Pictures matching games

Matching games for Adults - Online & Free

• Memory Games
• Matching Games
• For adults

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Author: Emmanuelle ROUGER  /   Published by Memozor

Published on 22 September 2011   /   Last modified on 07 August 2022

Find here many free and Online Matching games for adults . Perfect games to train your memory, or just pour fun!

You want to play a Matching game but you do not have the famous board game at home? No problem! These games are made for you! You will find below, a Large range of matching games specially designed for adults, impossible to be bored! The cards can be pictures, photos, people, objects, flags, letters, numbers, and many more. ..

You can play Alone or against the Computer. You can choose the Level of difficulty by increasing or decreasing the number of cards displayed thanks to the buttons located below the game. These matching games are compatible with all your devices: desktop, tablets and smartphones. So you can play wherever you are!

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How to play our online Matching games for adults?

In these online Matching games, the cards are laid in rows on the board. The number of cards vary from 12 (6 pairs) to 42 (21 pairs). You can increase the number of the cards in the matching game, and so the level of difficulty, thanks to the buttons located below the game.
For teachers who want to play matching games with their students or for all those who want to play together and remotely via screen sharing, a new feature is now available for each game: you now have the possibility to display numbered cards.

The principle of the game is to find all the pairs by returning the cards 2 by 2. If the cards turned up are the same (a pair), it's a match and you win the pair, otherwise, the cards are automatically turned face down and you have to make a new try.
In the "SOLO" mode: The principle is to find all the pairs with the fewest possible moves and in a shortest time.
In the "2 PLAYERS" mode: the player who found the most pairs wins.

Quickly understand how to play with the Quick matching game rules here, you will find there a step-by-step illustrated description, or you can also Download the Printable game rules in PDF format.

These matching games are compatible with all your devices: desktop, tablets and smartphones (IOS ou Android).The content and the game adjust automatically to your device, so do not hesitate to play on a tablet or a smartphone.

Many free Matching games on Memozor

We offer the adults a wide range of free Matching games to ensure that everyone can find themes that please him, to match their tastes, according to his desires, according to his passions or based on his interests.

• For sports fans, there are several games on the theme of sport, for example, the Matching game with object related to the Sport, with beautiful sport pictures, with ski and snowboard, with the best Baseball or Soccer player.
• For intellectuals, there are art and culture memory games such as Matching game with the most beautiful monuments, with paintings from famous painters, for example.
• For nature lovers, many memory games with animals such as the Matching game with common birds, with black dogs, or on the theme of nature: Matching game with mushrooms.
• For curious people who are thirsty for knowledge there are learning memory games such as Matching game with the names of the planets, with national flags...

Every time you start a new game, a random selection and a random positioning of the cards ensure you a different game than the previous one, so you can play again and again! On Memozor, all Matching games for adults are free and unlimited, so you can play as many games as you want.

The Matching game is an excellent memory game for adults

These free memory games are specifically designed for adults. We offer you several levels of difficulty and many themes that have been selected to please you.

The Matching game is an excellent memory game for adults. Indeed, everytime the player turns over two cards, he has to memorize their location in a few seconds. So, when later he turns over a card which is the same of a previously turned over card, he will use his memory to try find the double of the first card in the first instance because, in the case of a 2-player game, if he fails, there is a good chance that the next player will win the pair. And in the case of a single player game, this increases the number of moves played and therefore decreases his score. Matching games allows you to stimulate your memory while having fun. Find all types of memory games offered by Memozor.

If you want more difficult Matching games (with a larger number of cards), you will find here our Giant or Big Matching games.

Matching Games online,free match tile,color pictures game for kids preschoolers to play,no download

For children, teens & Big Kids - Play fun matching games, picture matching games, match tiles games, and color matching activities on your computer for free on Learn4Good. com. We believe that we have put some of the best online matching games for kids in one area. From simple games to more challenging ones. Happy playing!

Candy Crusher

Candy Crusher in an online matching game phenomenon that has taken the web by storm. Find out what all the fuss is about by playing the original browser version of this simple ‘match three’ game where you have to swap colorful candies around a large grid to make a match of three or more of the tempting sweets in a row. Earn as many points as you can before you use up all your moves (matches must be horizontal or vertical), and score huge bonuses for hitting combos.

Your ultimate goal is to score as many ‘Candy Points’ as you can within the moves limit; you have a certain amount of 'moves' to swap around the candy to try make 3 in a row! This fun and addicting matching game has proven to be a huge hit with little & Big kids around the world, especially fans of classic ‘Match 3’ games such as ‘Bejeweled’, or anyone who enjoys a good-old visual puzzle. Test your concentration, observation and decision-making skills as you scope out the match that will yield the highest points return. Your reactions and reflexes need to be quick! Are you sweet to start?

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Electrio

Sit back, relax and play a truly electrifying game in Electrio. Electrio is a great puzzle linking game, reimagined in an interesting science aesthetic with the goal being to connect all the electrons and protons within the overlapping lines. EG Electrode is not only a fun puzzle game for adults but also children, providing them with a game that might very well develop their interests in science. See if you have the brains to complete all 25 levels!

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Arkadium Bubble Shooter

Arkadium Bubble Shooter is a fun and bright match-three game that will have you aiming, firing and then dying for more. This is a game you can get sucked into and play again and again.

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Amazing Sticky Hex

Amazing Sticky Hex is a quirky and beautiful addition to the puzzle game genre where you need to fill in all the empty hexagons on the grid board by placing various shiny gems into the right spots. This is also a game that awards careful planning and a more think before you leap mentality, as the few mistakes you make, the more stars you will earn. These starts, in turn, can be used to pay for hints should you really get stuck later on. This game is sure to become a welcome addition to your daily routine!

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Path Finding Cakes Match

Path Finding Cakes Match - Connect chains of 3 of matching cakes by creating a clear path between them, and clear all the cakes before time runs out - complete quickly to get bonus points. Work quickly to spot the matching desserts and gobble them up. Have fun!

This is a challenging puzzle game where you need to concentrate hard to find and connect pairs of matching cakes in order to make them disappear from the picture grid. It will also test your eyesight! Initially, you should try to find some pairs side-by-side to help free up much-needed space, and to create a direct path between other pairs of items, ensuring that the path is not blocked by any other tiles. Happy clean up!

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Fruit Connect

Farm Connect 2 is a fun pairing game with a bunch of different plants!

Pair them up! Your job is simple: Pair the same plants together to get them off of the board. Sounds simple, right? Here’s the thing… They have to be right next to each other or have open space between them! There can only be 3 turns before two blocks are paired. Find as many pairs as you can before the timer runs out to progress to the next level. There are about one-hundred and forty blocks on the board at the start of the round. Can you clear it and move on?

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Sugar Heroes

Join a band of sugary sweet sweety heroes as they try to investigate the mysterious cause behind what has happened to their town and if it is linked to the fallen meteor in Sugar Heroes. Sugar Heroes is a tile-matching, or in this case sweet and fruit matching, puzzle game where your objective is to solve a series of puzzle matching games to progress the story. Sugar Heroes is a game that the whole family would enjoy playing, and its engaging gameplay and delightful visuals are guaranteed to keep you playing for hours.

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Jewel Legend

Jewel Legend: Come and have hours of fun on this addictive and simple game! Let the great Jewel Legend begin. The travelers from all around the world have come to the mines to dig those diamonds out. Join them in the effort to find as many diamonds as possible while engaging in various challenges that you will keep you entertained for long periods of time. What are you waiting for?

Match as many diamonds as possible to get them to vanish! The key to this game is speed. Have you got a fast enough eye to spot the opportunities the swap diamonds round and create a chain? Furthermore have you got a fast enough hand to take advantage of the quick spot? Lets find out!

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Mahjong Quest

In Mahjong Quest, play the timeless Chinese tile game. In this game, you need to match tiles to remove them from play. Removing all the tiles completes the level! While the basic rules are simple, the game itself is not. Tiles can only be matched when they have a minimum of one free side. Season tiles will match even when they have different pictures. Certain tiles are trapped or reversed, complicating things further!
Playing through levels quickly will unlock medals and awards, as well as more playable levels. See if you can complete your entire Mahjong Quest!

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Butterfly Kyodai

Butterfly Kyodai is a matching game similar to the classic tile game Mahjong. To play, you need to match pairs of butterfly wings, which must be connected by straight unblocked lines with a maximum of three changes of direction. Matching the wings will remove them from the game, and your objective is to completely clear the screen before time runs out!

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Onnect Pair Matching Puzzle

Onnect Pair Matching Puzzle: This is a dessert matching puzzle game where must match up the desserts on the board to make them disappear. They have to be either next to each other, or there must be a clear path from one to the other. You can create space for this by eliminating other desserts off the board. This is very addictive and will also make you hungry as well! Good luck!

The aim of the game is to clear the board of desserts. Do this by clearing them two at a time when you find a matching pair that can be connected. This game will test and develop your observational skills as you desperately search to find matches on the board. You must have a razor sharp focus with an eagle eye to spot and quickly dispatch the board of desserts.

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10 Blocks

10 Blocks is deceptively simple! Although it takes its inspiration from Tetris, it is quite the brain teaser - and at times even more difficult.

This game breaks the rule of Tetris and essentially gives you all the control. No more blocks careening down at you, now you can choose where to put them. Simple! You start with 3 pieces you need to put in an open square space. After you place them, you immediately get 3 more pieces you also have to fit into that square space. Soon you're running out of space and the grey screen hits you with a terrible ‘no more moves' sign. Despite having more control, it seems to be even harder than Tetris!

It does, thankfully, lend some other rules from Tetris. If you close a line with blocks that line will disappear, giving you some space to fill up again. But you'll notice it takes a little longer to do than in Tetris, and you'll struggle to fit them in to get that cathartic disappearing line.

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School Memory Deluxe

School Memory Deluxe: This game uses your memory and observation skills. Your challenge is to find matching pictures. You play where you have to select two matching pictures in order to remove them from the board. 

It's a fun game for children, and helps your child to practice and train visual memory skills. They must remember which cards are in which location, and then match them up! This is a very fun and challenging game and an extremely useful one in terms of development of photographic memory and awareness skills.

To play, click with the left click on the mouse to unveil the photo behind the card, then using your memory try and remember where the matching card is on the board. On mobile devices, just tap the card on the screen to unveil the card.

This HTML5 based game works on Mobile, tablets and PC/Mac browsers.

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Super Candy Jewels

Experience some sugar-induced excitement as you match and blow up an array of candies in Super Candy Jewels! Super Candy Jewels is a sweet take on the classic tile-matching genre where you earn points and blow-up candied tiles by matching three or more of the same kind into a solid line. Blow up as many candies as you can to earn as many points as you can before you run out of moves. Super Candy Jewels is a family-friendly game that will keep you entertained through many a boring weekend.

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A Chemical Match

A Chemical Match is an online science/ chemistry-based game that will send you on an atomic mind-bender of confusion - as well as provide endless hours of enjoyment! With super-slick ambient graphics and simple acoustics, it’s a learning experience that anyone can enjoy. Match up the chemical items to win!

The aim of the game is to match as many items as possible. This will test your observation skills and speed skills. The clock will be ticking so make sure you don't buckle under the pressure. Scan the board for matches of three or more and then move around accordingly! Lets see if you are up to the challenge.

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Jungle Temple Blast

Play a challenging, match 3 jewel-swapping game with different missions! Jungle Temple Blast is an interactive, multi-level matching puzzle where you must complete specific matching tasks by swapping jewels around in a grid so that they line up in horizontal or vertical groups of three or more. Playable on mobile phone, tablet, notebook, laptop and desktop PC, you must hit specific targets depending on what your mission is in order to progress to the next level.

Skills required: As in many match 3 grid puzzle games inspired by the Candy Crush phenomenon, you must utilize fast reactions, hand-eye coordination, problem solving skills, shrewd observation, and dogged determination in order to succeed. Due to the different level types and fluctuating time limits, you need to adapt your strategy each time you take on the grid.

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Mahjong Dimensions

Mahjong Dimensions is a game very similar to the classic mahjong but it is played on a three-dimensional cube, where you have to select two similar blocks to eliminate them until the whole level is cleared. Clear the sides and slowly make it to the center to finish the level.

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Woodventure

Woodventure: Mahjong Connect is a fun and colorful introduction to Mahjong for kids of all ages! In this game, you progress on a path through a forest of mahjong levels. In each level, you’ll need to combine pairs of matching animal themed tiles — though to match, you’ll need to be able to make an unobstructed line of any length, but with no more than two changes of direction between the two tiles. Matching the tiles removes them from the board, freeing up gaps to make new connections between other tiles! Remove all the tiles to win the level.

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The Gladiators

The Gladiators is a puzzle based matching game, in which you fight other gladiators! Power up your fighter’s attacks by making matches in the grid below the action of the designated icons. Making longer chains will cause more damage, denying your opponent the chance to attack you. Keep matching to keep attacking and to win the battles.

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BBQ Skewers

Strap on your apron and grab your hand fan as you test your sorting ability in this festive and culinary logic game. BBQ Skewers is a logic-based and sorting focused game where your objective is to sort and skewer all the same pieces of food onto the same skewer, using empty skewer sticks to move around the pieces as you sort. You won’t be able to place different pieces of food on top of each other, only the same types, so plan carefully! BBQ Skewers is a fun and simple game that any age group would enjoy playing.

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Ancient Chinese Match 3

Play Ancient Chinese Match 3, the third instalment of the series, and have lots of fun doing so. This is better than ever before with new graphics and better interactivity! Challenge yourself and compare your score with friends and family as you try to match up 3 in a row! Have fun!

The aim of the game here is to match 3 or more of the same Chinese symbols or items. This game will test your observational skills as well as your fast hands. You must be quick to react to a possible swap as the timer on the left will not hang around for you! This adds a sense of pressure to your game so have you got the cool calm collected mindset of someone who can beat this game? Come and find out.

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Jewel Magic

Come and take a walk through the magical jewel filled forest in Jewel Magic, a magical and dazzling gem matching game. In Jewel Magic, your objective is to earn points by matching at least 3 gems of the same colour together in order to remove them. The more points you earn, the more likely you are to earn some cool powerups that you can use when you get stuck! Jewel Magic is sure to keep you entertained with its 120 logic and puzzle themed levels and classic gameplay. A game that all ages can enjoy!

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Jelly Challenge

A fun, classic-style match 3 puzzle game available to play on desktop, laptop, tablet, or mobile! Jelly Challenge is a straight-forward online matching game for kids and grown-ups where you score points by switching colorful jelly around a large grid, and arrange as many 3-in-a-row matches as you can. Similar in style to Candy Crush and Bejeweled, this addicting activity rewards good observation skills combined with fast reactions and mouse-clicking / screen tapping. Happy Jelly matching!

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Bubble Shooter Pro

Bubble Shooter Pro is an awesome color matching game, in which you shoot bubbles to make lines of three and remove the bubbles from the game. Remove all the bubbles without running out of shots to complete the level! Activate fun power ups such as a bomb, firework, or aiming lines, and join groups of players online to make bubble busting a global experience!

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Gummy Block Evolution

Relive or experience the classic thrill of playing a good old tile-matching game, only instead of tiles here they are colorful and expressive little gummy blocks. In Gummy Blocks Evolution you will try to earn as many points as possible by using the colorful gummies to create and complete columns and rows within the play grid to remove them. Make sure to plan your moves carefully as you will only have so much space within the grid and running out of space will result in a game over.

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Crewmates & Impostors Memory

Crewmates and Impostors is a card matching game from the studios of the popular multiplayer game Among Us. Each level has a series of cards, face down, of which you can reveal just two at a time. Revealing a pair removes them from the level, and your aim is to completely clear the level in as few clicks as possible before time runs out! Every level adds one more pair than the last, so to beat all eighteen levels will be a real challenge to your recall skills!

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10x10 Block Match

10x10 Blocks Match provides a puzzle game that is both casual and relaxing as well as one which is very engaging. The objective of the game is simple; earn as many points as you can by using multicolored blocks to create complete rows or columns. Each round/turn you will be presented with three groups of blocks that need to be placed into the game grid. The quantity and alignment of the blocks in each group will vary so plan your placements carefully. There is no timer in 10x10 Blocks Match, the only thing you must be conscious of is how much space you have available to place the new blocks into.

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Jewel Christmas

Ho, ho, ho! Here comes Jewel Christmas! This is a typical but very fun and festive match-3 game that will make you feel like Christmastime!

You know how match-3 games work. You just need to line up three of the same objects to score your points. Only this time, each piece is a Christmas-themed one!

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Candy Super Match 3

Match 3 or more delicious candies vertically or horizontally. Collect points by quickly and strategically removing matching groups of 3 or more candies by clicking and dragging one candy to the group of matching candies. Playable on iOS and Android mobile phone, tablet, laptop, notebook, or desktop PC, Candy Super Match 3 is a straight-forward, multi-level, candy removal challenge and matching-based puzzle game for kids of elementary school age and up. Playing against the clock, you must click and drag a candy to matching candies to eliminate groups of three or more adjacent, same looking candies from the play area. You have 30 seconds at the beginning of the game and for each matched candy you get an extra second. This extra time gives you a buffer needed when you need time to think and find matching pairs.

This HTML5-based, matching block puzzle game should work on iOS and Android devices as well as most web browsers for PC / Mac. To play the game with full screen, you may have to turn your device horizontally. Skills required include good strategic planning skills where you tactically remove certain groups of candies in order to create new candy groups. Although you should have plenty of time to complete each level, sharp focus, a sense of urgency, and accurate mouse clicking / finger tapping skills are also important, especially in later levels when the block configurations are more complex.

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Mahjong Flowers

Mahjong Flowers is a classic-style, matching puzzle game where you must find and eliminate identical, unblocked pairs of tiles from a large, stacked grid. The catch is that you can only select tiles that are ‘free’; you cannot remove tiles if they are ‘blocked off’ by a tile on top, or by two neighboring tiles positioned on either side (right or left).

For those unfamiliar with the premise of the game, Mahjong (aka Mah jongg) is an ancient Chinese tile game. Playable on Android mobile phone, tablet, notebook, laptop and desktop, this particular mahjong simulation is a more accessible, one-player version of the game where you score points for making matches, and must clear the grid before the clock runs out. The theme of the game is of a ‘relaxing spa’, so the tiles depict various related items such as lotus flowers, scented candles, massage oils, etc. This fun visual matching puzzle activity requires good observation and concentration skills, good tactical strategy, fast reactions, and the tenacity to find new matches. Happy tile matching!

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Mathematical model of the game Dobble / Habr

Reading difficulty levels

Introduction and rules of the game

Several years ago I bought the game Dobble (Dobble, original name “Spot It!”). This is a very simple, fast and fun game that I consider to be one of the best board games ever.

The game comes with 55 cards with 8 different symbols on each. These cards look like this:

1. An example of game cards. nine0009

One and only one character matches on every two cards. In the figure below, this is the pencil symbol:

2. Matching symbols on cards.

The first player to see a match performs an action with one of the cards, depending on the round of the game. For example, he takes it to himself or throws it to his opponent.
Often this will result in one of the cards that the players are looking for a match for changing. Because of this, you have to look for a new match, which may be a completely different character:

3, 4. The first card is replaced with a new one. Now there is a new match between them - the clown symbol.

How do they do it?

At first glance, it seems incredible that two cards have exactly one match, no more, no less. Questions immediately arise - how many symbols are there in the game? There cannot be too few of them (then there will be more than one match on the cards) or too many (then there may not be any matches on the cards at all). nine0004 In addition, it is obvious that the symbols are arranged on the cards in a special order that guarantees a single match for any two cards.

The elementary skills of google-fu lead us to the stackoverflow site, where it is described why this happens: http://stackoverflow.com/questions/6240113/what-are-the-mathematical-computational-principles-behind-this-game

The game uses finite geometry principles. Although this phrase contains the word “geometry”, this concept refers more to combinatorics than to geometry. It operates on a finite number of points, which can be located, in particular, in the form of a projective plane. nine2+5+1 = 31. The projective plane of this configuration is used in a simpler version of the Dobble game called “Dobble 1,2,3”.

The connection between points and lines for the projective plane is specified using the incidence matrix. Its appearance is presented in the Incident Matrix for the Dobble Game section.

Finite geometry for babies

Much later than writing the original article, I attended a lecture by Alexei Savvateev, where he talked about projective geometry in a much shorter and clearer way. But since I have neither the strength nor the desire to rewrite half of the article because of this, I simply recommend his book "Mathematics for the Humanities" if my savage attempt to explain the structure of a car on my fingers is incomprehensible or boring. nine0016

More generally, a finite affine plane of order 92 + n straight; each line contains n points, and each point belongs to n + 1 of the line. [1]

With affine geometry finished, we pass to the second type of geometry on the plane — projective.

In projective geometry, on the contrary, any two lines intersect at the only possible point, and therefore there are no parallel lines. [1]

The previous sentence describes the second axiom of projective geometry. The first and third are the same as in the Athenian. nine0009

Since the third axiom requires the existence of at least four points, the plane must contain at least 7 points to satisfy the conditions of the first two axioms. This simplest projective plane also has 7 lines; each point belongs to three lines, and each line contains three points. Such a projective plane is often called the "Fano plane". [1]

Fig. 8. Fano plane. (Source en.wikipedia.org)

It's hard to make out all 7 lines in this picture at once, so here's a pony version of the same plane:

Fig. 9. Fano plane with colored lines. (Source mathpuzzle.com. Used with permission from Ed Pegg Jr.)

So the Fano plane is a 2nd order projective plane with 7 points and 7 lines.

What does the cards have to do with it?

What happens if we reformulate 2 axioms of finite geometry, replacing “line” with “symbol” and “point” with “card”?

You get this:

1. For two different cards, there is only one symbol, which is shown on both cards. nine0102
2. For two different characters, there is only one card that contains both of these characters.

Now, based on this knowledge, let's see what Dobble would look like in the simplest case. It would have 7 cards and 7 symbols, each card would have 3 symbols (since 3 lines intersect at one point):

Pic. 10. An example of the minimum possible set of cards for Dobble.

The following 7 characters are used here:

, , , , , ,
Whatever 2 cards we take, they will have a common symbol depicted next to the line on which both cards lie.
For example, a card in the lower left corner and a card in the middle of the right side have a common symbol . It is depicted next to the straight line.

Low order projective planes

A visual demonstration of low order projective planes can be found on the Wolfram website: http://demonstrations.wolfram.com/ProjectivePlanesOfLowOrder/
It is formatted as a CDF (Computable Document Format) document, for which you need to install the CDF Player.

Here is an example of a 3rd order projective plane:

11. Image of the projective plane of the 3rd order.

It's hard to understand what's going on, so let's take 2 arbitrary lines:

12. Intersection of two lines of the projective plane of the 3rd order.

As we can see, they intersect at exactly one point. The lines themselves contain 4 points. nine0009

To make sure that there are 4 straight lines going through each point, you have to switch the displayed line pairs in the interactive document and focus on one point.

Projective planes of higher orders are shown in the figures below.

Fig. 13. Projective plane of order 4

14. Projective plane of order 5

15. Projective plane of order 7

In the given sequence, there is no image for the projective plane of the 6th order. It's not a mistake.

Although Wolfram generates a graphical representation of such a structure, it does not satisfy the axioms of projective geometry, and is not a projective plane.

It is assumed, but not yet proven, that the order of a finite plane is always a power of a prime number. [1]

How to construct a projective plane?

The graphical representation of the projective plane looks interesting and illustrative, but how to find such a combination of points that it has the properties described above? nine0009

The easiest way is to visit sites where pre-calculated data for projective planes of different orders are posted.

For example, for a projective plane of order 7, you can visit this page: https://web.archive.org/web/20170619110638/https://www.uwyo.edu/moorhouse/pub/planes/pg27.txt
There is a matrix of numbers. Lines are cards (dots) in terms of Dobble. The numbers in the lines are the serial numbers of the characters (lines), starting from zero, which are drawn on each card (passing through the given point). nine0009

You can also use math packages such as Matlab to build the incidence matrix of the projective plane. [2] [3]

Incidence matrices

Incidence matrix is one of the forms of graph representation, in which links between incident graph elements (edge ​​(arc) and vertex) are indicated. Matrix columns correspond to edges, rows correspond to vertices. A non-zero value in a matrix cell indicates the relationship between a vertex and an edge (their incidence). [2]

One of the simplest examples of an incidence matrix is ​​a 2x1 matrix for an undirected graph of two vertices connected by a single edge:

16. An undirected graph of two vertices connected by a single edge and its incidence matrix.

A more complex example of a graph and its incidence matrix:

17. An undirected graph with 4 vertices and its incidence matrix. nine0009

As can be seen from the last example, in the incidence matrix of the graph, there are exactly two ones in each column, because one edge connects two vertices.
The projective plane is a hypergraph, since one line (edge) connects several points (vertices). Therefore, in the incidence matrix of the projective plane, units in each column occur n+1 times, where n is the order of the projective plane.

For the Fano plane shown in fig. 9, the incidence matrix will look like this:

Fig. 18. The incidence matrix of the Fano plane.

For ease of understanding, zeros are not shown, and ones are replaced by the symbol X .
In such a representation of the projective plane, the principle of duality of points and lines is clearly visible - the line passes through exactly 3 points, and, at the same time, the point belongs to exactly three lines.

Construction of the projective plane by enumeration

The current knowledge about the properties of the incidence matrix is ​​sufficient to construct it for the projective plane of any order n. You can use the following pseudocode for this:

 For all columns For all lines If there are n+1 ones in a column, then go to the next column If there are n+1 ones in a line, then go to the next line For each previous column X If there is one in column X on the current line and If there are already matches in rows for column X and the current column, then go to the next line Put a unit Go to next line Go to next column 

Following this algorithm, we will obtain a symmetric matrix for the Fano plane:

19. The incidence matrix of the Fano plane, built using the pseudocode algorithm.

This matrix does not match the previous one. Actually, it doesn't matter.
Permuting any two rows of the incidence matrix is ​​equivalent to renumbering the vertices of the graph.
Permuting any two columns of the incidence matrix is ​​equivalent to renumbering the edges of the graph (if they are numbered in advance). nine0009

Incidence matrix for Dobble

For Dobble, in the incidence matrix, the rows represent the cards, and the columns represent the symbols on them.
Thus, permuting any two columns of the incidence matrix is ​​equivalent to changing the order of characters on the card. However, the symbols on the card are out of order, so this operation does not affect the appearance of the cards.
Swapping two lines means that on all cards, two corresponding characters replace each other. nine0009

The last operation changes the appearance of the cards, which means that the set of symbols that we see in the game is just one of the possible combinations.
The number of character sets for a single card is a combination without repetition of 57 elements by 8 elements. It is calculated by the formula

The incidence matrix for the Dobble game is shown in the table below. It is transposed, i.e. the rows are the characters and the columns are the cards (the picture is clickable). Habr does not allow to insert a picture of the required size and quality, so the fullsize option is a separate link: https://github.com/Skybladev2/DobbleMathModel/blob/master/images/Dobble%20incidence%20matrix.png

Fig. 20. The incidence matrix of the Dobble game.

Which two cards are missing from the game?

There are 57 rows and 55 columns in the table with the game incidence matrix. This means that there could be 2 more cards in the game.
This means that the symbols that should be on these cards are less common in the game than the rest. The number of symbols in the game is shown in the last column of the table.

The number of characters from the missing cards is:

• , , , , , , , , , , , , and
  (total 14 characters) occur 7 times.
• occurs 6 times.

What do the missing cards look like? To answer this question, let's take any of the above characters in the incidence matrix (except for the snowman), and place it on the missing card (for example, the penultimate column).

Then we find all the cards (columns) on which this symbol is depicted. This means that on all these cards the symbols match, and there can be no other matches. nine0009

Since these cards already have a match with the selected symbol, we will delete from the penultimate column all the symbols that are found on the remaining cards.
The missing symbols that have not been crossed out make up the symbols of one of the remaining cards. Since there are exactly 8 of them, the type of the second missing card is uniquely determined.

These 2 cards are:

21. Possible view of missing cards #56 and #57. nine0009

It remains to answer the last question - does the absence of these cards affect the property of matching a single character between two cards (that is, suddenly there are no matches between some cards)?

The answer to it is obvious if you look at the game's incidence matrix - no, it doesn't. There is still only one match between any two cards (columns).

Why is there 2 cards less than the maximum possible number in the game?

Originally, the rules for the five mini-games were not in the booklet, but on five separate cards. At the same time, a maximum of 60 cards could be printed. Therefore, the authors of the game decided to remove 2 cards, so that in the end we get 55 cards with symbols + 5 cards with rules. (Special thanks to Guillaume Gille-Naves for the clarification). nine0009

Acknowledgments

I would like to express my deep gratitude to the network of board games stores “Igroved” for their help in writing this article.
Thanks to Ed Pegg Jr for providing the Fano plane image.
Separately, I want to note one anonymus and Master for their help in checking the article.
I thank the store "Desktop Grad" for their help in preparing the article for publication.
From the bottom of my heart I thank the authors of the game Igor Polouchine, Denis Blanchot, Guillaume Gille-Naves, as well as the Asmodee company for the right to use images from the game. nine0009

12 great family board games

Of course, board games have great benefits: they develop attention, memory, reaction time, and the ability to work in a team. But it's also a great activity for the whole family: here are 12 games from the Board Games - Lifestyle publishing house and the Igroved store that are definitely worth a try.

Tumbleweed

This Russian game has just won the prestigious international award in the world of board games "KinderSpiel des Jahres 2020", and in 2019won the French Grand Prix du Jouet - and deservedly so! It helps to develop an eye, coordination of movements, teaches you to follow the rules - but in addition to useful aspects, it is also just very fun, dynamic and children like it. Throw a hedgehog ball, harvest and hurry to the house so as not to meet the fox. You can play both competing with each other, and all together against the fox.
Age: from 4 years old

Rummikub

This game has simple and clear rules, and despite the lack of pictures, it is very exciting. Players make common digital combinations on the playing field, trying to be the first to get rid of their chips. The game is suitable for adults and children over 7 years old, but there is also a version for kids over 4 years old with large multi-colored figures (you still need to know the numbers). The game helps to develop logical and mathematical thinking. nine0004 Age: from 4 years old

Insidious Fox

A valuable pie has been stolen! To get it back, players will have to act together, study clues and apply deductive reasoning, assess the likelihood of different events and pay attention to details. There is no way to do without teamwork!
Age: from 5 years old