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Wooden puzzle instruction. Wooden puzzle knots from bars. Values in formulas

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PUZZLE

AT unlike games built on the competition of two or more partners, puzzles, as a rule, are intended for one person. When solving a puzzle, everyone acts independently, and his decisions do not depend on the actions of a partner who could change the course of the game and create a new situation.

Of course, competition is also possible in puzzles, but of a different order than in games. It can only consist in who solves the problem faster, more successfully.

Recently, in our country and in many other countries, the Rubik's Cube puzzle has become very popular. This is a really interesting invention that has received well-deserved recognition, an example of how millions of people can be captivated by the game. But there are many others interesting puzzles created in different time, which, moreover, is not difficult to make with your own hands (and this is also very important). They contribute to the development of spatial representation, creative imagination, constructive abilities and many other skills and abilities. However, no puzzle, no matter how attractive, can be universal. Puzzles are interesting in their entirety. That's why puzzle sets are needed.

Here you will find a description of a variety of puzzles, old and newly created. If you put them together, you can create a “puzzle game library” and conduct systematic “savvy contests”.

Using only cubes, you can come up with a whole series exciting games, entertaining tasks, puzzles of varying difficulty. For example, if cubes are connected in a known way, then from the resulting elements it is possible to assemble and design a wide variety of three-dimensional figures.

Cubes of catfish(Fig. 77)

In recent years, the so-called "cubes of catfish" have been especially popular. Their inventor, Dane Pete Heit, suggested gluing seven elements out of 27 cubes, as shown in the figure. Of these, you can add a 3x3x3 cube (in many ways) and various shapes resembling a skyscraper, tower, pyramid and other structures.

These seven elements are, as it were, a kind of constructor for compiling all kinds of three-dimensional figures.

Figures from nine identical elements (Fig. 78)

Of the seven elements of the game "cubes of catfish" it is possible to add up, as already mentioned, a 3x3x3 cube. But not everyone can complete this task. It is much easier to put together a cube of nine identical elements, each of which is glued together from three cubes. Babies often do this too. (The assembly method is shown in the figure.)

If in a cube composed of these elements, each of the six sides is painted a different color, we get new task. It will be more difficult to assemble such a cube while maintaining the color of the sides. The elements of this game are needed not only to assemble the cube. From them, you can build various structures according to own design and according to the given samples (see figure). For building games, it is better to have more than nine elements instead of nine.

Cube of four elements (Fig. 79)

Of the 27 cubes, four elements must be glued, as shown in the figure. From these elements, the player is invited to make a cube.

If two opposite sides of the cube are painted in different colors, the task is simplified.

"Devil's" cube (fig. 80)

This is an old English puzzle. Try to add a cube of six elements. All elements are "flat". They are made up of two, three, four, five, six and seven dice.

A significant number of dice games are based on color matching. There are many original and exciting tasks that the guys will be interested in. Among them there are both simple and more complex. Games should be offered in order of increasing difficulty.

chess cube(Fig. 81)

The game requires 8 dice, colored in two colors, as shown in the scans. With these cubes, you can solve several problems.

1. Fold a 2x2x2 cube so that on all its six sides the color of the cubes alternates in a checkerboard pattern. If the problem turns out to be difficult, you can initially simplify it: fold the cube so that the color of the cubes in a checkerboard pattern alternates only on the five visible sides of the cube (the bottom side is not taken into account).

2. From 8 cubes, add two 2x2x1 prisms, in which the upper and lower sides, as well as four side faces, are painted in a checkerboard pattern.

3. From the same cubes, add a 2x2x1 prism, in which the upper and lower sides, as well as four side faces are painted in a checkerboard pattern, and a 4x1 prism, on the four sides of which the cubes alternate in color in a checkerboard pattern.

4. Collect 2 prisms 2x2x1, the top and bottom sides of one color, and the sides of another.

The solution of all problems is shown in the figure.

So that the color does not repeat (Fig. 82)

From four cubes, the sides of which are painted in four different colors (as shown in the development), it is proposed to assemble a prism, on each side of which all four colors must be represented. This is not possible for everyone.

The task can be offered to younger students in a simplified form (Fig. 83): take 6 cubes, drill a through hole in each and put them on a round rod. It is necessary to rotate the cubes so that the same color does not repeat on any side of the prism (how to color the cubes is shown in the figure).

Almost a Rubik's Cube (Fig. 84)

The game requires 9 dice. All sides of each cube are painted in different colors, as shown in the scan. From the cubes it is necessary to add a 3x3x1 prism, in which the upper face of all the cubes is painted in the same color. The player's task is to rotate the cubes so that on the upper side they all change their color. But you can only rotate the cubes three together in a horizontal or vertical row around its axis.

This problem is also solvable for any other initial arrangement of the cubes. You can also, adhering to the same rules, create a pattern on the upper plane of the prism (for example, cubes located at the corners of one color, in the center - another, etc.).

Chameleon Cube(Fig. 85)

The game requires 27 dice, painted in three colors (let's say red, yellow and blue). From these cubes it is necessary to fold a 3x3x3 cube so that all its sides are red, then from the same cubes fold a cube so that all its sides are yellow, and then blue (A).

If you arrange the cubes into groups as they are located on the scans, it will be easier to find the right ones.

It is more convenient to assemble the cube in four steps: first, the upper layer horizontally, then the lower, middle layer, and then combine them by folding the cube.

The Chameleon Cube puzzle set allows you to solve many other, less difficult problems based on matching cubes by color. Here are a few of them.

1. Fold three 2x2x2 cubes so that in one of them the four sides are blue, and the top and bottom are red; in another, the four sides are red and the top and bottom are blue; in the third, the four sides are yellow, and the top and bottom are red (B).

2. Fold a 3x3x1 prism out of 9 cubes so that the top side is red, the bottom is blue, and the four sides are yellow (B).

3. Fold a 3x3x1 prism out of nine cubes so that the color of the cubes on all sides is staggered, as shown in Figure (D).

4. From 16 cubes, fold a 4x4x1 prism so that the edges of the cubes are of the same color, and four cubes in the center of the other, as shown in the figure (E). The color of the cube on the bottom does not matter.

colorful squares (Fig. 86)

For the game, you need to make ten squares from plywood or cardboard pasted over with paper and paint them as shown in the figure. (Here and in subsequent games, the colors are indicated by a different number of dots: one dot is red, two is yellow, three is blue, four is green). From these squares, the players must add the figures shown in the figure, observing the following rule: the sides of the adjacent squares must have the same color.

This game is especially suitable for competitions in which many children can participate at the same time. Making a game is really easy. All sets are the same, but in order not to confuse the squares, it is necessary to put a certain sign (or number) on the back of each set.

colorful triangles (Fig. 87)

This game is similar to the previous one, but all the figures are not made up of squares, but of triangles. One set includes 10 triangles, which must be painted as shown in the figure.

The figures must be folded so that the sides or corners of the adjoining triangles match in color.

If there are several sets of the game, each set must be different in color or have a mark on the back of the triangles.

This game, like the previous one, is suitable for competitions with a large number participants. Each of the participants should receive a plate with the image of a figure on which triangles must be laid out.

colored hexagons (Fig. 88)

The variant of the game with colored hexagons is very interesting, but it is more difficult than the previous two. The kit includes seven hexagons, colored as shown in the picture. From them it is necessary to add the figures given here, observing the following rule: the hexagons must touch

only sides of the same color. Each participant must have plates with the image of figures on which hexagons are laid out.

OSS(Fig. 89)

The puzzle consists of three rectangular pieces of wood with slots, as shown in the picture. One detail resembles the letter O, the other two resemble the letter C, which is why the puzzle was called OSS.

It is not difficult to assemble a puzzle from three parts. How to do this is shown in the figure.

airplane(Fig. 90)

You can assemble an airplane in this three-piece puzzle.

Cube of five parts (Fig. 91)

What parts should be cut into a wooden cube, shown in the figure. It is impossible to do this from one wooden cube; each part must be cut out separately. Despite the presence of only five parts (of which four are the same), not everyone succeeds in folding the cube.

The same puzzle can be made planar (figure on the right), it is easier to solve.

Puzzle of six bars (Fig. 92)

The puzzle consists of six blocks square section with cutouts. The assembly order is shown in the figure.

Puzzle of Admiral Makarov (Fig. 93)

In the office of the famous Russian admiral Stepan Osipovich Makarov there was a small collapsible puzzle that he had brought from China. S.O. Makarov often suggested that many people take apart and reassemble this intricate toy. Especially often he asked those who boasted of their omniscience or position to take care of it, slyly hinting that for a guest with his abilities, knowledge and character, this would hardly be a big difficulty. However, not everyone was able to collect it.

The puzzle, like the previous one, also consists of six identical square bars, but the cutouts in the bars are different.

How to assemble the puzzle is shown in the drawing. Learn to do this without looking at the drawing (puzzle lovers even manage to assemble it with their eyes closed).

Puzzles by Sergey Ovchinnikov (fig. 94, 95)

When one day a competition for the best home game library for a schoolboy was announced on television, Sergei Ovchinnikov, an 8th grade student from one of the Moscow schools, brought to the competition a box with several puzzles that he invented himself. One of the puzzles exactly resembled the well-known puzzle of Admiral Makarov. When it was dismantled, it turned out that the details are completely different and it is assembled differently. Sergey was offered to create the same puzzle from seven bars. He completed this task. Then he brought a puzzle of eight pieces. In the future, he created a number of voluminous wooden puzzles.

Here we place drawings of two puzzles, invented by Sergey Ovchinnikov, from seven and eight bars of square section.

Pentomino(Fig. 96)

This game has gained popularity in recent years and has been published frequently in magazines.

For the game you need 12 pieces (elements). Each of them can close five cells of the chessboard (hence the name of the game: in Greek "tape" - five). It is most convenient to cut out parts of the pentomino from a rectangular piece of plywood according to the drawing shown in the figure. In this case, you will have to cut only in straight lines, without making turns (with the exception of one detail resembling the letter P, in which you will have to additionally cut out a square marked with a cross). All items are double sided.

Elements can be composed of many different geometric shapes, silhouette images of animals, etc. These tasks are exciting, but not easy. Nevertheless, many people (and even younger guys) can be interested in this game if you use the hint method. It is necessary to place some of the elements on the figures proposed for assembly, then the players will have to select only the missing parts. The degree of difficulty will depend on the number of pre-placed elements (three, four, five or more).

Among the tasks of pentomino there are tasks for compiling congruent (that is, coinciding, combined when superimposed) elements. They are more accessible to children, as the figures are made up of four different elements. You can make the game easier if you paint every four elements in a different color or add “congruent pairs”, in which each element consists of two figures.

Hexatrion(Fig. 97)

The game consists of 12 elements, each of which can be divided into 6 triangles ("six" in Greek "hexa", hence the name of the game). These 12 elements make up various shapes.

You can cut out game elements from a piece of plywood according to the drawing shown in the figure. You will only have to cut in a straight line (no turns), the arrows show which cuts should be made first. On separate cards made of thick paper, it is necessary to draw the contours of the figures that the players must fold.

As in the previous game, you can make the task easier by “hinting” - place two or three or more elements on the figures so that the guys can pick up only the missing ones.

amazing square (Fig. 98)

This puzzle is one of the classics. She was born in China, as scientists suggest, more than three thousand years ago and is still popular in many countries of the world.

Of the seven elements into which the square is cut, one can make many characteristic images of people in different poses, animals, various items, geometric shapes.

For younger students, for folding figures, it is better to offer not a contour drawing made on one scale or another, but plywood in which the contour of the figure is cut out. Within this contour, no error can be made when laying, and this facilitates the solution of the problem and the possibility of verification.

From parts of a hexagon (Fig. 99)

In this puzzle, the starting figure is a hexagon. From the drawing it is clear how to divide it into seven parts, from which many different figures can then be added. Responses are shown with dotted lines. The players receive sets of puzzle parts and on the cards the contours of the figures that need to be folded.

From five parts(Fig. 100)

Of the five parts into which the square is divided, you can add the figures shown in the figure.

Of ten parts (Fig. 101)

There are five different parts in the puzzle, each in duplicate. From all ten parts, try to fold a large square, and from one set (five different parts) - a smaller square. From the same details, but without a small square, another smaller square is obtained.

From the 10 pieces of this puzzle, you can build many different characteristic silhouette images, which are shown in the figure.

As in the previous puzzles, those who play along with the puzzle pieces receive cards with contour images of the figures.

Split letters and numbers (Fig. 102)

It would seem that it can be difficult in such a task: from the letter T, cut into four parts, again add this letter. Try it - and you will see that this task is not so simple at all. The letter M will cause no less trouble for the players. We give here samples of 10 folding letters (A, B, I, M, N, P, R, C, T, U) and two numbers (4 and 7). Each folding letter and number is its own puzzle.

To store the details of folding letters, make special frames according to the same pattern as for the letters T and M (see figure).

You can invite the players to compose a whole word from two or three split letters (for example, “mind”, “world”, etc.), but in this case, each letter should have its own color.

Collect the ring(Fig. 103)

The ring is sawn into a square piece of plywood and cut into several pieces. The task of the player is to assemble the ring and put all the parts in their place.

From the same parts (Fig. 104)

How to cut puzzle pieces from a rectangle is shown in the drawing. From the same parts, you can add a square and a triangle, but this is not very easy.

In the second puzzle of five triangles, you need to add a regular hexagon, and then a rectangle and a rhombus.

Souvenir puzzle (Fig. 105)

At one of the foreign exhibitions in Moscow, visitors were offered a puzzle souvenir. The joking inscription read: “It is easier to raise money to buy a car than to put together a square of these seven parts.” Indeed, the task is not easy, but maybe someone will try to cope with it.

Put down the records(Fig. 106)

The square plate inside the frame is sawn into several parts. 8 squares are glued on the bottom in different places. The player's task is to put all the pieces of the puzzle in their places, bypassing the squares.

To keep the line from breaking (Fig. 107)

The plate lying inside the frame is cut into pieces. They must be taken out and put back in place so that the line drawn on all parts of the plate is not interrupted anywhere.

folding pictures (Fig. 108)

In the frame on the left - the fish is sawn into several parts of different shapes. Pull the details out of the frame, and then lay them again, restoring the picture. Based on this sample, you can create a whole series split pictures using ready-made reproductions, illustrations from books and magazines. If you mix parts of two pictures, the game will become more difficult.

The figure on the right shows how to cut a duck. You can then put in the frame only part of the details of the picture so that the contour of the bird forms on the bottom.

Decide right(Fig. 109)

This game is very convenient to make from empty matchboxes (or from wooden dice of the same size). On five boxes, the word “decide” is written on the top, and “correct” is written on the bottom. In the second row, three boxes are glued on top, two passages are left between them.

The player's task is to swap the boxes, using only the aisles, so that the word "correct" can be read at the top, and the word "solve" - at the bottom.

Tower of Hanoi Puzzle (Fig. 110)

For this game, you need a small board with three round sticks inserted into it. A "turret" consisting of 8 circles is put on one stick - the largest one is at the bottom, and each next one is smaller than the previous one. Circles are painted in different colors.

The player's task is to shift all the circles from one stick to another, using the third one as an auxiliary one. In this case, the following rules must be observed: you can shift only one circle at a time, you cannot put a larger circle on a smaller one. We must try to reach the goal faster, avoiding unnecessary rearrangement of circles. You should start with a small number of circles (4-5) and then gradually add one at a time.

Non-repeating figures (Fig. 111)

4 different shapes are drawn on 16 squares (circle, triangle, square and rhombus). Fold a 4x4 square out of them so that figures of the same shape and the same color do not meet either horizontally or vertically.

Vertically and horizontally (Fig. 112)

For the game, prepare nine squares and draw nine cells in each of them. Some cells need to be painted in three colors, as shown in the figure.

The player's task is to fold a large 3X3 square out of the squares so that cells of the same color do not repeat either vertically or horizontally.

broken chain (Fig. 113)

The square consists of 14 identical rectangles cut out of plywood or cardboard. One part of the chain is drawn on each rectangle. It is necessary to shift the rectangles so that one closed chain is obtained that does not have breaks. The answer is shown in the picture.

Tricky permutations (Fig. 114)

There are nine plates in a wooden frame. The task is to transfer plate 1 to the upper left corner by successive movements. The plates are not allowed to be taken out.

Solution. Lift plate 5 up, 1 - to the left, 2 - down, 3 - to the right, 5 - to the right and up, 1 - up, 9 - to the right, 8 - down, 7 and 6 together - down, 4 and 5 together - to the left (under plate 4), 1 - to the left, 3 - to the left, 2 - up, 8 and 9 - to the right, 6 and 7 - to the right, 4 and 5 - down, 1 - to the left.

Puzzle Game Library (Fig. 115)

Before the start of the game, checkers with letters are placed in disorder on eight circles arranged in a semicircle. The two circles below remain free.

Using free circles (1 and 2), you need to move the checkers and place them so that the letters, when read from left to right, form the word “game library”. You can move the checkers in any direction, but only to the adjacent free circle. It is impossible to pass through a busy circle to a free one.

The solution to this puzzle can be more or less difficult depending on the initial arrangement of the letters.

Swap(Fig. 116)

Here are the drawings of three puzzles. In each of them, there are chips of two colors on the circles. The circles are connected to each other by lines. The task of the player is to swap the chips. You can move them only along the lines connecting the circles, using the circles free from chips.

Try to solve problems with the least number of moves.

Chess board(Fig. 117)

A chessboard cut into pieces, which must be folded correctly, is one of the well-known and popular puzzles. The complexity of the assembly depends on how many parts the board is divided into. The figure shows several variants of this puzzle. The board is divided into five, seven and eight parts, and in the latter case, letters are written on the cells of the board, by which you can read the saying. This will make the task easier, especially if the saying is familiar to the player.

Of great interest is also a chessboard, divided into 9 parts so that each of them forms a letter. You can assemble a board from these letters in different ways, but it is necessary that the color of the cells alternate correctly.

The figure shows another, more complex version of the chessboard. It is cut in such a way that in some cases the cells are also divided.

Striped triangles (Fig. 118)

As in chessboard, in this large triangle, all small triangles are colored in two colors.

From the 12 parts shown in the figure, it is necessary to fold the triangle so that small light and dark triangles alternate in it.

Will you get 5?(Fig. 119)

Of the eight geometric figures laid in a square, it is necessary to make the number 5. The contours of this figure must be given.

The answer is shown in the picture.

maneuvers(Fig. 120)

Many have probably observed how often the machinists have to maneuver with the locomotive and wagons, sorting them into tracks to make up trains. This requires not only experience, but also ingenuity.

Try and you solve an interesting problem of moving wagons. To do this, you need to make two cars, a steam locomotive and a railway track with a branch and a bridge.

The device and dimensions of all parts of the game are shown in the drawing. The railway track is made of three layers of plywood: the bottom layer is solid, two narrow strips are glued on it along the edges and two wider strips on top. Thus, a groove is formed along the entire path, having the form of an inverted letter T (see the section of the path in the drawing).

Cars and a steam locomotive are cut out of wooden bars. One car is painted, say, red, the other - blue. The locomotive can be painted black. A bridge is installed on a branch of the tin track. To the right and left of it are two conventional sign- Red and blue.

Both wagons and the locomotive have a metal leg (a screw with a wide head) at the bottom. It is made in such a form that the wagons and the locomotive move freely along the entire path along the groove, but cannot be removed.

By the beginning of the game, the wagons must be placed to the right and left of the bridge: red is against the blue sign, and blue is against the red.

The task conditions are as follows.

The driver was given the task to swap the cars standing on a branch of the railway track. Car A (red) must be put in place of car B (blue), and car B in place A.

The side track passes through the bridge, which is being repaired, and therefore the weight of the wagon is supported by the bridge, but the weight of the steam locomotive is not. After rearranging the wagon, the locomotive must remain on the main track.

How did the driver get out of the predicament?

The player is invited to perform maneuvers, bearing in mind that the wagons can be attached to the locomotive in front and behind, depending on the need, but can only move with its help.

Maneuvers on the triangle (Fig. 121)

Imagine a railroad track laid out in a curved triangle, as shown in the figure. Such a triangle is very common at railway stations near the locomotive depot. It is used to turn the locomotive 180 degrees. If, for example, a steam locomotive went in any direction with a tender forward, then such a triangle allows it to turn around and go in the same direction, but already with a tender back. This becomes possible if you first lead the locomotive to a dead end located at the top of the triangle.

Another problem with the same triangle is much more difficult.

In the figure, there is a black car on the curved line on the left, and a white car on the curve on the right. There is a locomotive on a straight line. With the help of a steam locomotive, you need to rearrange the cars: black - in place of white, and white - in place of black. The difficulty lies in the fact that in the dead end, located at the top of the triangle, only one wagon (either white or black) fits along the length, while the locomotive cannot fit in it.

To play, you will need two small wagons, a locomotive and a platform with a section of the railway track. The railway track is made of three layers of plywood: the bottom one is solid, two narrow strips are glued along the edges and two wider strips are glued on top. Thus, a groove is formed along the entire path, the section of which has the form of an inverted letter T.

Cars and a steam locomotive are cut out of wooden blocks. The locomotive can be painted black, and the wagons can be painted in two other colors.

Both wagons and the steam locomotive at the bottom have a metal leg in such a shape that the wagons and the locomotive can move freely along the entire track along the groove, but they could not be removed.

The solution of the problem is shown in the figure.

On the railway line (Fig. 122)

Two trains going towards each other met on a single-track track: a steam locomotive with one wagon and a steam locomotive with two wagons. The drivers had to separate these trains in different directions, using a short branch, which could fit either one locomotive or one wagon. The machinists coped with this task.

The players must also cope with it. A locomotive with one wagon must be placed to the left of the branch, and a locomotive with two wagons - to the right and, gradually moving the locomotives and wagons (using the branch), separate them in different directions. At the same time, the locomotive can move forward and backward, hitch the cars in front and behind and take them to the right and left of the branch at any distance. It is impossible to move wagons without the help of a steam locomotive.

The structure of the railway track, locomotive and wagons is the same as in the previous game.

The scheme for solving the problem is shown in the figure.

Wire puzzles (Fig. 123)

For the manufacture of puzzles, a wire of medium hardness with a thickness of 1.5-2 mm is usually used. The size of the puzzle can be arbitrary, but in order for the puzzles to be convenient to use, they should not be made too small.

Each puzzle, before proceeding with its manufacture, must first be drawn in full size.

At the same time, make sure that the dimensions of the various pieces of the puzzle exactly match their purpose. When the drawing is completed, measure the length of the wire necessary for the manufacture of each part separately with a cord, and make blanks (cut pieces of wire of appropriate sizes).

Manually bending the wire along all contours in strict accordance with the pattern is quite difficult. We advise you to use a special device - metal plates, on which vertical pins and guide bars holding the ends of the wire are fixed for each part separately (at the wire bends). You can make the plates wooden and use short thick nails instead of pins.

In each puzzle, it is important not only to find a way to separate one figure from another, but also to be able to connect them later. To do this, the player needs to have the image of the puzzle assembled.

Two boots (A)

The boots will come apart easily if the toe of the smaller boot is passed through ring A and circled around ring B.

Three letters (B)

In this puzzle, three letters are connected to each other: A, E and T. You need to remove the letter E. To do this, the upper end of the letter E must be brought to ring B, passed through this ring and circled around bracket C.

Boom brace (B)
To remove the bracket C from the arrow A, you need to slightly raise the arrow, thread the bracket into the circle B, circle the arrow with it and remove the bracket from the ring in the opposite direction.

Two letters (G)

The letters P and C, made of wire, are interconnected. Raise the letter C to the top of the letter P and bring its end to the loop B, then, bending the wire slightly, insert it from the outside into the ring A, circle the figure B with it, and the letters will be disconnected.

Chained Elephant (D)

To free the elephant, you need to pass one of its legs (for example, A) through the ring of the arc B and circle the ring C with it.

Magic chain (E)

The "magic chain" is more of a trick than a puzzle, but the trick is spectacular, always causing the audience to be bewildered and want to unravel the "mystery" of the chain.

The chain usually consists of 24 metal rings of the same diameter. All rings are interconnected in a certain sequence, which is shown in the figure.

The first three rings form, as it were, the first tier. Two other rings are threaded into the upper ring, which in the figure are turned to the viewer with an edge.

These rings, in turn, are threaded: in the left - one ring, and in the right - the same ring as in the left, and one more. Thus, one ring hangs on the left, and two rings hang simultaneously on the right. One ring is threaded into the back ring, and one ring wraps around the front and back at the same time. Further, in each tier, consisting of two rings, the sequence of clutches is repeated. The last ring, connecting the two rings of the last tier, closes the chain.

It is necessary to connect the rings, exactly adhering to the pattern. It is very convenient to use key rings to make a “magic chain”. They are easily connected to each other and do not form gaps. If the rings are homemade, then it is better to solder the joints.

When the chain is ready, take the upper ring A with your left hand, and ring B with your right hand, then, without releasing ring B, separate the fingers of your left hand. The top ring will fall and "run" down the chain. Next, from the right hand, transfer the ring that turned out to be upper to the left hand, and take the new ring B with your right hand. Release the ring in your left hand, and it will again “run” to the end of the chain.

If your rings will not run away, it means that you made a mistake and took the wrong ring with your right hand. To restore the original arrangement of the rings, the easiest way is to rotate the chain about its axis by 180 degrees and start demonstrating the trick from the other end.

In order to check whether you took the ring with your right hand, there is this way: holding the upper ring with your left hand, slightly lift the ring taken with your right hand. If at the same time only part of the chain rises, then you took it correctly, and if the whole chain, then it is wrong.

Spectators are always struck by the unusualness of this phenomenon. They cannot understand why the rings "run" down one after the other. After all, the chain consists of identical rings that cannot pass through each other, and the chain does not lengthen or shorten when the rings fall.

This is explained very simply. The sliding of the ring along the chain is only apparent, in fact, the upper ring, turning over, releases the lower ring, which, in turn, releases the next lower one, and so on.

Bound Staples (W)

Two brackets with crossbeams are interconnected by a wire figure in the form of a triangle with a loop. We need to free the triangle. To do this, first remove the triangle from one bracket, as shown in the figure, and then in the same way from the other.

Bracket with two hangers (Z)

In this case, you need to remove the ring. This is hindered by two brackets hanging at the ends of a curved rod. However, there is a trick that makes the task easy to do.

Move the bracket along the rod so that one of its ends goes around the bend of the rod, as shown in the figure. After that, the ring will freely pass through the bend of the rod and the bracket at the same time and can be easily removed from the rod.

Double staples (I)

In this puzzle, the hook in the form of a triangle with a loop is put on double staples. It is necessary to remove it from both the small and large brackets. This is more difficult to do than in the previous case.

First, remove the triangle from the small bracket. To do this, holding the large bracket and the crossbar, thread the loop of the triangle into the eye of the small bracket, as shown in the figure, then put it on the ring of the crossbar and on the eye of the large bracket. The loop will be on the crossbar. Then it is passed through the loop of the large bracket and the ring of the crossbar is circled around it. The triangle will be released from the small bracket and remain on the large one. You can remove it from this bracket in the same way that was used in the previous puzzles.

Snail (K)

To remove the shuttle from the cochlea, draw it along the entire outer contour of the figure to the ring, thread it into the ring from the inside and circle the entire spiral with the shuttle. After that, the shuttle is pulled back, and it turns out to be free.

Shackle with coil (L)

In this puzzle, the removal of the shuttle is complicated by the fact that it is inserted not only into the bracket, but at the same time inside the curl. First free it from the curl. To do this, turn the shuttle accordingly, thread it into the eye of the bracket, circling the ring, and pull it back out. The shuttle will be free from curl. To remove the shuttle from the bracket and release it completely, the same manipulation must be done again.

Zigzag (M)

This puzzle is solved in the same way as the previous one. Having a few bends doesn't make a difference.

Lace puzzles (Fig. 124)

Lace puzzles are a kind of wire puzzles. There is a lot in common in their design and solving techniques, but they are not made of wire, but of plywood, wood or plastic and are interconnected with the help of laces (hence the name “lace-up puzzles” came from).

With the help of a cord, such connections of parts and parts can be made that are impossible in wire puzzles. Therefore, cord puzzles can serve as a good and interesting addition to wire puzzles.

In cord puzzles, as in wire puzzles, the task of the players is to separate the figures or parts connected to each other, and then return them to their place, using, as a hint, a card with a picture of the puzzle. It is not allowed to untie knots.

Making string puzzles is a simple matter. However, in order to make each puzzle beautiful, attractive (and this is important), sometimes you have to spend a lot of work.

If plywood is used to make puzzles, you can use burning and coloring (with aniline or other paints), varnishing for decoration. Plexiglas is an excellent material for puzzles.

For many puzzles, in addition to various figures, you will need balls, rings, circles. They can be replaced with beautiful buttons of various shapes, rings for hanging curtains.

Puzzle sizes can be arbitrary. Therefore, before proceeding with their manufacture, it is necessary to establish the most convenient and desirable size, accordingly enlarge the drawings and prepare templates for each part separately.

The quality of the cord is of great importance in the puzzle, because all actions are mainly performed with it. It should not be woven, as it will quickly get confused and complicate the solution of the problem. Do not use too thin cord. To connect the parts, you can use a soutache (it comes in different colors, and this is very convenient), shoelaces are also suitable for this purpose. The length of the cord should be such that all manipulations are feasible.

Sometimes guys, without understanding the puzzle, will confuse the cord so much that it is very difficult to put it in order. In such cases, it is easier to untie the knots or cut the cord at the joints and re-tie (or sew) it after the puzzle is restored. It is also necessary to have spare laces to replace those that have become unusable.

When solving all string puzzles, there is one obligatory rule: leading a loop along the cord through the holes in the figures and rings and passing any details through it, you can never turn it over. Even with the right decision, an inverted loop can ruin the whole thing.

Rocket on the moon (A)

To separate the rocket, it is necessary to pass the loop P through the hole A, pass the button through the loop and pull it back.

Ring and anchor (B)

To remove the anchor, pull out loop P and thread it into hole B (from the bottom of the cord). Having missed the button in the loop, pull the loop back. Then a loop is threaded through hole B, a button is passed through it and pulled back.

Two cars (B)

The task is to disengage the wagons. A good “coupler” will immediately guess that the loop must be passed through the left window (on the right car, and if on the left, then into the right window), pass both the hitch and the second car through the loop at once, pull the loop back.

Clock with a pendulum (G)

To remove the pendulum from the clock, you need to stretch the loop as far as possible, thread it (along the cord) into hole 10 and then sequentially into holes 9, 8, 7, 6, 5, 4, 3, 2, 1, pass a button through the loop and pull it out loop back through all holes.

Skydiving (D)

Pull the loop as far as possible, thread it through the center hole, pass it through the parachutist's loop, pull the loop back - now the parachutist can be removed freely.

Two bears (E)

The task is to separate bears 1 and 2.

To do this, pull the P-2 loop attached to the second bear along the cord to hole A, thread the loop into hole A and pass ring B through it. Pull the loop back, thread the loop into hole C, pass ring D into it and pull back to failure. Loop P-2 will be free.

Now you need to pull the P-1 loop along the cord to the third bear, let the entire second bear into it and pull the loop back.

Lock with two keys (W)

The lock can be easily released from the keys if loop P is passed through the eyelet of the first key (along the cord), pass key B into the loop and pull the loop back.

Take off the ring (O)

The loop is pulled along the cord and passed through the window (right), then the ball is threaded into the loop and pulled back. The same must be done in the left window. The ring will be free.

Two owls (I)

To separate the owls, it is necessary to skip the loop of the right owl into the hole covered with the eye (button) of another owl. Then skip the eye (button) through the loop and pull it back.

Dog team (K)

The sled can be easily released from the harness if the loop is pulled out, threaded through hole 1, the dog is passed through the loop, pulled back and removed from all holes.

Girl with a jump rope (L)

It is very easy to separate tangled ropes. To do this, you need to thread the loop P into the loop formed by knot A, skip the handle of the rope into the loop and pull it back.

Dog and kennel (M)

To free the dog, you need to pass the loop formed by the "chain" through the ring of the collar and the ring, pass the ball through it and pull the loop back.

The date: 2013-11-07 Editor: Zagumenny Vladislav

The world is arranged in such a way that things in it can live longer than people, have different names at different times and in different countries, we can even play Simpsons games. The toy you see in the picture is known in our country as "Admiral Makarov's puzzle". In other countries, it has other names, of which the most common are "devil's cross" and "devil's knot."

This knot is connected from 6 bars of square section. There are grooves in the bars, thanks to which it is possible to cross the bars in the center of the knot. One of the bars does not have grooves, it is laid into the assembly last, and when disassembled, it is removed first.

The author of this puzzle is unknown. It appeared many centuries ago in China. In the Leningrad Museum of Anthropology and Ethnography. Peter the Great, known as the "Kunstkammer", there is an old sandalwood box from India, in 8 corners of which the intersections of the frame bars form 8 puzzles. In the Middle Ages, sailors and merchants, warriors and diplomats amused themselves with such puzzles and at the same time carried them around the world. Admiral Makarov, who twice visited China before his last trip and death in Port Arthur, brought the toy to St. Petersburg, where it became fashionable in secular salons. The puzzle also penetrated into the depths of Russia by other roads. It is known that a soldier who returned from the Russian-Turkish war brought a devil's bundle to the village of Olsufyevo in the Bryansk region.

Now the puzzle can be bought in the store, but it is more pleasant to make it yourself. The most suitable size of bars for a homemade design: 6x2x2 cm.

Variety of damn knots

Before the beginning of our century, for several hundred years of the existence of toys in China, Mongolia and India, more than a hundred variants of the puzzle were invented, differing from each other in the configuration of the cutouts in the bars. But the most popular are two options. The one shown in Figure 1 is quite easy to solve, just make it. It is this design that is used in the ancient Indian box. From the bars of Figure 2, a puzzle is formed, which is called the "Devil's Knot". As you might guess, it got its name for the difficulty of solving.

Rice. one The simplest option devil's knot puzzle

In Europe, where, since the end of the last century, the "Devil's Knot" has become widely known, enthusiasts began to invent and make sets of bars with different cutout configurations. One of the most successful sets allows you to get 159 puzzles and consists of 20 bars of 18 types. Although all the nodes are outwardly indistinguishable, they are arranged completely differently inside.

Rice. 2 "Puzzle of Admiral Makarov"

The Bulgarian artist, Professor Petr Chukhovski, the author of many bizarre and beautiful wooden knots from a different number of bars, also worked on the Devil's Knot puzzle. He developed a set of bar configurations and explored all possible combinations of 6 bars for one simple subset of them.

The most persistent of all in such searches was the Dutch mathematics professor Van de Boer, who made a set of several hundred bars with his own hands and compiled tables showing how to assemble 2906 knot options.

It was in the 60s, and in 1978 the American mathematician Bill Cutler wrote a program for a computer and determined by brute force that there are 119,979 variants of a puzzle of 6 elements that differ from each other in combinations of protrusions and depressions in the bars, as well as the placement bars, provided that there are no voids inside the knot.

Surprisingly large number for such a small toy! Therefore, to solve the problem, a computer was needed.

How a computer solves puzzles?

We will proceed from the fact that we have a set of 369 bars that differ from each other in the configuration of the protrusions (this set was first identified by Van de Boer). Descriptions of these bars must be entered into the computer. The minimum notch (or protrusion) in a block is a cube with an edge equal to 0.5 of the block's thickness. Let's call it a unit cube. The whole bar contains 24 such cubes (Figure 1). In the computer, for each bar, a "small" array of 6x2x2=24 numbers is entered. A bar with cutouts is given by a sequence of 0 and 1 in a "small" array: 0 corresponds to the cut out cube, 1 - to the whole. Each of the "small" arrays has its own number (from 1 to 369). Any of them can also be assigned a number from 1 to 6, corresponding to the position of the bar inside the puzzle.

Let's move on to the puzzle now. Imagine that it fits inside an 8x8x8 cube. In a computer, this cube corresponds to a "large" array consisting of 8x8x8=512 cells-numbers. To place a certain bar inside a cube means to fill the corresponding cells of the "large" array with numbers equal to the number of the given bar.

Comparing 6 "small" arrays and the main one, the computer (i.e., the program) adds together 6 bars, as it were. Based on the results of adding numbers, it determines how many and which "empty", "filled" and "overflowing" cells formed in the main array. "Empty" cells correspond to an empty space inside the puzzle, "filled" cells correspond to protrusions in the bars, and "overflowed" cells correspond to an attempt to connect two single cubes together, which, of course, is prohibited. Such a comparison is made many times, not only with different bars, but also taking into account their turns, the places they occupy in the "cross", etc.

As a result, those options are selected in which there are no empty and overflowing cells. To solve this problem, a "large" array of 6x6x6 cells would suffice. It turns out, however, that there are combinations of bars that completely fill the internal volume of the puzzle, but it is impossible to disassemble them. Therefore, the program must be able to check the node for the possibility of disassembly. To do this, Cutler took an 8x8x8 array, although its dimensions may not be sufficient to check all cases.

It is filled with information about a particular variant of the puzzle. Inside the array, the program tries to "move" the bars, i.e., it moves parts of the bar with a size of 2x2x6 cells in the "large" array. The movement is 1 cell in each of the 6 directions parallel to the axes of the puzzle. The results of those of the 6 attempts, in which no "overflowed" cells are formed, are stored as starting positions for the next six attempts. As a result, a tree of all possible movements is built until some bar completely leaves the main array, or after all attempts, "overflowing" cells remain, which corresponds to a variant that cannot be parsed.

This is how 119,979 variants of the "Devil's Knot" were obtained on a computer, including not 108, as the ancients believed, but 6402 variants, having 1 whole bar without cutouts.

Supernode

Note that Cutler refused to study the general problem - when the node also contains internal voids. In this case, the number of nodes of 6 bars increases greatly and the exhaustive search required to find feasible solutions becomes unrealistic even for modern computer. But as we will see now, the most interesting and difficult puzzles are contained precisely in the general case - then disassembling the puzzle can be made far from trivial.

The more manipulations you need to do during disassembly, the more interesting and difficult the variant of the puzzle. The grooves in the bars are arranged so cunningly that the search for a solution is like wandering through a dark labyrinth, in which you constantly come across either walls or dead ends. This type of knot certainly deserves a new name; we'll call it a "supernode". A measure of the complexity of a superknot is the number of movements of individual bars that must be done before the first element is separated from the puzzle.

We don't know who invented the first supernode. The most famous (and most difficult to solve) are two superknots: "Bill's thorn" of complexity 5, invented by W. Cutler, and the "Dubois superknot" of complexity 7. Until now, it was believed that complexity 7 could hardly be surpassed. However, the first of the authors of this article managed to improve the "Dubois knot" and increase the complexity to 9, and then, using some new ideas, get superknots with complexity 10, 11 and 12. But the number 13 remains insurmountable so far. Maybe the number 12 is the biggest supernode complexity?

Supernode solution

Drawing drawings of such difficult puzzles as superknots and not revealing their secrets would be too cruel to even connoisseurs of puzzles. We will give the solution of superknots in a compact, algebraic form.

Before disassembling, we take the puzzle and orient it so that the part numbers correspond to Figure 1. The disassembly sequence is written as a combination of numbers and letters. The numbers indicate the numbers of the bars, the letters indicate the direction of movement in accordance with the coordinate system shown in Figures 3 and 4. A bar over a letter means movement in the negative direction of the coordinate axis. One step is to move the bar 1/2 of its width. When the bar moves two steps at once, its movement is written in brackets with an exponent of 2. If several parts are moved at once that are linked to each other, then their numbers are enclosed in brackets, for example (1, 3, 6) x. The separation of the block from the puzzle is marked with a vertical arrow.

Let us now give examples of the best supernodes.

W. Cutler's puzzle ("Bill's thorn")

It consists of parts 1, 2, 3, 4, 5, 6, shown in Figure 3. An algorithm for solving it is also given there. Curiously, Scientific American (1985, No. 10) gives a different version of this puzzle and reports that "Bill's thorn" has a unique solution. The difference between the options is just in one bar: details 2 and 2 B in Figure 3.

Rice. 3 "Bill's Thorn", computer-designed.

Due to the fact that part 2 B contains fewer cutouts than part 2, it is not possible to insert it into Bill's thorn according to the algorithm shown in Figure 3. It remains to be assumed that the puzzle from "Scientific American" is assembled in some other way.

A similar mistake was made in another publication (J. Slocum, J. Botermans "Puzzles old and new", 1986), but in another bar (detail 6 C in Figure 3). What was it like for those readers who tried and, perhaps, are still trying to solve these puzzles?

Classes with a puzzle develop attention, memory, figurative and logical thinking, communication skills of children. Objective: Take the puzzle apart and then put it back together. The puzzle can become both an interesting interior detail and a wonderful gift. Our puzzles are a great leisure option for all lovers of smart and fun entertainment. Puzzles are made of natural material - wood.

Interest in mysterious objects, things and places associated with some kind of secret, was preserved by people at all times. Today we will talk about one curious toy that can still be found in the old Pomor settlements on the shores of the White Sea. During the long polar night, in their free time from hunting and fishing, men's favorite pastime was carving household, household and church utensils, children's toys and puzzles from wood.

The puzzle in question is in the form of a small box in the shape of a cube. In ancient times, some valuable thing was hidden inside the cube, and in later times, peas or pebbles were simply poured into the box, a handle was attached, and the cache turned into a rattle toy. Such a rattle, made two hundred years ago, can be seen in the Zagorsk Toy Museum. For the uninitiated, the box looks non-separable and attempts to get to its contents lead to nothing. All six planks that make up the cube fit snugly together and do not disassemble. Although there is a void inside the cube, it is completely incomprehensible how something can be put there. The secret is small, but it is not easy to think of it. We will first talk about how to make our own cache cube.

The blanks for the puzzle are six bars measuring 65x40x6 mm. Their production must be taken seriously. Every detail must be done very carefully and precisely. Be sure to pick up a tree that is dry, otherwise after a while the pieces of the puzzle will begin to hang out and the secret of the cube can be easily unraveled. After making each element, it is cleaned with sandpaper so that all surfaces are smooth. Bar 3 is done last. Before cutting a groove in it, you need to put the five bars made together as shown in the figure. Then you should measure the grooves between the elements 1 and 2, which should include the bar 3. Depending on the resulting dimensions of these grooves, you should change the dimensions of the bar 3, fit it in place. It is important that bar 3 enters the groove with little effort, and at the end of the stroke snaps into element 2.

It doesn’t matter if you don’t have the boards of the indicated sizes. You can make a cube from any planks. Just keep in mind that the size of the cache and the entire cube depend on their width. Let the width of the bar be 6 mm. Then the length of the groove a in the blanks is calculated by the formula a = b + 3 mm. Other dimensions can be left as shown.

Now about how to disassemble the cube. The secret is in element 3, which acts as a latch. To open the cache, you need to click on this element up, and then move it inside the cube.

Materials and tools:
Square rail

This puzzle was designed by the famous Admiral Makarov, the leader of two round-the-world voyages.

Prepare six identical bars from the rail. On one of them it is unnecessary to make any cutouts (I). On the other, it is necessary to cut a groove with a width the thickness of a bar and a depth of half this thickness (II). On the third block, two grooves are made: one is the same as on the previous block, and next to it, retreating half the thickness of the block, the other is the same deep, but twice as narrow (III).

The remaining three blocks will be the same; two cuts are made on each of them: one is two thicknesses of the bar wide and half the thickness deep; the other, on the adjacent surface (for which the bar is rotated 90 °), is the width of the bar and a depth of half the thickness ( IV, V, VI).

Now assemble the puzzle. Take two bars of type IV, V, VI, fold them as shown in the pictures. Insert a type III bar into the resulting “window”. Holding all three bars so that they do not “disperse”, insert the remaining bar of type IV, V, VI from above so that it enters with its thin part into the gap b. Next to this bar, a type II bar should be placed; turn it upside down and insert

side open "window" a. Consider the figure formed by five bars. Between those two bars that you put together at the very beginning, a square “window” has been preserved c. If the remaining bar-juice (solid, without cutouts) is introduced into this “window”, then the whole structure will be firmly connected.

Materials and tools:
rail with a square cross section (e.g. 1 cm2)

Cut three bars 8-9 cm long from the rail. In the middle of one of them, make a cutout so that a jumper with a square cross section is formed. The thickness of the jumper should be equal to half the thickness of the bar (0.5 cm2). Process the second block in the same way, but cut off the corners at the jumper and then turn (using a file) its section from square to round.

In the third block, cut a transverse groove with a width and depth of 0.5 cm, then, turning the block 90 °, make a second groove of the same size on the adjacent surface (c).

The puzzle is ready. Collect it.

Holding the block with two slots vertically, insert the block with the round bar into the groove, then insert the block with the square bar 90° counterclockwise into the second groove, and the puzzle takes the form of a solid, non-crushing figure.

Materials and tools:
wooden plank

From a wooden plank, the width of which is three times the thickness (for example, thickness 8 mm, width 24 mm), saw off three identical pieces 8-9 cm long. according to the dimensions of the cross section of the bar you have taken.

It is necessary that the bar just enters the recess-window, with some, maybe even effort. Therefore, it is better if the window is at first somewhat smaller than necessary, and then with the help of a file you bring it to the required size.

You leave one of the three parts you made unchanged, and in the other two you make a cut on the side, the width of which is exactly equal to the thickness of the bar (or, which is the same, the width of the window). Thus, these two parts have a T-shaped cut.

The puzzle is ready. Now you can collect it. Insert one of the T-cut strips into the window of the part you made first, advance it so that the end of the side cutout is “flush” with the surface of the strip. Now take the third piece (also with a T-neck) and slide it over the window bar on top, with the side cutout facing back. Lower it all the way down, then push back (also all the way) the first T-bar, and the puzzle will take the form shown in the figure placed in front of the problem.

Puzzle "Pig"

All photos from the article

Puzzles, as you know, develop intelligence, thinking and attentiveness well, so they are recommended for children to solve. True, some of them are not easy to handle even for adults, who are also not averse to “twisting” funny details in their hands. In this article, we will look at how to make some DIY wooden puzzles that will be fun for both children and adults to play with.

General information

First of all, it should be said that making wooden puzzles with your own hands is no less exciting than solving. Moreover, there is nothing complicated in their manufacture, so everyone can cope with this task.

The only thing you need for this is a simple set of tools that every home master has:

Jigsaw (preferably electric jigsaw);
Chisels;
Electric drill ;
Files and files;
Sandpaper.

Advice!
To simplify the task and avoid mistakes in the manufacturing process of products, you first need to complete the drawings of wooden puzzles with your own hands.

As for the materials, the most often required are:

small boards;
Bars;
Plywood sheets;
Lacquer on wood.

Even if these materials were not at hand, they can be purchased at a hardware store. Their prices are usually low.

Manufacturing

There are a lot of options for wooden puzzles for children and adults. Next, we will consider the most popular and common ones, which are easy to do on your own.

To make this puzzle, you will need a rail, the width of which is three times the thickness, for example, if its thickness is 8 mm, then the width should be 24 mm.

The product is made as follows:

A rail of suitable parameters must be cut into three parts of the same length.
Next, in each plank, you need to cut a cutout corresponding to its cross section with a jigsaw. As a result, the strips should enter this hole with little effort. Therefore, it is better that the window be a little smaller, in which case it can be brought to the desired parameters using needle files.
In two planks on the side, you need to make a cut, the width of which should exactly equal their thickness. As a result, a T-shaped cut should be obtained in two parts.
At the end of the work, the parts must be sanded and varnished.

This completes the puzzle making process.

Now you need to assemble it by doing the following:

One of the parts with a T-shaped cutout must be inserted into the window, and it must be advanced so that the end of the side cutout is “flush” with the surface of the bar.
Next, you should take the third part and put it on top of the bar with a window until it stops.
After that, it is necessary to upset the first bar with a T-shaped cut to the stop.

As a result, the puzzle takes the form of a solid product.

crossroads

To complete this craft, you will need a 1 cm square bar.

The instruction for its manufacture is as follows:

From the rail you need to cut off three bars about 8-9 centimeters long.
In the middle of one of them, it is necessary to make a cutout 1 cm wide so that as a result a square jumper with sides of 0.5 cm is formed.
The second part should be done in exactly the same way, only the jumper should turn out not square, but round.
In the third bar, you need to cut a groove with a depth and width of 0.5 cm.
Then the same bar must be rotated 90 degrees, and another similar groove should be made on the adjacent surface.
Further, all parts should also be sanded and varnished.

The world is arranged in such a way that things in it can live longer than people, have different names at different times and in different countries. The toy that you see in the picture is known in our country as the “Admiral Makarov Puzzle”. In other countries, it has other names, of which the most common are "devil's cross" and "devil's knot."

You can buy one of these puzzles, for example, on my-shop.ru

And also here are various variations on the theme of one, two, three, four, five, six, seven, eight.

The author of this puzzle is unknown. It appeared many centuries ago in China. In the Leningrad Museum of Anthropology and Ethnography. Peter the Great, known as the "Kunstkamera", an old sandalwood box from India is kept, in 8 corners of which the intersections of the frame bars form 8 puzzles. In the Middle Ages, sailors and merchants, warriors and diplomats amused themselves with such puzzles and at the same time carried them around the world. Admiral Makarov, who twice visited China before his last trip and death in Port Arthur, brought the toy to St. Petersburg, where it became fashionable in secular salons. The puzzle also penetrated into the depths of Russia by other roads. It is known that a soldier who returned from the Russian-Turkish war brought a devil's bundle to the village of Olsufyevo in the Bryansk region.
Now the puzzle can be bought in the store, but it is more pleasant to make it yourself. The most suitable size of bars for a homemade design: 6x2x2 cm.

Variety of damn knots

Rice. 1 The simplest version of the devil's knot puzzle

In Europe, where, starting from the end of the last century, the "Devil's Knot" became widely known, enthusiasts began to invent and make sets of bars with different cutout configurations. One of the most successful sets allows you to get 159 puzzles and consists of 20 bars of 18 types. Although all the nodes are outwardly indistinguishable, they are arranged completely differently inside.

Rice. 2 "Puzzle of Admiral Makarov"

Surprisingly large number for such a small toy! Therefore, to solve the problem, a computer was needed.

How does a computer solve puzzles?

Not like a human, of course, but not in some magical way either. A computer solves puzzles (and other problems) according to a program; programs are written by programmers. They write how it is convenient for them, but in such a way that the computer can also understand. How does a computer manipulate wooden blocks?
We will proceed from the fact that we have a set of 369 bars that differ from each other in the configuration of the protrusions (this set was first identified by Van de Boer). Descriptions of these bars must be entered into the computer. The minimum notch (or protrusion) in a block is a cube with an edge equal to 0.5 of the block's thickness. Let's call it a unit cube. The whole bar contains 24 such cubes (Figure 1). In the computer, for each bar, a “small” array of 6x2x2=24 numbers is entered. A bar with cutouts is specified by a sequence of 0 and 1 in a "small" array: 0 corresponds to a cut out cube, 1 - to the whole. Each of the "small" arrays has its own number (from 1 to 369). Any of them can also be assigned a number from 1 to 6, corresponding to the position of the bar inside the puzzle.

Let's move on to the puzzle now. Imagine that it fits inside an 8x8x8 cube. In a computer, this cube corresponds to a "large" array consisting of 8x8x8=512 cells-numbers. To place a certain bar inside the cube means to fill the corresponding cells of the "large" array with numbers equal to the number of this bar.

Comparing 6 "small" arrays and the main one, the computer (i.e., the program), as it were, adds together 6 bars. Based on the results of adding numbers, it determines how many and which “empty”, “filled” and “overflowing” cells formed in the main array. "Empty" cells correspond to an empty space inside the puzzle, "filled" - correspond to the protrusions in the bars, and "overflowed" - an attempt to connect two single cubes together, which, of course, is prohibited. Such a comparison is made many times, not only with different bars, but also taking into account their turns, the places they occupy in the “cross”, etc.

As a result, those options are selected in which there are no empty and overflowing cells. To solve this problem, a “large” array of 6x6x6 cells would be enough. It turns out, however, that there are combinations of bars that completely fill the internal volume of the puzzle, but it is impossible to disassemble them. Therefore, the program must be able to check the node for the possibility of disassembly. To do this, Cutler took an 8x8x8 array, although its dimensions may not be sufficient to check all cases.

It is filled with information about a particular variant of the puzzle. Inside the array, the program tries to “move” the bars, i.e., it moves parts of the bar with a size of 2x2x6 cells in the “large” array. The movement is 1 cell in each of the 6 directions parallel to the axes of the puzzle. The results of those of the 6 attempts, in which no "overflowed" cells are formed, are remembered as the starting positions for the next six attempts. As a result, a tree of all possible movements is built until some bar completely leaves the main array, or after all attempts, “overflowed” cells remain, which corresponds to a variant that cannot be parsed.

This is how 119,979 variants of the "Devil's Knot" were obtained on a computer, including not 108, as the ancients believed, but 6402 variants that have 1 whole bar without cutouts.

Supernode

Note that Cutler refused to study the general problem - when the node also contains internal voids. In this case, the number of nodes of 6 bars increases greatly and the exhaustive search required to find feasible solutions becomes unrealistic even for a modern computer. But as we will see now, the most interesting and difficult puzzles are contained precisely in the general case - then disassembling the puzzle can be made far from trivial.

Due to the presence of voids, it is possible to successively move several bars before it is possible to completely separate any bar. The moving bar unhooks some bars, allows the movement of the next bar, and simultaneously engages other bars.
The more manipulations you need to do during disassembly, the more interesting and difficult the variant of the puzzle. The grooves in the bars are arranged so cunningly that the search for a solution is like wandering through a dark labyrinth, in which you constantly come across either walls or dead ends. This type of knot certainly deserves a new name; we'll call it a "supernode". A measure of the complexity of a superknot is the number of movements of individual bars that must be done before the first element is separated from the puzzle.

We don't know who invented the first supernode. The most famous (and most difficult to solve) are two superknots: the "Bill's thorn" of complexity 5, invented by W. Cutler, and the "Dubois superknot" of complexity 7. Until now, it was believed that the degree of complexity 7 could hardly be surpassed. However, the first of the authors of this article managed to improve the "Dubois knot" and increase the complexity to 9, and then, using some new ideas, get superknots with complexity 10, 11 and 12. But the number 13 remains insurmountable so far. Maybe the number 12 is the biggest supernode complexity?

Supernode solution

W. Cutler's puzzle ("Bill's thorn")

Rice. 3 "Bill's Thorn", developed with the help of a computer.

If this is the case and we collect it, then after that we can replace part 2 B with part 2, since the latter takes up less volume than 2 V. As a result, we will get the second solution to the puzzle. But "Bill's thorn" has a unique solution, and only one conclusion can be drawn from our contradiction: in the second option, an error was made in the drawing.
A similar mistake was made in another publication (J. Slocum, J. Botermans "Puzzles old and new", 1986), but in another bar (detail 6 C in Figure 3). What was it like for those readers who tried and, perhaps, are still trying to solve these puzzles?

Philippe Dubois puzzle (Fig. 4)

It is solved in 7 moves according to the following algorithm: (6z )^2, 3x . 1z, 4x, 2x, 2y, 2z?. The figure shows the location of parts on the b tag of disassembly. Starting from this position, using the reverse order of the algorithm and changing the directions of movement to the opposite ones, it is possible to assemble the puzzle.

Three supernodes D. Vakarelov.

The first of his puzzles (Fig. 5) is an improved version of the Dubois puzzle, it has difficulty 9. This superknot is more like a maze than others, since when it is disassembled, false moves arise that lead to dead ends. An example of such a deadlock is the moves 3x, 1z at the beginning of the disassembly. And the correct solution is:

(6z)^2, 3x, 1z, 4x, 2x, 2y, 5x, 5y, 3z?.

The second puzzle of D. Vakarelov (Fig. 6) is solved by the formula:

4z, 1z, 3x, 2x, 2z, 3x, 1z, 6z, 3x, 1x, 3z?

and has complexity 11. It is remarkable in that bar 3 takes a step Zx on the third move, and returns back on the sixth move (Zx); and bar 1 on the second step moves along 1z , and on the 7th move it makes a reverse move.

The third puzzle (Fig. 7) is one of the most difficult. Her solution:
4z, 1z, 3x, 2x, 2z, 3x, 6z, 1z, (1,3,6)x, 5y?
up to the seventh move, it repeats the previous puzzle, then, on the 9th move, a completely new situation occurs in it: suddenly all the bars stop moving! And here you need to guess to move 3 bars at once (1, 3, 6), and if this movement is counted as 3 moves, then the complexity of the puzzle will be 12.

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Wooden puzzle instruction. Wooden puzzle knots from bars. Values ​​in formulas