I have implemented math as a language in Scrabble3D. It worked already in the old version. Attached are some screenshots of demo play in the latest version.
Math scrabble could be a fun tool for math learners, but it can be played by anyone with more complex operators in the operator set (letter set).
This implementation works with changes only in the dictionary and the letterset,as any other scrabble3D language does. Dictionary is handmade almost from scratch, but it is not even needed for human games. It's small but can easily be expanded.
I prepared a dictionary (attached) with numbers from 0..99 by 0..99 calculated with all operations, and generated a letter set based the resulting count of 'letters' (as follows; just copy/paste).
Human games make sense if a move can be checked. And that makes it necessary to have a good dic. I'd like to generate a good basis for the version. Therefore we should discuss which ops we add.
Unlike the other scrabble languages, the number of "words" or equations is unlimited. You can add to any equation. So allowing only equations in the dictionary is not flexible, especially because in math there is no doubt if the equation is ok or not. I haven't played online but I thought you can decide if a word is ok without the dictionary.
I think any operators could be added to letterset and dictionary categorized by operators or difficulty level or perhaps both. It would be interesting to have decimal numbers. The idea is that you can always select any subset of the letterset and dictionary categories.
Could it be done automatically: change the letterset math symbol amount to zero if the corresponding category is not checked? Perhaps this is unnecessary.
I think that it would be better to replace ∜ by mod (remainder obtained whenever one number is divided by another number). Although no equation present in maths dictionary make use of mod, so it has to be manually validated always, not useful against computer opponent players but only with human opponent players. We can manually build up a maths dictionary, but number of mathematical equations is unrestricted. Where do you think that the precedence of mod operator goes on?
Computer programming languages also make use of special operators like bitwise and, bitwise or, bitwise xor, left shift, right shift, etc. but they are not fundamental operators that are taught at primary school levels. Because computer is binary system, they are suitable and used for binary computer systems. Including them means that too many secondary operators will be included into the letter set. But making use of that mod, it is only a basic operator and not a contrived operator at all whatever ever.
Zitat von Raman im Beitrag Unfixed bugs in Scrabble3D application.I am trying off to figure out optimal tile distribution for maths equations Scrabble for 200 tiles on a 21×21 board.
In the Wikipedia page for Scrabble tile distributions, in IPA English, in the tile distribution with use of diphthongs (and not the alternate one by Scrabble3D without use of diphthongs), the phoneme ɝ is missing from the tile set. Or is that intentionally done so with the aim of substituting some other phoneme for it? There are currently 106 tiles that are being defined in the tile set. In my humble opinion, 3 extra ɝ and 1 extra ŋ could be added up to the tile set, thereby bring the total count of used tiles to 110 there.
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Zitat von Scotty im Beitrag DictionaryPS: It makes sense to increase the number of letters on rack to 9.
Announcements Forum and dictionary prepared by Jouni Tolonen (xyz) recommends players to set rack size to 9. However 10 is the ideal number in my opinion, as players would need more flexibility between digits, operators and = and possibility of short words is completely ruled out in Scrabble with maths equations. It would be more interesting to have 11 or 12 tiles in rack to encourage players to form maths equations with longer numbers in them, however they need more equations in the dictionary to play with the computer and would be suitable only to play with other human players online.
Scrabble3D application currently allows having upto 20 tiles in rack. It can be also increased easily by editing the source code and compiling Scrabble3D application from that, as I tried out with board size, but at least in Windows 10, crash occurred during computer's turn from my own modified and compiled version of Scrabble3D application. I am not sure about what happens with other operating systems and by the way I do not have other operating systems with me also right now for me to test them with by myself.
It is possible to play with only 7 tiles in rack as long as only all numbers are taken in rack. And if playing with a type of variant in which players have the freedom to choose operators and = at their own wishes, each of which are unlimited in number, from the publicly available operator (and =) pool. This type of play is not currently supported by Scrabble3D application and it requires a lot of work, by editing the source code and adding a lot of new code and compiling Scrabble3D application from that, in order to play with this type of variant.
For playing Scrabble with maths equations with the computer, for the best results, it would be good enough to parse every equation whether it is valid or not, by making use of a context free grammar, instead of using a finitely manually defined dictionary that is loaded for Scrabble with maths equations along with the Scrabble3D application. Building a trie data structure would be a good idea to check out what possible next letter can come in a maths equation after a certain sequence of letters instead of trying out with all permutations of tile racks at all possible locations of the board along all 2 axes (for 2D games) and along all 3 axes (for 3D games). I think that brute force search for searching for all possible computer moves that are available for play during any given turn by Scrabble3D application is only done by making use of the former approach that I have mentioned and not the latter approach at all.
[Replace] %=mod
S → Z=Z Z → T | -T | T+E | -T+E | T-E | -T-E | T×E | -T×E | T÷E | -T÷E | T^E | -T^E | T%E | -T%E E → T | T+E | T-E | T×E | T÷E | T^E | T%E T → N | √T | ∛T | ∛-T | ∜T | T² | T³ | T⁴ | T! N → L | L.R L → D | PY Y → D | DY R → P | MP M → D | MD D → 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 P → 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
Some of this information had already been posted by me in 'Unfixed bugs in Scrabble3D application' thread in 'Bugreports and Suggestions' forum in 'English' group in this forum. I am just accumulating left over information from my previous posts in this thread about maths dictionary related points from that thread here.
I do not recommend players to make use of useless operators like ∞, < and > in the maths dictionary. What mathematical equations make use of ∞? Anything divided by 0 is ∞ and anything divided by ∞ is 0? I do not like using that in Scrabble boards. < and > will allow players to form wild high scoring mathematical equations at their own wishes.
The maths dictionary that had been contributed by Jouni Tolonen contains invalid mathematical equations like 18-9=7, 18+5=13 and 0^0=1. At least if a valid mathematical equation is played in Scrabble board that is not present in the maths dictionary, then it can be accepted by concensus of current human player and other human players. But if an invalid mathematical equation is played in Scrabble board that is present in the maths dictionary, then it cannot be rejected by the concensus of current human player and other human players. I assume that human players will always play honestly enough and other human players newly downloading maths dictionary from sourceforge website page through Scrabble3D application or not, they might not have knowledge about such mistakes in the maths dictionary and so it will be an issue only with computer opponent players to enjoy playing any of such of types of games with, if I cannot find other sufficient enough human players to play any of such of types of games with, whoever will have enough amount of free time with them to spare with that. 0^0 and 0÷0 are indiscriminate forms and so any number on the right hand side is suitable for them and so 0^0=[something] or 0÷0=[something] are not valid mathematical equations to be included in the maths dictionary.
∜16=2 is the only mathematical equation containing ∜ that is present in the maths dictionary. What the hell are mathematical equations such as those like ∞>15 and ∞=∞+1? Why not ∞>16 and ∞=∞-1 be present as mathematical equations in the maths dictionary instead of them?
Zitat von Bussinchen im Beitrag #12How did you find out those mistakes? By a computer program? Or manually? Or by accident when playing Maths-Scrabble3D against the computer?
Invalid mathematical equations like 18-9=7 (in 15×15 size of Scrabble board) and 18+5=13 (in 21×21 size of Scrabble board) were played by the computer against me when I was trying out a game of Scrabble of mathematical equations against the computer. I found out 0^0=1, ∞>15 and ∞=∞+1 by browsing through the Maths dictionary word list through Scrabble3D application because that dictionary file had been protected by its own author, Jouni Tolonen. Just go to File → Word Search. Keyboard shortcut key for it is Ctrl + W. How did he generate maths dictionary with limited longer enough mathematical equations in them? And errors shouldn't have occurred in them if he generated them through computer program and he should have checked them out before submitting it to Scotty for uploading it on sourceforge website page.
I will post more screenshots of all such Scrabble boards in the future period of time whenever I find time and having completed my research thoroughly. Right now accumulating all my points in its own appropriate thread only. There might be more mistakes in the maths dictionary that I can find out only by playing furthermore games against computer as other opponent players (only offline in the same computer and never online over a network connection) and against humans as other opponent players (either offline in the same computer or online over a network connection).
It's a pity that the Maths.dic is protected/crypted by its author Jouni Tolonen, so that it is impossible for you to check and analyse it systematically. Check it by playing games is what I call "by accident", because you may play many many games where no mistake occurs. It occurs only by accident.
Scrabble with mathematical equations should be open to everyone in the world and not limited to speakers of a specific language, if it would be made popular with everyone all round the world anyway and if any tournaments are conducted with them anyway.
Scrabble with perfect squares and equally O(n²) dense triangular numbers are lot of fun to play with 7 or 8 tiles in rack but that Scrabble with perfect cubes might need furthermore tiles in rack to be fun because of the fact that they are rare enough. For Scrabble with perfect squares, I put each digit tile with equal distribution in bag but points of tiles are based upon frequency in dictionary, with more points for rarely used digits and less points for frequently used digits. Anyway that variation in frequency between each of the digits that is present in the dictionary is not much of variation in frequency either, just simply to make the play of Scrabble game within Scrabble board furthermore spicy enough. 2 points: {4, 6}, 3 points: {0, 1, 2}, 4 points: {5, 8, 9} and 5 points: {3, 7}. People cannot play this without the aid of any helper tools to be suitable for tournament play unless a player can by heart all such list of numbers by heart in memory and can recall from memory in an instant or an human computer can calculate such list of numbers in an instant.
Scrabble with Roman numerals is also a lot of fun to play with 7 or 8 tiles in rack and should be open to everyone in the world without the aid of any helper tools and should be suitable for tournament play. Considering Roman numerals from 1 to 3999, tiles {V, L, D} and tiles {I, X, C, M} should be in the ratio 1:3 as they appear in the dictionary. For Scrabble with Roman numerals, I put each digit tile with equal distribution in bag but points of tiles are based upon frequency in dictionary, with more points for rarely used digits and less points for frequently used digits. Anyway that variation in frequency between {I} and {X, C, M} that is present in the dictionary is not much of variation in frequency either, just simply to make the play of Scrabble game within Scrabble board furthermore spicy enough. 2 points: {X, C, M}, 3 points: {I} and 5 points: {V, L, D}.
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