsDeadblockRec (x + 1, y); if LABIRINT = BLANK then setBlankAsDeadblockRec (x, y + 1); end; end; end; procedure setDeadblock; var i, j: integer; begin for i: = 1 to N-1 do for j: = 1 to N-1 do setBlankAsDeadblockRec (i, j); end; ...

Conclusion

I got a "complete" working algorithm that can be used to find all the paths in the maze. The latter exceeded all expectations in terms of speed. I hope my little work will benefit someone or encourage new thoughts.

Program code and maze traversed:

// Please don't kick for the programming language used. unit Unit1; interface uses Windows, Graphics, Forms, Dialogs, ExtCtrls, StdCtrls, Controls, Classes; const WALL = -1; BLANK = -2; DEADBLOCK = -3; type TForm1 = class (TForm) Button1: TButton; OpenDialog1: TOpenDialog; procedure Button1Click (Sender: TObject); private (Private declarations) public (Public declarations) end; var Form1: TForm1; N: integer = 600; LABIRINT: array of integer; implementation ($ R * .dfm) procedure genBitmap; var bit: TBitmap; i, j: Integer; begin bit: = TBitmap.Create; bit.Width: = N + 1; bit.Height: = N + 1; for i: = 0 to N do for j: = 0 to N do begin if LABIRINT = BLANK then bit.Canvas.Pixels: = clWhite // else if LABIRINT = WALL then bit.Canvas.Pixels: = clBlack else bit.Canvas .Pixels: = clRed; end; bit.SaveToFile ("tmp.bmp"); bit.Free; end; procedure rebuildArr2; var i, j: integer; begin for i: = 0 to ((N div 3)) do for j: = 0 to ((N div 3)) do LABIRINT: = LABIRINT; N: = N div 3; end; procedure setBlankAsDeadblockRec (x, y: integer); var k: integer; begin k: = 0; if LABIRINT = blank then begin if LABIRINT<>BLANK then k: = k + 1; if LABIRINT<>BLANK then k: = k + 1; if LABIRINT<>BLANK then k: = k + 1; if LABIRINT<>BLANK then k: = k + 1; if k = 4 then LABIRINT: = DEADBLOCK; if k = 3 then begin LABIRINT: = DEADBLOCK; if LABIRINT = BLANK then setBlankAsDeadblockRec (x-1, y); if LABIRINT = BLANK then setBlankAsDeadblockRec (x, y-1); if LABIRINT = BLANK then setBlankAsDeadblockRec (x + 1, y); if LABIRINT = BLANK then setBlankAsDeadblockRec (x, y + 1); end; end; end; procedure setDeadblock; var i, j: integer; begin for i: = 1 to N-1 do for j: = 1 to N-1 do setBlankAsDeadblockRec (i, j); end; procedure TForm1.Button1Click (Sender: TObject); var bit: TBitmap; i, j: integer; begin bit: = TBitmap.Create; If OpenDialog1.Execute then begin bit.LoadFromFile (OpenDialog1.FileName); for i: = 0 to N do for j: = 0 to N do if bit.Canvas.Pixels = clWhite then LABIRINT: = BLANK else LABIRINT: = WALL; bit.Free; setDeadblock; genBitmap; end; end; end.

To find the shortest path, it is planned to apply the wave algorithm to the found passages of the maze. It would be interesting to hear what other algorithms can be applied to quick finding your way in a big maze?

A labyrinth in Path of Exile is a dungeon filled with traps, a variety of puzzles, and monsters. After completing the level, you can return to the labyrinth, while using the Statue of the Goddess, located in Sandria. In the labyrinth itself, you will find not only traps, but numerous tests of the Ascent, while one trap is hidden, which few people know about. But you can't just find a trap, because it will be hidden randomly in any of the groups presented, where such a test is already considered fatal, for this we have prepared the passage of this labyrinth.

With an increase in difficulty at the level, a new structure of rooms appears (the passage of the labyrinth becomes more difficult), where they remain the same for only one day. But the rooms themselves, in fact, are the same among themselves, but not all may be the same in terms of planning accuracy. The structure of the rooms is changed every day. Of course, it's not easy to go through, where there are special keys to open the doors, but they will be behind difficult traps. If you open the room with the key, then a whole hall will appear, connecting several rooms.

After the player finds himself in this maze, he will constantly meet with Izariy. Your every action will affect the subsequent battles. Where the first battle will continue until the health bar of your enemy reaches 2/3, after 1/3, and then you need to completely win. But in the last battle, do not forget that there will be traps and you must act carefully.

Exactly 45 minutes will be required by an experienced player who already knows what and what refers to. If you are in the ruler's labyrinth, then you will not have the right to teleport to the city, thus you will have to go through the labyrinth again. Accordingly, there are no restrictions in this game, and you can test all the methods of passing.

Initially, when you play the game for the first time, only the Ascend class will be available. Each time you will receive points throughout the game, which can then be exchanged for skills. In this case, you can enchant items, but by choosing only one.
If one of the players goes through the labyrinth faster than anyone on any of the days, then he is given a special prize with unique gems. Moreover, you can see all the ratings about the passages on the official website. The higher the difficulty of the level, the higher the reward for it will be provided.

How to open and enter the maze?

In order to find ourselves in the main labyrinth, which we need, we first need to find six small labyrinths, where they must first be found and passed.

• Stage 1: The Lower Prison;
• Stage 2: Chamber of Sins Level 2;
• Stage 2: The Crypt Level 1
• Stage 3: The Crematorium;
• Stage 3: The Catacombs;
• Stage 3: The Hedge Maze - a full-fledged teleport to this map was not originally provided, but you can still get there if you get into it through The Imperial Gardens.

Thus, the main labyrinth will be in the 3rd stage, which will be located in the city. Each of the mini-labyrinths must be passed once, thereby opening access to the main labyrinth, and this will be done forever, for the difficulty on which you pass.

Guide - how to complete the ruler's labyrinth in Path of Exile

Boss battles

In the main labyrinth, there are three difficult battles with Izarius, who has versatility and a change of image, that is, with each battle, he will have assistants, but they are constantly different.

• First step. At this stage, statues appear that will begin to help him. But they do not appear immediately, where there are two options for how to deal with the statues. This will temporarily neutralize and destroy them permanently. After you find the only solution to them, then you will have to inflict subsequent damage already on the boss. If you don't deal with the statues, then he will have additional protection at the final moments, where it will not be so easy to defeat him.

• Second phase. At this stage, he is helped by small bosses, which are not as effective as the main boss, but can do good damage. Their appearance occurs gradually, where you need to adhere to the same tactics. We remove the assistants, and then we deal with the boss.

• Stage three. At this stage, it is important for you to take such a position so that the traps do not reach you in any way and can safely inflict damage on the boss. But this is only at the moment when you have reached this stage without assistants, that is, dealt with them in the previous stages.

And also it is worth remembering that in one of the versions there is Izarius, who knows how to use a teleport against you directly to the traps, which will complicate the task of fighting the boss.

After passing the third stage, you find yourself on a new map. In it, you have the right to enchant some items, take an additional subclass, open chests that can be opened with the keys that you found during the passage of the labyrinths.

It should be borne in mind that in the labyrinths such zones sometimes appear, which are called "the beast". If you find this zone and destroy it, then the future boss will be a significantly weak rival. Although this will make things easier for you, there will be no special adrenaline in the passage, so it's up to you.

Traps in the ruler's maze Path of Exile

Undoubtedly, there are traps in the labyrinths, but not of one type, but several, which are not only dangerous, but also deadly things. Where they can take away not only the state of the shield, but also health. Most of the traps can be found in Trials of the Ascents, which shows a considerable number of such traps.

In some square areas there are thorns that are not immediately noticeable, because they appear after a certain amount of time. Moreover, some of these traps appear only when you step on them. Damage is about a quarter of your total health, meaning that it includes not only your health, but your shield as well. Stepping on a trap will slow you down for a couple of seconds and get good bleeding. This type of trap is the most harmless, because its repeated action does not take place immediately, but after some time. Moreover, the damage is inflicted once and does not continue its effect. Such inflicted damage can be restored using flasks filled with health.

To find out how traps of this type work, you can look at the locations of the first stage, or more precisely, in the Prison Dungeon.

Saws are able to move along a given trajectory, repeating their actions over and over again. Where damage can be done gradually, but it is much more effective than regular spikes. Where the damage is not important in this case. Sometimes the saws can be temporarily turned off by finding and turning off the lever. To find out how they work, then go to the map of the second stage in the Chamber of Sins 2.

Rotating blades have a complex system of movement and impact on the player who is on the floor. If the player comes into contact with this trap, he will receive devastating damage, from which it will be difficult to heal. Where the trajectory of their movement can constantly change. But everything can be temporarily turned off if you find the levers. They can be seen in the Crypt in the second stage.

Melting traps are empty squares that are gradually replenished with magma and it takes a certain amount of time. A magma kill takes five seconds, where health instantly decreases, but you can get rid of it if you drink a bottle of health and leave that trap. Such damage does not pass through monsters, because they resist fire. Such traps are in the Crematorium, and this is the third stage.

Guardians with blades, they are quite large traps that cannot be overlooked, from which significant damage is inflicted, the damage done can be gradual. The closer you are to the center of this trap, the damage will increase. In this case, the trap changes its trajectory, which complicates the passage of the maze. They are the ones who are in the Catacombs at the third stage.

Flying darts, a trap that shoots extremely small projectiles, it can change its direction. Projectiles are fired at a specified time interval. The damage done is not so great, but you can survive several shots, while it will slow you down. Such traps will be located on walls and pillars, some of them are activated by pressing certain plates. To evaluate the shooting of traps, you can visit the Green Labyrinth in the third stage.

Sentinels, those traps that have harmful damage on you and the environment for a certain time, and such traps are found only at level 75.

Additional (secret) traps in the labyrinet

Of course, there are also other traps that are less known to humans. One such trap is rotating blades that rotate vertically in doors.

Players are constantly sorted by the system, and this depends on the amount of time spent on passing the maze. To gain sole leadership in the maze, you need to go through the maze alone. Moreover, the labyrinth must be completed by the end of the day, until there have been any changes. The result is a total of twelve labyrinth leaders at different difficulty levels.

• To play on the list of regular players, you need not go over the 40th bar.
• To play on the list of violent players, you need to stay within the 60th level.
• To play on the list of ruthless players, you need to reach level 60 or higher.

At midnight, the fate of all the players who decided to take part is decided, where the most interesting begins, or more precisely, the distribution of prizes, awards and other interesting things. And it all depends on the complexity of the level, the time spent, and so on. Moreover, awards are awarded to some players during the day, and this is done about 4 times.

Find an item you can use to mark each trail. It is important that the device chosen is suitable for making notes on the floor of the labyrinth. For example, chalk can be used on a hard surface such as wood or concrete. For other surfaces, consider what you might leave behind, such as bread crumbs or pebbles.

• Whatever item you use, you should be able to make two different types of markings. You need to distinguish between the paths: which you have passed once, and which - two.

Choose a random path and follow it until the next intersection. Each maze has its own layout at the start. Some may start at an intersection, while others will only have one trail. In any case, take any trail and walk forward until you reach an intersection or dead end.

Mark trails as you go. For the Lucas-Tremaud algorithm to work, it is very important to keep track of which paths you have already traveled. Be sure to mark the beginning and end of each trail in any way you choose.

• If you are walking the trail for the first time, you need to make one mark on it. If you are using chalk, one simple line is enough. If you are using items, such as a handful of pebbles, leave pebbles at the beginning and end of the trail.
• If you are walking the trail a second time, mark it again. If using chalk draw a second line, and for objects just leave the second one behind.
• If you are at a dead end, mark the trail to recognize it as a dead end. For example, if you are using chalk, mark the path with a "T". Make this mark next to the intersection that the path leads to.

At intersections, prefer unmarked trails. Whenever you enter an intersection, take a moment to inspect the markings on each trail. Some of them may be unmarked, while others will show that you have selected them once (or twice). It is worth giving preference to trails without marks. This will make you more likely to move forward. If all trails are marked once, pick one at random.

Avoid the paths marked twice. If you are forced to follow a trail that you have already marked once, you should mark it a second time. According to the Luc-Tremaud algorithm, the double-marked trail will not lead you to the exit. If you find an intersection where one path is marked twice, always choose the other path, even if that means you have to go back.

Go back if you stumbled upon a dead end. If you are at a dead end, you need to return to the last intersection that you crossed. Remember to mark the trail to remember that it leads to a dead end. Once you get to the crossroads, choose one of the remaining paths and continue to cross the maze.