tag:blogger.com,1999:blog-5303307482158922565.post7420074739907508772..comments2024-03-22T13:39:55.941-07:00Comments on Math Mama Writes...: Math Adventures: Thinking about Spot it, and Learning PythonSue VanHattumhttp://www.blogger.com/profile/10237941346154683902noreply@blogger.comBlogger20125tag:blogger.com,1999:blog-5303307482158922565.post-57326989119256632152014-12-15T09:55:41.077-08:002014-12-15T09:55:41.077-08:00Yes you can also generate a set for N = power of p...Yes you can also generate a set for N = power of prime using projective plane theory (4, 8, 16, 9 27, 25, ...).<br />It is more complex than for N prime because calculation needs polynomials.<br /><br />It was demonstrated impossible for N=6 mathematically, and for N=10 by brute force search.<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-53621571836764022512013-12-02T19:43:35.344-08:002013-12-02T19:43:35.344-08:00Your N is one less than the number of pictures on ...Your N is one less than the number of pictures on a card, right? Some of the readers here have seen this before. Others, like me, discovered it for the first time through analyzing Spot It. I'm curious about your algorithm. Mine is pretty messy. I think there may be a way to use 5 pictures per card (so N=4), but I'm not sure of that.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-1792470840554767852013-12-02T18:06:09.717-08:002013-12-02T18:06:09.717-08:00From Jim - sorry I don't have any online accou...From Jim - sorry I don't have any online account to sign with.<br /><br />My 4 year old granddaughter just got Spot It and I was excited to find this and a couple other discussions going on. I am a bit late getting in on the conversation but I have an algorithm for creating a set of N(N+1)+1 cards for any N prime and a proof that it works. I can't tell whether this is old hat to the readers or not. I can upload it if there is any way to do so. I don't know all the notation being tossed around but I think it's pretty readable.<br /><br />I also can't figure out whether anyone has actually seen or generated a set with N not prime. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-87797964138463594922013-11-29T18:35:04.000-08:002013-11-29T18:35:04.000-08:00Can you tell me the name of this game with 3 symbo...Can you tell me the name of this game with 3 symbols matching? I'd love to look at it.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-24030870430180238262013-11-29T10:55:27.762-08:002013-11-29T10:55:27.762-08:00thanks, becuase i just played the game the first t...thanks, becuase i just played the game the first time today, | was more wondering about the missing cards. We theory behind having one match, no more or no less on every card is very interesting. Further, there is a game using 9 cards that has a 3 symbol match. Since i don't own the game (played while visiting relatives) i wonder if the 9 card game only has a single match of 3 symbols or if there are multiple 3 symbol matches. I'm going to go out and buy the game this weekend, and probably the kids simplified version too ! Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-67282680654346296722013-11-29T08:33:31.962-08:002013-11-29T08:33:31.962-08:00"I emailed the company to ask how they did it..."I emailed the company to ask how they did it and why they left out two cards. I hope they reply."<br /><br />They did reply (promptly, almost two years ago). They asked me not to share what they said. I figured I should honor their request. I will say that what they said is nothing earth shattering. (It fit our hypotheses above.)<br /><br />Anonymous, you don't need to be a math whiz to figure this out, but you do need to be *very* persistent. If you get hooked on thinking about this, you're welcome to email me (mathanthologyeditor on gmail) with any questions.<br /><br />Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-47136345437030947332013-11-29T08:16:39.762-08:002013-11-29T08:16:39.762-08:00I'm no math whiz, but i liked reading the anal...I'm no math whiz, but i liked reading the analysis trying to figure out how this array of pictures was created. No email esponse from company yet?<br />Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-38144386983338266062013-11-03T06:17:32.953-08:002013-11-03T06:17:32.953-08:00Go you, indeed! I'm not sure I ever realized t...Go you, indeed! I'm not sure I ever realized that one of the pictures appears only 6 times. Which one?<br /><br />Have you tried figuring out how they managed to arrange the pictures properly?Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-41216974101401215392013-11-03T04:52:27.009-08:002013-11-03T04:52:27.009-08:00Hello my name is JOE from Australia. My son and I ...Hello my name is JOE from Australia. My son and I have a loan of a pack and it intrigued us how did this work - only one match with any two cards. So we counted the number of pictures (57) and listed them. then counted by tally the number of each picture - 42 had 8, 14 had 7, 1 had 6. So quickly figured that the one with 6 and the 14 (2 x 7) means that 2 cards were missing - so why are there only 55 cards and published as 55 cards. Is it because 55 is easier to understand than 57? Go me!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-35505874458335740542012-11-30T10:08:53.553-08:002012-11-30T10:08:53.553-08:00I'm still hooked on this. I did a math circle ...I'm still hooked on this. I did a math circle last night on it, and will follow up next Thursday. Turned out we had a very small group. It was exciting to watch pairs and trios, each working on this in their own ways.<br /><br />I also got an email from someone in Indonesia recently, wanting the solution. Turns out he's not interested in learning how to think about it. Why would anyone want the solution to this if they don't want to think about it?<br /><br />Anyway, I wrote up my procedure, and drew out what goes wrong when there are 5 symbols per card.<br /><br />He sent me <a href="https://docs.google.com/open?id=1ZqZ0no5ZGlkjCHkYdz2a2V5FT50dozllFAnX-4vl8YCT-D4AHAlpxJJgnGKg" rel="nofollow">this pdf</a>. Interesting.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-46243576562713541122012-01-22T22:08:08.870-08:002012-01-22T22:08:08.870-08:00>the stuff Owen was drawing pictures of
>mi...>the stuff Owen was drawing pictures of <br />>might be related<br /><a href="http://vlorbik.wordpress.com/2011/01/07/some-finite-projective-spaces/" rel="nofollow">some finite projective spaces</a> (e.g.).<br /><br />>It's not a math game at all.<br /><br />i'm not sure i agreee with you<br />100% on your police work...<br />here we are, not only *talking<br />about* it, but *analyzing* it...<br />"why 57?"!<br /><br />>This morning I got my program working, and it verified that my method worked!<br /><br />pretty exciting. i've long since<br />believed that it was half-past-time<br />i figured out at least a *little*<br />about "python" (for example; other<br />freely-available-online programming<br />tools, too [of course]). thanks for<br />leading the way!<br /><br />still. it's the plain-language<br />"paper-and-pencil" stuff that <br />i long for (& still haven't figured<br />out as of now). what's the clearest<br />statement of the relevant theorem?<br />how is it most easily seen?<br />(by a human...?)<br /><br />so. i've got my grading *nearly*<br />done... let's look at joshua's<br />"spoilers".<br /><br />ah. yes. N = P^2 + P + 1.<br />i know how to make a<br />"projective plane" over <br />"the field with P elements"<br />(or for that matter, the <br />field with Q = P^k <br />[k \in {1, 2, 3, ...}]<br />elements); yes. <br /><br />so 7^2+ 7^1 + 7^0 = 57<br />qualifies. i've drawn<br />this (P^2(F_7)) & even<br />run off copies. but it<br />was ugly and (as it turns<br />out) incorrect. <br /><br />anyhow, here's my "projective<br />spaces" *category*:<br /><a href="http://vlorbik.wordpress.com/category/projective-spaces/" rel="nofollow">VK on P^r(F_q)</a>.<br />.<br /><br />almost everything worth knowing<br />is understood by considering<br />*small examples*.<br /><br />MMW rox. V.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-71678542721399045322012-01-22T19:16:29.502-08:002012-01-22T19:16:29.502-08:00I had written what I wanted in pseudo-code, so it ...I had written what I wanted in pseudo-code, so it was mostly learning how to represent and manipulate arrays (more like a list of lists in Python), get file input, and stuff like that.<br /><br />I'm happy to send my program to anyone who wants to see it. It doesn't seem like the thing for a blog post, but if folks would like it here, I can do that.<br /><br />Yep, that w'pedia article describes the sort of thing I would have done in generalizing this.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-23862902892847537272012-01-22T18:17:48.665-08:002012-01-22T18:17:48.665-08:00There is a whole area in combinatorics called comb...There is a whole area in combinatorics called combinatorial design.<br /><br />http://en.wikipedia.org/wiki/Combinatorial_design<br /><br />I don't remember much about it, but finite geometries are involved.<br /><br />In Python, it is easy to over think your programs. It is different than C/C++ in that all of the basic functions you would want are already implemented. You often find that most of the program you're writing is already implemented. Python programmers call it "Guido's Time Machine."<br /><br />The first Python program that I wrote required me to rearrange the elements of an array in a random order. I accidently found the shuffle method while learning how to generate random numbers. My program turned into three lines of code.Chris Searshttps://www.blogger.com/profile/17011015768708974448noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-89734046095784592112012-01-22T01:03:48.967-08:002012-01-22T01:03:48.967-08:00Oh, I'm dumb. The Hoffman-Singleton thing has ...Oh, I'm dumb. The Hoffman-Singleton thing has only 50 cards, as that page states clearly enough. (I got confused because the next line down from it on the table on the page I linked had a 57 in it, but that's a different graph, and the 57 would not represent the number of vertices/cards for a hypothetical deck based on it. Sorry about that.Alexandre Muñizhttp://puzzlezapper.com/blognoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-8750179150940924922012-01-21T20:41:48.997-08:002012-01-21T20:41:48.997-08:00That's what I love about math. Things that see...That's what I love about math. Things that seem entirely different turn out to be the same problem. <br /><br />(I don't know if Spot it and the Hoffman-Singleton graph deck are isomorphic, but if they're not, I suppose Spot it will be isomorphic to something else that seems unrelated.)Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-36939477222699365672012-01-21T18:32:04.030-08:002012-01-21T18:32:04.030-08:00I'm also wondering if this deck (with the miss...I'm also wondering if this deck (with the missing cards) is isomorphic to Ed Pegg's <a href="http://www.maa.org/editorial/mathgames/mathgames_11_01_04.html" rel="nofollow">Hoffman-Singleton graph deck</a>, which also has 57 cards.Alexandre Muñizhttp://puzzlezapper.com/blognoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-35004318949055929682012-01-21T18:21:51.855-08:002012-01-21T18:21:51.855-08:00I suspect that the reason for the missing cards co...I suspect that the reason for the missing cards comes from the cards' production method. Most cards are printed on rectangular sheets, which are then cut into individual cards. So the number of cards in a rectangular sheet needs to have two factors that are neither too large nor too small. Also, you want to be able to make a standard poker deck, which is 54 cards, so the number of cards in a sheet should not be less or much more than that. It appears that 5×11 is a pretty common size, just judging by what I've seen in Magic: the Gathering sets. So it probably just comes down to it being more expensive to make a game with a non-standard number of cards.Alexandre Muñizhttp://puzzlezapper.com/blognoreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-19091534724079877052012-01-21T16:52:23.688-08:002012-01-21T16:52:23.688-08:00Thank you, Josh. I had no idea this was connected ...Thank you, Josh. I had no idea this was connected to 'finite field planes'. Now I'm thinking the stuff Owen was drawing pictures of might be related.<br /><br />I emailed the company to ask how they did it and why they left out two cards. I hope they reply.<br /><br />Cindy, I wasn't planning on explaining it. If you want to play with it, I'd be happy to give you hints. My solution is pretty complicated, but I bet there's a more elegant way to see it. <br /><br />If you're interested in playing with it, one place to begin is to do the mini-version I mentioned, with each card having 4 pictures on it.Sue VanHattumhttps://www.blogger.com/profile/10237941346154683902noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-53056854835663482332012-01-21T14:30:10.746-08:002012-01-21T14:30:10.746-08:00I can't wait for you to explain what you found...I can't wait for you to explain what you found!!!! :)Cindyhttps://www.blogger.com/profile/06419042339830317651noreply@blogger.comtag:blogger.com,1999:blog-5303307482158922565.post-51783463916255702312012-01-21T12:39:07.411-08:002012-01-21T12:39:07.411-08:00At the risk of maybe giving too many spoilers here...At the risk of maybe giving too many spoilers here:<br /><br />I spent a lot of time thinking about these cards, too. There's a beautiful card <-> picture symmetry in there somewhere. And it's not a coincidence that there are 7+1 pictures per card, each picture is on 7+1 cards, and there are a total of 7^2+7+1 pictures (and there should be that many cards, too -- which two are missing? I haven't figured that out yet, nor do I have a clue about why they're missing).<br /><br />http://en.wikipedia.org/wiki/Projective_plane#Finite_field_planesJoshua Zuckerhttps://www.blogger.com/profile/04689961247338617418noreply@blogger.com