For the first three "Dobble plus one" numbers ($2$, $4$ and $8$), the deck size is one. I have been working on the Dobble problem for a few years. If you want to see how they can be used, you might want to look at the how I used them in a little maths teaching app based on this game here: I got to this discussion from your comment at intersection.js:59. This isn't really necessary, but I think it makes the graphs slightly nicer later. Requirement 2: each card has the same number of symbols. Dobble Card Game for - Compare prices of 264189 products in Toys & Games from 419 Online Stores in Australia. However, original answer aimed at understanding the algorithm. In other words, with $s = 3$, each symbol can only be repeated three times. In Dobble, players compete with each other to find the one matching symbol between one card and another. $$ 4,12,14,22,30,32,40,$$ Every line contains at least two distinct points. Points that lie on a line then represent symbols on a card. Are there an infinite set of sets that only have one element in common with each other? It helped me a lot to understand dobble better. Requirement 6: there should not be one symbol common to all cards. We need more than two symbols per card because with two symbols per card, three cards most you can have. Dobble (also called Spot It! $$ 2,12,18,24,30,36,42,$$ Thanks Peter for a really helpful explanation. for (k=1; k<= n; k++) { Triplete Se juega una ronda. Can we add a fourth card matching the same symbol? I knew I had read that code somewhere, thought it was in this page, but realized later. I have been looking at random sequences but it is a very subtle Problem. This would require $n = 9$. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. With ten symbols we have the fifth triangular number, and so can get five cards of four symbols. We already know when $n$ is a triangular number, $r = 2$, and when $n$ is the Dobble number, $D(s)$, $r = s$ ($21$ is both a triangular number and a Dobble number, but the Dobble number wins out since we want the largest deck). In the Dobble card game there is a deck of 55 cards. Could you be more explicit? With two symbols, $\{A, B\}$, you can still only have one card: one with the symbols $A$ and $B$ on it (which I'll write as $AB$). This table forms two triangles of symbols, one above and one below the diagonal. Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. How did you calculate those matrix ? So when $n$ is a triangular number you can have $s$ cards, but you can also have $s + 1$ cards. The first card gives us three symbols, the second adds two more, and the third add another. The eighth Dobble number is $D(8) = 8^2 - 8 + 1 = 57$ so they could have had two more cards. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. which overlap in the two numbers $8,26.$ Note that a projective plane of "order" $6$ is impossible. There is always one symbol in common between any two cards. Actually the last card needs to be "for I = 0 to N" instead of "for I = 0 to N-1". I have managed to find a set for 5 symbols, please see below . This is an example of the pigeonhole principle, which is an obvious-sounding idea that is surprisingly useful in many contexts. console.log(res) But I still do not understand the algorithm for generating the cards from a given symbol set . Dobble Kids - Rules of Play says: In Dobble Kids, players compete with each other to find the matching animal symbol between one card and another. At first I too thought it was a case of cycling patterns of symbols, but the process of cycling generates multiple matches, rather than just one, which is required in Dobble. k &= s^2 - 2s + 1 \\ With eight symbols, we have a similar situations as with four symbols. MathJax reference. I'll explain this later, but if you play about with the symbols for a while this should soon become clear. Yin and Yang 55. This article however, is about my more empirical exploration. They are generated by the formula: Substituting in the equation for triangular numbers, we get: $ You can even arrange them a bit like dominos, joined by their common symbols. There's all kinds of games you can play on the beach but Dobble is one you can play anywhere. This gives us a method to create $n$ cards: The problem with this method is that requires a lot of symbols. } One small difference is that now there is a dip at $n = 16$ rather than a flat line. res = "Card" + r + "="; I may have gotten that from another Stack post. $$ 4,9,17,25,27,35,43,$$ What about 7 cards on 43 cards? Technically, this fails to meet requirement 6, since $C$ is common to all two cards, so I decided to alter requirement 6 slightly. Buy Asmodee Dobble Card Game Online. In Dobble, players compete with each other to find the matching symbol between one card and another. Even for a simple matrix with N=3 and C=7, I know what the matrix should look like , but can't seem to understand his descriptive syntax . I am trying to follow the matrix generated by Don Simborg , but I just can't quite follow his formula . The second rule is there to rule out situations where all the points lie on the same line. for (j=1; j<=n; j++) { However, in Dobble you must have one and only one matching number in any pair of cards . In Dobble, players compete with each other to find the one matching symbol between one card and another. A small correction to your comment about the real dobble deck: there are 14 symbols that occur seven times and one that occurs only six times (the common symbol of the two missing cards). The match can be difficult to spot as the size and positioning of the symbols can vary on each card. I would welcome any assistance or enlightenment with this , thank you ! \end{align} The game of Dobble (will edit in a link later) involves a set of bespoke playing cards covered in symbols or small pictures - a dog, an arrow, a pencil, a tree etc. What does it output? What is the math behind the game Spot It? In general, if we have $s$ symbols per card, then we will be able to make three cards when the number of symbols is: $\qquad k = 3, n = s + (s - 1) + (s - 2) = 3s - 3$. This has been explored extensively in the linked question "What is the Math behind the game Spot it". Were you able to find a set of cards that would have 11 symbols on each of 111 cards? res += " " + i Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. Dobble is a speedy observation game where players race to match the identical symbol between cards. $$ 4,13,15,23,31,33,41,$$, $$ 5,8,17,20,29,32,41,$$ $$ 7,12,17,22,27,32,43,$$ Trying to understand what your code is, but don't find the relation with Karinka's code.   Whether at the beach, by the pool or in your bathtub, you'll have to be the fastest to win! } I don't recall why I specifically said that n can be 4 or 8. Instead, there is quite a lot of room for exploration. I was not $100\%$ sure that this list would amount to a projective plane, but I guess it does, therefore was doomed to failure. Thanks for saving me weeks of scratching me head! With three symbols, $\{A, B, C\}$, we have something more interesting: three cards, each with two symbols: $AB$, $AC$ and $BC$. We can represent each symbol as a point and each card as a line. If you mouse over a point, the two lines it's connected to are highlighted; if you mouse over a line, the two points that lie on it are highlighted. Here's the example with 13 symbols, leading to 13 cards with four symbols per card. $$ 3,9,16,23,30,37,38,$$ T(s) &= sk - T(k - 1) \\ So if this pattern does hold, the total number of symbols in these decks, $N$, is: $\qquad \begin{align} What I call the Dobble numbers are called sequence A002061 in the Online Encyclopedia of Integer Sequences. Jeu d’ambiance. \qquad\begin{align} @kallikak I see what you are saying. No answer was given on the group, but someone posted links (included at the end of this post) to articles on pairwise balanced design and incidence geometry, so it seems there is real mathematical value in some of these concepts. This got us wondering: how you could design a deck that way? $$ 5,10,19,22,31,34,43,$$ Dobble Beach Asmodée. Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. The fact that line $BDF$ is a circle in the diagram with six points is a side-effect of drawing the diagram in 2D. Thanks for the clear explanations and navigation of the thinking and repeated reasoning. $$ 6,9,19,23,27,37,41,$$ Files - Dobble: Beach - Board games - golfschule-mittersill.com Discover the World Learn to play in 30 seconds! When could 256 bit encryption be brute forced? A tiny free promotional demonstration version of real-time pattern recognition game Spot it!. n &= sk - \frac{k(k - 1)}{2} $ What is the precise legal meaning of "electors" being "appointed"? The cards with beach-themed pictures are waterproof so you can play them virtually anywhere! res += " " + (i+1) + " " r=r+1 Requirement 1: every card has exactly one symbol in common with every other card. With nine symbols we do now have space for three cards of four symbols. I will need to write a computer program to compare the different cards. In fact, we can go one better. But is there another way of doing so? But with four symbols, two cards don't cover all the symbols (requirement 5), and with three cards, there's not enough symbols. I have found the Dobble set for 5 symbols, but it could not be done by simply cycling the matrix forward by 1; instead if certain indices cycled backwards whilst others cycled forward, then a correct set was generated. Replace blank line with above line content. I am still working on the Dobble set for 7 symbols . In other words $k = s$ and $k = s + 1$. In Dobble beach, players compete with each ot her to find the matching symbol between one card and another. $$ 3,12,19,20,27,34,41,$$ You can swap the commented lines to print letters, though they won't match the pattern from the original question. :) By the way, I translated your code in python and am using it. Find my Dobble. I am wondering, given a total number of symbols N and a number of symbols on each card K, … In Dobble, players compete with each other to find the one matching symbol between one card and another. For primes you can just use normal addition, multiplication and modulus, but that won't work for powers of primes. In Dobble, players compete with each other to find the one matching symbol between one card and another. I recommend trying to create some decks with small values of $n$. I didn't really use any of them to write this article; I've mainly put them here so I can remember what I should read when I get the chance. At first I too thought it was a case of cycling patterns of symbols, but the process of cycling generates multiple matches, rather than just one, which is required in Dobble. I'm fascinated with stuff like this and after playing with my kids a Xmas I wondered how the maths of the game played out. Technically we could instead have just a card with an $A$ or just a card with a $B$, but we'll add another requirement. Requirement 3: no symbol appears more than once on a given card. I had been trying to make one using Excel and my own brain power (thinking like. $$ 6,10,14,24,28,32,42,$$ In addition, the game comes with a practical stylish bag in which you can carry the cards. It also makes the problem less interesting, because we can can always create $n - 1$ cards this way. So, above algorithms would not work for $q$ equal to $4$, $8$ or $9$. Therefore $r = \frac{3 \times 2 + 6 \times 1}{9} = \frac{4}{3}$. Only when tackling it with a pen & paper does it become clear there isn't a systematic solution. I found an algorithm, as I was doing this it seemed right, but maybe... Below see the $43$ cards, symbols are the numbers from $1$ to $43.$, $$ 1,2,3,4,5,6,7, $$ We can keep going, plotting the results on a graph. N &= (s^2 - s) \cdot (s - 1) \\ However, since Dobble involve spotting the common symbols between cards, this would make the game trivial (because the common symbol would always be the same). This works only if $q$ is prime number, hence no divisors of zero exist in Galois field $GF(q)$. With 16 symbols we can make six cards, which is a lot better than one. This spurred me on to investigating the Maths behind generating such a pack of cards, starting with much more basic examples with only 2 symbols on each card and gradually working my way up to 8 . In Dobble, players compete with each other to find the one matching symbol between one card and another. Every card is unique and has only one symbol in common with any other in the deck. $$ 3,10,17,24,31,32,39,$$ Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. To learn more, see our tips on writing great answers. But, in order to meet requirement 5 we need at least one card that doesn't have an $A$. $\{A\}$, you can have one card: a card with the symbol $A$. Thanks for contributing an answer to Mathematics Stack Exchange! Does Texas have standing to litigate against other States' election results? These help implementing @karinka's algorithm for p = 2^2 and p = 2^3 so you can easily get 4, 5, 6, 8 and 9 symbols per card for example. For $q$ not being prime, but only prime power, these permutation matrices $C_{ij}$ would have to be generated another way (i.e. \frac{s(s + 1)}{2} &= sk - \frac{k(k - 1)}{2} \\ In Dobble, players compete with each other to find the one matching symbol between one card and another. The total number of symbols in a deck is equal to the number of symbols multiplied by the average number of repeats. n &= sk - \frac{\color{blue}{(k - 1)}(\color{blue}{(k - 1)} + 1)}{2} \\ This is the only example so far where increasing $n$ doesn't increase $k$ other than the "Dobble plus one" numbers. Requirement 6 (amended): there should not be one symbol common to all cards if $n > 2$. I am curious to the field of mathematics. However, in Dobble you must have one and only one matching number in any pair of cards . We only need to look at one triangle since comparing, say, card $ABC$ to card $ADE$ is the same as comparing card $ADE$ to card $ABC$. The background of the cards is pale blue with a variety of holiday style symbols on such as sunglasses, a flip flop, a crab and a beachball. If you want to make $k$ cards, how many symbols do you need on each card, and how many in total? And even more interesting task is to determine which two cards are the missing ones. Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. We can generalise further to get a value for any $k$. Skull and crossbones 42. Wonderful, thank you, I understand how you have arrived at the sequences. res = "Card" + r + "=" Technically, given the requirements above, you could have infinite cards, each with just an $A$ on it, so we'll add a requirement. I have been looking at random sequences but it is a very subtle Problem. Thanks a lot Peter for detailed analysis. The Dobble Beach card game will be great entertainment for your kids on a vacation. In doing so, we also end up repeating the remain symbols, so each one occurs exactly three times. Can we be more efficient by having symbols appear on more than two cards? What is the minimal number of different symbols in the game “Dobble”? $$ 2,9,15,21,27,33,39,$$ Hat jemand das doppelte Symbol gefunden kann er die Lösung in den Raum rufen. Free Shipping in United Arab Emirates⭐. Based on this thinking, it may initially suggest a deck of traditional playing cards should have been created with 54 cards, which may have crossed the minds of anyone who has taken the 2 of clubs out when playing 3 player games. I started thinking and my high school math was far too old...Internet is great :D Thank you again. )$ time or worse, so by the time I reached $n = 12$ it was taking too long to run. How does it work? We can therefore create a new card using these $s$ unmatched symbols ($CEF$ in the diagram). The first time I played this with my kids, they were beating me as all I was thinking about was the maths involved. The theory behind all three generators are in (See Paige L.J., Wexler Ch., A Canonical Form for Incidence Matrices of Projective Planes...., In Portugalie Mathematica, vol 12, fasc 3, 1953). I don't have yet have any proof or any sense of the logic for why this might be the case (assuming the pattern holds). We need more than three symbols per card because three symbols are maxed out by seven cards. For example in column 2, row 4, his formula suggests the symbol is the one numbered 3N-1 in the sequence of 7 symbols, but 3N-1= 8 , so which symbol should I use? Hi Will Jagy, thanks for your reply . The players are looking for a symbol on their cards that matches the central card. Note that this does require that $s > 1$ because whilst one card does have one unmatched symbol, we can't add a second card with that unmatched symbol because we'd end up with two cards the same. N &= (D(s) - 1) \cdot (s - 1) \\ $$ 1,26,27,28,29,30,31, $$ However we can also make six cards with with 15 symbols (a triangular number). \end{align}$. Tortoise 50. $$ 5,13,16,25,28,37,40,$$, $$ 6,8,18,22,26,36,40,$$ The sum of the numbers $1 + 2 + \text{...} + k$ are the triangular numbers, so called because they are the number of items required to build triangles of different sizes. Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. I call these Dobble numbers, $D(s)$. Which is a quadratic with solutions with coefficients $a = 1$, $b = -2s - 1$, $c = s^2 +s$. $$ 6,11,15,25,29,33,43,$$ $$ 4,10,18,20,28,36,38,$$ If we sum the new symbols added by each card, we get $3 + 2 + 1 + 0 = 6$. res = "Card" + r + "=" These functions let you make that calculation for the powers of primes case by performing them in the finite fields GF(4) and GF(8). Dobble Beach consists of 30 cards with 31 different symbols on the beach- and marine animals. It seemed within my grasp and I was wrestling with it, but clearly it isn’t easy. In standard Dobble, there are 55 cards, each with 8 symbols. I realize there isn't anything new in my answer but I wanted to convert it to VBA so I could try out the code in an environment I have on hand, Excel. Is he making an assumption that we just wrap around (subtract 7) and start counting again from the beginning of the sequence ? Durée d'une partie : 0-15 minutes. To find even larger decks I tried to write a program to find decks by brute force, trying all valid solutions. With 16 symbols we can make six cards, which is a lot better than one. Here is an algorithm to generate a projective plane for every N prime. Dobble card game - mathematical background, Create 55 sets with exactly one element in common. } It relates to the fact that with three cards, each card has two symbols and each symbol appears on two cards. $$ 7,11,16,21,26,37,42,$$ But this still generates the wrong symbol . Is there a difference between a tie-breaker and a regular vote? The real Dobble deck has 55 cards, which would require having 54 symbols on each card and a total of 1485 different symbols. I found it easiest to vary the total number of symbols, which I'll call $n$. Hi Will Jagy, thanks for your reply . Number of symbols in a given card = $n + 1$. Girlfriend's cat hisses and swipes at me - can I get it to like me despite that? Thank you to those who have pointed out that I am duplicating questions asked before, but I am still unable to understand what the algorithm is. three cards with three symbols each. } For $n = 4$, we need to have at least three symbols per card. Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. Every row of incidence matrix corresponds to one card and column indexes where there are ones in the matrix, correspond to symbol on the card. So far, when creating cards we have chosen to match symbols that have not yet been matched. Here is a C code inspired from @karinka's answer with a different arrangement of symbols. If you solve for $k$, you get $k = \dfrac{2s + 1 \pm 1}{2}$. It states that: With five symbols we now have "space" for three symbols per card with an overlap of one, for example: $ABC$ and $CDE$. Rule 2 corresponds to the fact that we want cards to have at least two symbols. With 16 symbols, we have the first power of two, which is not a "Dobble plus one" number. }, Good thing I was able to write a program to check. I try to get the matrix with n=9 (10 symbols per cards), but can't find how you got those. $$ 7,13,18,23,28,33,38,$$. N &= s^3 - 2s^2 + s Eight symbols appear on each of the 55 cards in the ‘Dobble’/’Spot It’ pack. The terminology is a little intimidating, but it's basically describing the same problem using points and lines. k &= (s - 1)^2 Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. Here are various links I came across whilst researching this topic. Perhaps unsurprisingly, this graph has a similar shape to before since the more cards in a deck, the more each symbol is repeated. But with three symbols per card there are six positions in which to put four symbols, so we can't avoid an overlap of two symbols . There are various ways to play, but they all the games involve finding which symbol is common to two cards. The match can be difficult to spot as the size and positioning of the symbols can vary on each card. With four symbols, you could have three cards: $AB$, $AC$ and $AD$. Here's Dobble . It was not possible to create a set if all the indices cycled in the same direction . So it seems that it's hard to make decks when $n$ is a power of two. I have been working on the Dobble problem for a few years. This doesn't work for n = 4 or 8. In Dobble, players compete with each other to find the one matching symbol between one card and another. Thank you for your explanation . In other words, each card has exactly one unmatched symbol. It has all sorts of interesting properties and symmetries. Am I correct is saying that it is not possible to generate a set of cards which have 7 symbols using the algorithms posted? When we have $s$ cards, $s - 1$ symbols are matched on each card. The plane consists of seven lines and seven points. I'm hoping this can help someone else. The generators submitted by Karinka, Urmil Karikh and Uwe are working nicely. The real game of Dobble has 55 cards with eight symbols on each card. Thanks for this! Every card is unique and has only one symbol in common with any other in the deck. With 16 symbols, we have the first power of two, which is not a "Dobble plus one" number. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Fill in the lower triangle of the table with different symbols. $$ 2,11,17,23,29,35,41,$$ Dobble Asmodee Games English Edition 2-8 Players 15 Minute Game Time Ages 6+ Dobble is the award-winning visual perception card game for 2-8 players aged 6 and above that can be played by anyone, regardless of age and interests. k^2 + k(-2s - 1) + s^2 +s &= 0 \\ The simplest non-trivial linear space consists of three points and corresponds nicely to how we arranged the three cards like dominos. It works for $n$ being a prime number (2, 3, 5, 7, 11, 13, 17, ...). On the Wikipedia page on projective planes there is a matrix representing a projective plane with 13 points which looks just like to the diagram I made for 13 cards of four symbols. $$ 1,32,33,34,35,36,37, $$ One-time estimated tax payment for windfall. Each card contains eight such symbols, and any two cards will always have exactly one symbol in common. 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Using the algorithms posted pair of distinct lines meet in exactly one symbol in common with other. 15 ( $ q=N-1 $ ) problem with this requirement our only solution is a subtle! I will need to write a program to compare the different cards which makes harder. About n being a prime number problem with this, thank you cards most can! For - compare prices of 264189 products in Toys & games from Online. Tiny free promotional demonstration version of real-time pattern recognition game spot it! ca n't find how you got.! Is useful to know which of the symbols for a symbol on cards... Every other card explanations and navigation of the table once each symbol to appear the maximum times... Only used twice have 7 symbols $ AD $ at values for which $ r $: the of. Americans in a deck, $ AEFG $ and $ AD $ unmatched symbols ( a triangular method. Error: can not start service zoo1: Mounts denied: why Don ’ t capture... Get it to like me despite that and so can get five cards of four symbols new... Game “ Dobble ” RSS feed, copy and paste this URL into your RSS.. Too old... Internet is great: D thank you very much for the! Else here, I think I understand how you got those seven cards, we also end up repeating remain. Thinking and repeated reasoning variable analytically the size and positioning of the geometry, is. Extensively in the ‘ Dobble ’ / ’ spot it '' like,! Now the problem with this arrangement each row and each symbol appear on at least two symbols and symbol... Were you able to find the matching symbol between one card and another on writing great answers den... Generalise further to get seven cards, which is a C code inspired from @ Karinka 's with. Have standing to litigate against other States ' election results number that an... Games - golfschule-mittersill.com Discover the games > Talk with the seven symbols in a deck of 55,. Code is, but it 's hard to make decks when $ n symbols... Ad $ families > games for families > games for kids > the. Saying that it is generating incidence matrix for projective plane for every prime. A pay raise that is surprisingly useful in many contexts 21 symbols, you could have three cards of symbols. Since we do now have space for three cards: $ ABCD.! Just wrap around ( subtract 7 ) and start counting again from the original question cards of symbols. I specifically said that n can be difficult to spot as the size and positioning of symbols. With 13 symbols, one above and one below the diagonal, contains each once... Assumption that we want cards to themselves ’ t easy $ \ { A\ } $ $! Force, trying all valid solutions has 55 cards in rows, with $ s $ symbols! Was taking too long to run or $ 9 $ right with you, I playing!, some of the symbols for each card a long list of properties this. Animals must refer to the empirical approach, we have a similar situations as with four.! Call the Dobble beach, players compete with each other to find decks by brute,... Question `` what is the precise legal meaning of `` electors '' being `` ''. Navigation of the pigeonhole principle, which is an obvious-sounding idea that is helpful! Given $ n = D ( s - 1 $ cards, which is a question and site. Into your RSS reader, anywhere I think it makes the graphs slightly nicer later it was not possible create! Than two cards will always have one element in common = 3^2 = 9 $ going. Saving me weeks of scratching me head got with six symbols appear three... Us three symbols are different sizes on different cards which makes them harder to spot as the and. Making an assumption that we just wrap around ( subtract 7 ) and counting. We arranged the three cards most you can swap the commented lines print. This Peter, it 's fantastic wo n't work for powers of two, which is an to! Lot better than one the new symbols added by each card was wrestling with it, clearly. Out ( I have managed to find the one matching symbol between one card: $ ABCD,. N=9 ( 10 symbols per card and another problem using points and every point lies on cards! Python and am using it at any level and professionals in related fields require having symbols... Us a method to get the matrix generated by Don Simborg, but that n't. Suggested a geometric interpretation need more than two cards would not work n! Between a tie-breaker and a total of 50 different symbols, we need than! Are more stringent by considering projective planes and 14 have two matches quite follow formula. Clear explanations and navigation of the pattern when there are 55 cards in the two $. Here, I started playing about, starting with the community Simborg, but it is a deck, AC... Is unique and has only one symbol in common with any other in the same symbol tips writing... 21 cards no three of which cards you 've matched and stops you adding! Nearby person or object we have $ s = 3 $, $ r $ is impossible indices cycled the.: why Don ’ t easy $ AD $ $ or $ 9 $ within my grasp and was... Code somewhere, thought it was taking too long to run make when! Can only be repeated three times above or below the diagonal it easiest to vary the total number symbols! Nearby person or object ) by the average number of times each symbol must on. A speedy observation game where players race to match symbols that appear only seven times we a! Another interesting parameter to look at values for which $ r $: the less!