How to solve a Rubik's cube of an unusual shape. The most unusual Rubik's cubes in the world

In this article we will look at the varieties of the Rubik's Cube, not only as puzzles, but also as household items.

In addition to the standard size - 3x3x3, there are others, smaller and larger sizes:2×2×2, 4×4×4, 5×5×5, 6×6×6, 7×7×7, 8×8×8, 9×9×9, 11×11×11, 17× 17x17:

Along with the traditional 6-color design of the 3×3×3 cube, there are cubes with various images on the faces:

Rubik's cube with playing cards

Rubik's cube with traffic signs

Rubik's cube with world map

Rubik's cube of unusual shape:

Rubik's cube in the shape of an apple

Rubik's cube in the shape of Homer Simpson's head

Rubik's cube in the shape of Mickey Mouse's head

Rubik's cube in the shape of a brain

Rubik's Cube combined with other games and puzzles:

Rubik's Cube Scrabble is a cube for those who love board game Scrabble. It is a combination of Scrabble and a Rubik's cube. The goal is to rotate the sides of the cube so as to form the word with the highest value.

Rubik's Sudoku Cube - instead of the usual colored faces, the cube has numbers on it. To solve the puzzle, you need to assemble the cube in such a way that all numbers from 1 to 9 appear exactly once on all faces of the cube.

The Rubik's Cube Tic Tac Toe is a hybrid of a cube and the game Tic Tac Toe. On each face it is necessary to make winning combination a game of tic-tac-toe. If they are on each of the six sides of the cube, the puzzle is solved.

Lego Rubik's Cube - a puzzle made from Lego. You can choose to either solve the puzzle or play the construction game. But you can show a little trick - if you are unable to solve the Cube, then you can always rearrange the necessary parts of the construction set, and the cube is completed!

Rubik's Cube Tangle - When solving this cube, you must make sure that all the ropes of the same color are connected to each other.

TO Rubik's cube made from unusual materials:

Rubik's cube made from keyboard keys

Rubik's cube made of glass

Rubik's cube made from dice

Rubik's cube for the blind

A person with poor eyesight can assemble these cubes. One of the options is made of different materials: leather, wood, fabric, etc. On the surface of the other, there are special symbols written in Braille.

Mirror Rubik's Cube

The color of all the edges is the same, but the highlight of this puzzle lies elsewhere - in the proportions of the edges.

LED Rubik's Cube

Unlike a regular Rubik's Cube, which requires you to rotate the sides, this cube has LED digital squares that can be moved by pressing buttons.

Touch Rubik's Cube

This is the most modern variation of the classic Rubik's cube. In this puzzle there is no need to rotate the cube, everything happens with one touch, just like on the screen of your smartphone or tablet computer.

Unusual applications of the Rubik's Cube idea in everyday life:

Flash card reader

Speaker

Watch

Notebook

Dresser

The human intellect needs constant training no less than the body needs physical activity. The best way develop and expand the abilities of this mental quality - to solve crosswords and solve puzzles, the most famous of which, of course, is the Rubik's cube. However, not everyone manages to collect it. Knowledge of diagrams and formulas for solving the assembly of this intricate toy will help you cope with this task.

What is a puzzle toy

A mechanical cube made of plastic, the outer edges of which consist of small cubes. The size of the toy is determined by the number of small elements:

• 2 x 2;
• 3 x 3 (the original version of the Rubik's cube was exactly 3 x 3);
• 4 x 4;
• 5 x 5;
• 6 x 6;
• 7 x 7;
• 8 x 8;
• 9 x 9;
• 10 x 10;
• 11 x 11;
• 13 x 13;
• 17 x 17.

Any of the small cubes can rotate in three directions along axes represented in the form of protrusions of a fragment of one of the three cylinders of the large cube. This way the structure can rotate freely, but small parts do not fall out, but hold on to each other.

Each face of the toy includes 9 elements, painted in one of six colors, located opposite each other in pairs. The classic combination of shades is:

• red opposite orange;
• white opposite yellow;
• blue is opposite green.

However, modern versions can be painted in other combinations.

Today you can find Rubik's cubes of different colors and shapes.

This is interesting. The Rubik's cube even exists in a version for the blind. There, instead of color squares, there is a relief surface.

The goal of the puzzle is to arrange the small squares so that they form the edge of a large cube of the same color.

History of appearance

The idea of ​​creation belongs to the Hungarian architect Erna Rubik, who, in fact, created not a toy, but visual material for your students. So in an interesting way the resourceful teacher planned to explain the theory mathematical groups(algebraic structures). This happened in 1974, and a year later the invention was patented as a puzzle toy - future architects (and not only them) became so attached to the intricate and colorful manual.

The release of the first series of the puzzle was timed to coincide with the new year of 1978, but the toy came into the world thanks to entrepreneurs Tibor Lakzi and Tom Kremer.

This is interesting. Since its introduction, the Rubik's cube ("magic cube", "magic cube") has sold about 350 million copies worldwide, making the puzzle the number one most popular toy. Not to mention dozens computer games, based on this assembly principle.

The Rubik's Cube is an iconic toy for many generations

In the 80s, residents of the USSR became acquainted with the Rubik's cube, and in 1982, the first world championship in speed puzzle assembly - speedcubing - was organized in Hungary. Then the best result was 22.95 seconds (for comparison: a new world record was set in 2017: 4.69 seconds).

This is interesting. Fans of solving colorful puzzles are so attached to the toy that speed-assembling competitions alone are not enough for them. Therefore in last years puzzle solving championships appeared with eyes closed, one hand, legs.

What are the formulas for the Rubik's cube

To assemble a magic cube means to arrange all the small parts so that you get a whole face of the same color, you need to use God's algorithm. This term refers to a set of minimum actions that will solve a puzzle that has a finite number of moves and combinations.

This is interesting. In addition to the Rubik's cube, God's algorithm is applied to such puzzles as Meffert's pyramid, Taken, Tower of Hanoi, etc.

Since the magic Rubik's cube was created as math manual, then its assembly is decomposed according to the formulas.

Solving a Rubik's cube is based on the use of special formulas

Important Definitions

In order to learn to understand the schemes for solving a puzzle, you need to become familiar with the names of its parts.

1. An angle is a combination of three colors. In the 3 x 3 cube there will be 3 of them, in the 4 x 4 version there will be 4, etc. The toy has 12 corners.
2. An edge represents two colors. There are 8 of them in a cube.
3. The center contains one color. There are 6 of them in total.
4. The faces, as already mentioned, are simultaneously rotating puzzle elements. They are also called “layers” or “slices”.

Values ​​in formulas

It should be noted that the assembly formulas are written in Latin - these are the diagrams that are widely presented in various manuals for working with the puzzle. But there are also Russified versions. The list below contains both options.

1. The front edge (front or façade) is the front edge, which is the color facing us [F] (or F - front).
2. The back face is the face that is centered away from us [B] (or B - back).
3. Right Face - the face that is on the right [P] (or R - right).
4. Left Face - the face that is on the left [L] (or L - left).
5. Bottom Face - the face that is at the bottom [H] (or D - down).
6. Top Face - the face that is at the top [B] (or U - up).

Photo gallery: parts of the Rubik's cube and their definitions

To explain the notations in the formulas, we use the Russian version - it will be clearer for beginners, but for those who want to move to the professional level of speedcubing without the international notation system English language not enough.

This is interesting. The international notation system is adopted by the World Cube Association ( World Cube Association, WCA).

1. The central cubes are designated in the formulas by one lowercase letter - f, t, p, l, v, n.
2. Angular - three letters according to the name of the edges, for example, fpv, flni, etc.
3. Capital letters F, T, P, L, V, N indicate the elementary operations of rotating the corresponding face (layer, slice) of a cube 90° clockwise.
4. The designations F", T", P", L", V", N" correspond to the rotation of the faces by 90° counterclockwise.
5. The designations Ф 2, П 2, etc. indicate a double rotation of the corresponding face (Ф 2 = ФФ).
6. The letter C indicates the rotation of the middle layer. The subscript indicates which face should be viewed from in order to make this turn. For example, C P - from the right side, C N - from the bottom side, C "L - from the left side, counterclockwise, etc. It is clear that C N = C " B, C P = C " L and etc.
7. The letter O is a rotation (turn) of the entire cube around its axis. O F - from the side of the front edge clockwise, etc.

Recording the process (Ф "П") Н 2 (ПФ) means: rotate the front face counterclockwise by 90°, the same - the right edge, rotate the bottom edge twice (that is, 180°), rotate the right edge 90° along clockwise, rotate the front edge 90° clockwise.

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It is important for beginners to learn to understand formulas

As a rule, the instructions for assembling a puzzle in classic colors recommend holding the puzzle with the yellow center facing up.

This advice is especially important for beginners.

This is interesting. There are sites that visualize formulas. Moreover, the speed of the assembly process can be set independently. For example, alg.cubing.net

How to solve a Rubik's puzzle

• There are two types of schemes:
• for newbies;

for professionals.

Their difference is in the complexity of the formulas, as well as the speed of assembly. For beginners, of course, instructions appropriate to their level of puzzle proficiency will be more useful. But after practice, they too will be able to fold the toy in 2–3 minutes.

How to solve a standard 3 x 3 cube

Let's start by solving the classic 3 x 3 Rubik's cube using a 7-step diagram.

The classic version of the puzzle is the 3 x 3 Rubik's Cube

This is interesting. The reverse process used to solve certain misplaced cubes is the reverse sequence of the action described by the formula. That is, the formula must be read from right to left, and the layers must be rotated counterclockwise if direct movement was specified, and vice versa: direct if the opposite is described.

1. Step-by-step assembly instructions

   We start by assembling the cross on the top edge. We lower the desired cube down by rotating the corresponding side face (P, T, L) and bring it to the front face using the operation H, N" or H 2. We finish the removal stage with a mirror rotation (reverse) of the same side face, restoring the original position of the affected rib cube of the upper layer. After this, we carry out operation a) or b) of the first stage. In case a) the cube has reached the front face so that the color of its front face coincides with the color of the front. In case b) the cube must not only be moved up, but also rotated. , so that it is correctly oriented, falling into place.

2. Collecting the top line cross The required corner cube is found (having the colors of the faces F, B, L) and, using the same technique described for the first stage, is brought to the left corner of the selected front face (or yellow). There can be three possible orientations for this cube. We compare our case with the figure and apply one of the operations of the second stage a, beat c. The dots on the diagram mark the place where the desired cube should go. We find the remaining three corner cubes on the cube and repeat the described technique to move them to their places on the top face. Result: upper layer The first two stages cause almost no difficulties for anyone: you can quite easily monitor your actions, since all attention is paid to one layer, and what is done in the remaining two is not at all important.

   Selecting the top layer

3. Our goal: to find the desired cube and first bring it down to the front face. If it is at the bottom, simply turn the bottom edge until it matches the color of the facade, and if it is in the middle layer, then you must first lower it down using any of operations a) or b), and then match it in color with the color of the facade edge and perform the third stage operation a) or b). Result: two layers are collected. The formulas given here are mirror ones in the full sense of the word. You can clearly see this if you place a mirror to the right or left of the cube (edge ​​facing you) and do any of the formulas in the mirror: we will see the second formula. That is, operations with the front, bottom, top (not involved here), and back (also not involved) faces change their sign to the opposite: it was clockwise, it became counterclockwise, and vice versa. And the left side changes from the right, and, accordingly, changes the direction of rotation to the opposite.

   We find the desired cube and bring it down to the front face

4. Operations that move the side cubes of one face without ultimately disturbing the order in the assembled layers lead to the goal. One of the processes that allows you to select all the side faces is shown in the figure. It also shows what happens to the other cubes of the face. By repeating the process, choosing another front face, you can put all four cubes in place. Result: The rib pieces are in place, but two of them, or even all four, may be oriented incorrectly. Important: before you start executing this formula, look at which cubes are already in place - they may be oriented incorrectly.

   If there is none or one, then we try to rotate the top face so that the two located on two adjacent side faces (fv+pv, pv+tv, tv+lv, lv+fv) fall into place, after which we orient the cube like this , as shown in the figure, and execute the formula given at this stage. If it is not possible to combine the parts belonging to adjacent faces by rotating the top face, then we perform the formula for any position of the cubes of the top face once and try again by rotating the top face to put in place 2 parts located on two adjacent side faces.

5. We take into account that the unfolded cube must be on the right side; in the figure it is marked with arrows (pv cube). Figures a, b, and c show possible cases of arrangement of incorrectly oriented cubes (marked with dots). Using the formula in case a), we perform an intermediate rotation B" to bring the second cube to the right side, and a final rotation B, which will return the top face to its original position, in case b) an intermediate rotation B 2 and the final one also B 2, and in case c) intermediate rotation B must be performed three times, after turning over each cube, and also completed with rotation B. Many people are confused by the fact that after the first part of the process (PS N) 4, the desired cube unfolds as it should, but the order in the assembled layers is disrupted. confusing and makes some people throw the almost completed cube halfway. Having performed an intermediate turn, not paying attention to the “breakage” of the lower layers, we perform operations (PS N) 4 with the second cube (the second part of the process), and everything falls into place. Result: the cross is assembled.

   The result of this stage will be an assembled cross

6. We put the corners of the last face in place using an 8-step process that is easy to remember - forward, rearranging the three corner pieces in a clockwise direction, and reverse, rearranging the three cubes in a counterclockwise direction. After the fifth stage, as a rule, at least one cube will sit in its place, albeit in the wrong direction. (If after the fifth stage none of the corner cubes are in their place, then we apply any of the two processes for any three cubes, after which exactly one cube will be in its place.). Result: All corner cubes are in place, but two (or maybe four) of them may be oriented incorrectly.

   Corner cubes sit in place

7. We repeat the sequence of turns PF"P"F many times. We rotate the cube so that the cube we want to expand is in the upper right corner of the facade. An 8-turn process (2 x 4 turns) will turn it 1/3 turn clockwise. If the cube has not yet oriented itself, we repeat the 8-move move again (in the formula this is reflected by the index “N”). We do not pay attention to the fact that the lower layers will become disordered. The figure shows four cases of incorrectly oriented cubes (they are marked with dots). In case a) an intermediate turn B and a final turn B are required, in case b) - an intermediate and final turn B 2, in case c) - turn B is performed after turning each cube to the correct orientation, and the final turn B 2, in case d) - intermediate rotation B is also performed after turning each cube to the correct orientation, and the final one in this case will also be rotation B. Result: the last face is assembled.

   Possible errors are shown by dots

Formulas for correcting the placement of cubes can be shown as follows.

Formulas for correcting incorrectly oriented cubes at the last stage

The essence of Jessica Friedrich's method

There are several ways to assemble the puzzle, but one of the most memorable is the one developed by Jessica Friedrich, a professor at the University of Binghamton (New York), who is developing techniques for hiding data in digital images. While still a teenager, Jessica became so interested in the cube that in 1982 she became the world champion in speedcubing and subsequently did not abandon her hobby, developing formulas for quick assembly"magic cube" One of the most popular cube folding options is called CFOP - according to the first letters of four assembly steps.

Instructions:

1. We assemble a cross on the top face, which is made up of cubes on the edges of the bottom face. This stage is called Cross.
2. We assemble the bottom and middle layers, that is, the face on which the cross is located, and the intermediate layer, consisting of four side parts. The name of this step is F2L (First two layers).
3. We assemble the remaining edge, not paying attention to the fact that not all the parts are in place. The stage is called OLL (Orient the last layer), which translates to “the orientation of the last layer.”
4. The last level - PLL (Permute the last layer) - consists of the correct placement of the cubes of the top layer.

Video instructions for the Friedrich method

The method that was proposed by Jessica Friedrich was so liked by speedcubers that the most advanced amateurs are developing their own methods to speed up the assembly of each of the stages proposed by the author.

Video: speeding up the assembly of the cross

Video: assembling the first two layers

Video: working with the last layer

Video: last level of assembly by Friedrich

2 x 2

A 2 x 2 Rubik's cube or mini Rubik's cube is also folded in layers, starting from the bottom level.

Mini cube is a light version of the classic puzzle

Beginner's instructions for easy assembly

1. We assemble the bottom layer so that the colors of the last four cubes match, and the remaining two colors are the same as the colors of the adjacent parts.
2. Let's start organizing the top layer. Please note that at this stage the goal is not to match the colors, but to put the cubes in their places. We start by determining the color of the top. Everything is simple here: this will be the color that did not appear in the bottom layer. Rotate any of the top cubes so that it gets to the position where the three colors of the element intersect. Having fixed the angle, we arrange the remaining elements. For this we use two formulas: one for changing diagonal cubes, the other for neighboring ones.
3. We complete the top layer. We carry out all operations in pairs: we rotate one corner and then the other, but in the opposite direction (for example, the first one clockwise, the second one counterclockwise). You can work with three angles at once, but in this case there will be only one combination: either clockwise or counterclockwise. Between rotations of the corners, rotate the top edge so that the corner being worked is in the upper right corner. If we are working with three corners, then place the correctly oriented one at the back left.

Formulas for rotating angles:

• (VFPV · P"V"F")² (5);
• V²F·V²F"·V"F·V"F"(6);
• VVF² · LFL² · VLV² (7).

To rotate three corners at once:

• (FVPV"P"F"V")² (8);
• FV·F"V·FV²·F"V² (9);
• V²L"V"L²F"L"F²V"F" (10).

Photo gallery: 2 x 2 cube assembly

Video: Friedrich method for 2 x 2 cube

Collecting the most difficult versions of the cube

These include toys with a number of parts from 4 x 4 and up to 17 x 17.

The Rubik's cube, or, as it is popularly called, the Rubik's cube, is a mechanical puzzle, a plastic cube measuring 3 × 3 × 3 elements. Its external elements are 54 faces of small cubes that make up one large cube. Each cube is capable of rotating around three axes. Each face represents nine elements and is painted in one of six colors, which in turn are located in pairs opposite each other.

The Rubik's Cube was invented in 1974 by the Hungarian sculptor and architecture teacher Erné Rubik. He patented it in 1975. This puzzle was originally called "Magic Cube".

The essence of the puzzle is to rotate the faces of small cubes, order them by color and make up a large face of the cube with elements of the same color, i.e. solve a Rubik's cube.

The history of the creation of the Rubik's cube

The Rubik's Cube was not originally a toy. Erne Rubik taught industrial design and architecture and created this cube as a teaching aid, with the help of which I wanted to clearly explain to students the basics of mathematical group theory. However, young people liked the cube so much that it gradually became a toy.

The first production of cubes took place at the end of 1977. The manufacturer of the cube was a small one from Budapest, and the release of the cube was timed for Christmas 1978.

However, the puzzle became widely known and popular only after a certain Tibor Lakzi became interested in it. He was a computer entrepreneur with a passion for mathematics. He began promoting the toy together with Tom Cramer, the inventor of games and founder of Seven Towns Ltd.

After this, the popularity of the Rubik's Cube peaked in 1980. The toy appeared in the USSR in 1981. Entire articles were published in magazines devoted to methods for solving the intricate cube.

And in 1982, the first world championship in solving the Rubik's Cube was held in Hungary. Representatives from 19 countries took part in it. Participants in the competition had to solve the cube in no more than one minute. Best time assembly was 22.95 seconds. Today the record is 8 seconds.

After 1983, interest in the toy began to gradually subside, and it received a second wind only in the 90s. This is explained by the advent of personal computers and the creation of a Rubik's cube simulation game for them.

This puzzle has become a toy for all times. In 1980, she received the Hungarian national prize for the best invention and won competitions for the best toy in the USA, Great Britain, France and Germany. In 1981, the cube was placed in the gallery of the New York Museum of Modern Art.

One of the most popular puzzles of the USSR, which subsequently gained wide popularity throughout the world, was developed in Hungary.

We are, of course, talking about the famous cube, which was named after the inventor, Erno Rubik, who at that time worked as a teacher at the Academy applied arts and crafts. The first finished prototype was presented in 1974, and the patent for the invention was issued a year later. The puzzle became so popular (by 2007, 9 million copies had been sold) that it allowed the former teacher to become one of the first millionaires in the USSR. Thanks to this demand, new species have appeared that differ from the original sample.

What it is?

The original has the following characteristics:

• configuration – 3x3x3 (consists of 27 parts);
• edge width – 5.4 cm;
• design method – color.

A special feature is a rotating mechanism that allows you to rotate the edges to make all surfaces the same color. The design of the rotating mechanism is such that when used, the toy made a characteristic creaking sound. However, in subsequent modifications of the product this drawback was eliminated.

What types of Rubik's cubes are there?

Considering the types of Rubik's cube, it can be noted that they differ mainly in configuration and design. For example, in addition to the original 3x3x3, there are its analogues 2x2 (“Children’s”), 4x4x4 (“Rubik’s Revenge”) and 5x5x5 (“Professor’s”).

If we talk about differences in design, then there is a variety without moving edges. This option was presented by British inventor Andrew Fentham. His development has touch-sensitive surfaces and sensors that respond to rotation. Instead of static multi-colored squares, 216 LED screens are used that change color depending on touches and position in space.

Another interesting model is made from dice. This option can be assembled on your own; for this you will need 108 magnets, 27 dice, several clamps and a simple tool (screwdriver and drill).

Regardless of its origin (factory or handmade), fascination with this puzzle will help not only pass the time, but also develop spatial thinking.

Back in 1974, the first Rubik's cube was born. When Erno Rubik created it, he did not even think that his creation would become the most popular puzzle in the world. Today, many championships and competitions are organized, and more and more new records are constantly being set. There are many models and varieties of Rubik's cube, and beginners can get confused in this huge and very interesting field.

Sooner or later, every beginning speedcuber has the question: “What’s next? What puzzle should I learn to solve next? Especially for them, we have prepared a short tour of the main puzzles.

Since the classic and most popular puzzle is, let’s first look at models similar to it.

The smaller brother 2x2x2 is much easier to solve, assembly can take a few seconds, but it is still a very interesting puzzle that does not get boring, and you want to play it very often. If you wanted something similar to a regular cube, but not too complicated, then a 2x2x2 cube would be a great option.

Many continue their speedcubing path with the 4x4x4 cube - a logical development of the three-ruble cube. It is in this puzzle that the basic principles of assembling large cubes are laid down. If you have mastered the four, then any big cube will not be a problem!

If the 4x4x4 cube is not enough for you, then you need a 5x5x5 cube! It has an even more complex structure and large quantity elements that need to be organized. To assemble it, you also need to first assemble the centers, then the ribs, but in the end you can still expect parity, but only one. To assemble, you will have to show ingenuity and logic, but the skills of assembling smaller cubes will definitely come in handy!

Logic will also have to be applied when solving larger puzzles, such as cubes, and so on.

Their assembly takes much longer, but the puzzles have a solution process similar to their predecessors and all the same parities. Any self-respecting cuber has larger cubes in his collection.

All cubes from 2x2x2 to 7x7x7 are disciplines of all the largest tournaments, which are held under the auspices of the World Cubing Association (WCA). But besides them, there are other WCA puzzles.

One of these puzzles was invented in 1972, which even predates the Rubik's cube! - a pyramid, each side of which is divided into 9 regular triangles. It was invented by Uwe Meffert. A fairly simple puzzle, but every cuber should have it - it’s a classic, just like the 3x3 cube! The pyramid has many versions, such as 2x2 or 4x4. For those who have already acquired a pyramid, this is a good way to get acquainted with something new.

Another fairly simple, but at the same time interesting puzzle is. With each rotation of the faces, half of its elements move: the rotation occurs with four axes parallel to the diagonals of the cube. The world record for assembly is less than a second! An excellent option for the collection, which will allow you to relax after a hard day, because the assembly will not cause big problems for cubers of any level.

For those who liked solving the Rubik's cube and who are looking for new sensations, there is a more difficult puzzle - a very scary one. But although this 12-sided puzzle looks bulky and incredibly complex, in practice it is solved quite simply, you just need to be able to assemble the classic 3x3x3. Such a puzzle can really surprise many friends, and you will get quite an interesting experience.

But if you need something completely new and complex, then you need. In Square-1 the central elements are locked, and when disassembled it is not even a cube - it changes its shape! The first assembly can be quite difficult, but numerous tutorials published on the Internet can come to your aid. This is a great way to get introduced to shape-shifting puzzles, and because of the new algorithms and unusual situations, the solution will be very interesting.

One of the most unusual puzzles that are assembled at competitions is. The idea is very simple - you need to combine all the dials and point them at 12 o'clock. It is not a must-have for a beginner, but those who want a break from cube puzzles should consider this puzzle.

In addition to WCA puzzles, there are other types of hinged puzzles that should not be overlooked, and the list goes on for an incredibly long time: Void, Fisher, Mirror, the Gear family, and much, much more. Now you can choose both a budget and an expensive model, both simple and incredibly complex. Speedcubing is developing, more and more people are interested in this activity, which means that manufacturers will continue to delight us with new exquisite puzzles, which you can always find in the store.