The Pentomino Puzzle (and Tetris) - Numberphile
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6 жыл бұрынFeaturing Alex Bellos on Polyominoes. See the accompanying coin hexagon video: • The Coin Hexagon - Num...
More links & stuff in full description below ↓↓↓
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Confessions of a Tetris Addict (video by Brady): • Confessions of a Tetri...
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@numberphile 6 жыл бұрын
See also the coin hexagon video released along with this one: kzfaq.info/get/bejne/ldaAkqZoravdY5s.html And plenty more links in the expanded video description
@michaelzeller2542 6 жыл бұрын
Does only one solution exist?
@AlucardNoir 6 жыл бұрын
I take it he's never heard of Oskar Van Deventer?
@AstroHolden 6 жыл бұрын
There was a Tetris sequel by Pajitnov that used polyonimos, called Welltris.
@hps362 6 жыл бұрын
Hey is this the puzzle from last year's intermediate team maths challenge final? No wait that was a 3*20 grid.
@FrankHarwald 6 жыл бұрын
There's another video game where it's the objective to form different rectangles & other shapes out of tetrominoes: It's Mr Pants developed by Rare Ltd
@Biped 6 жыл бұрын
There is also the boring brother, the monominoe. Also pretty fun to arrange into a square.
@soulsilversnorlax1336 6 жыл бұрын
It only took me like 5 minutes to figure that puzzle out.
@totaltotalmonkey 6 жыл бұрын
There is the same number of unique monominoes as dominoes.
@Biped 6 жыл бұрын
Me too! even though the packaging said 2-3 years!
@Oshisaure 6 жыл бұрын
The thing is about monominoes you can turn them into dice
@carnsoaks1 6 жыл бұрын
try a triangle, bet you cant.
@Galenus0 6 жыл бұрын
BOOM! Tetris for Jeff!
@jasondoe2596 6 жыл бұрын
I'm sad so few people got the reference in your comment xD
@fluffyplayery3017 5 жыл бұрын
I was wondering how far down I'd have to scroll to find this.
@reformCopyright 4 жыл бұрын
BOOM! Pentis for Jeff!
@AlexKing-tg9hl 4 жыл бұрын
I am one of the few
@kevinderoo3880 4 жыл бұрын
BOOM! Tetris for Jonas!
@magicianstuff 6 жыл бұрын
A bit surprised they didn't mention the story about how when Tetris was being created it was originally going to be with pentominoes instead of tetrominoes, but it was thought to be a bit hard because of the more complex shapes and wider variety compared to tetrominoes. (Also another fun fact: Tetris is a portmanteau of "tetra" (four) and "tennis" which was the creator's favourite sport at the time.)
@pss360 6 жыл бұрын
The dudeney puzzle seems to feature the black and white of the chess board, shouldn't that affect the solution in some way? Like, does this solution coincide with the way he's colored the pieces in the puzzle book?
@Minihood31770 6 жыл бұрын
I am the man who arranges the blocks that continue to fall from up above
@TheSentientCloud 6 жыл бұрын
They come down and I spin them around til they fit in the ground like hand in glove
@mediocreman6323 3 жыл бұрын
Oh. So, you are the guy who NEVER GAVE ME THAT 4×1 WHEN I NEED ONE, AAARRR!!!
@md.sazzadhossain6680 6 жыл бұрын
You guys didn't even use the "GREAT" brown paper.
@WildStar2002 5 жыл бұрын
I first learned about pentominoes (without the errant square tetromino here) from Arthur C, Clark's book "Imperial Earth". I've been fascinated with tessellations of all kinds ever since!
@theomeletteguy9353 6 жыл бұрын
This makes me so happy! I am a big fan of numberphile and I love polyominoes and I've always wondered why they didn't have a video about polyominoes!
@alejandrogarridogouro388 6 жыл бұрын
Once again. You bring us interesting videos and amazing math. Thank you Brady Haran.
@frmcf 6 жыл бұрын
I never knew Andy Serkis was into puzzles!
@marnixvlot1868 6 жыл бұрын
And funny enough that Ernest guy looks a lot like Saruman :)
@BLenz-114 6 жыл бұрын
Serkis?!! Don't you mean Michael Sheen?
@roboninja565 6 жыл бұрын
I used to play an online game that was basically 3d tetris, it gave you a birds eye veiw of the board, i think it was like 10×10 squares or something? Youd get points by clearing entire planes of shapes, rather than just a row. Very fun.
@MegaPhester 6 жыл бұрын
A video on the polyomino enumeration problem would be amazing!
@unfetteredparacosmian 5 жыл бұрын
And the tree enumeration problem
@amatos4444 6 жыл бұрын
I know that Tetris is pretty commonplace, but this exact kind of puzzle with pentominoes is the basis for the Game Boy game Daedalian Opus. No dropping pieces - instead, a selection of pentominoes are given for the player to try to fit correctly into the shape provided. Check it out, it's a pretty neat game.
@t.s8025 6 жыл бұрын
I read some of his books and really enjoyed them
@inkpanther 6 жыл бұрын
I'm disappointed that the solution doesn't have the 2x2 piece in the middle. ;)
@bennylofgren3208 6 жыл бұрын
Ink Panther There are plenty of solutions with the square in the middle as well. :-)
@inkpanther 6 жыл бұрын
I know, but it kind of irks me that they didn't show one of them. ;)
@AbarothsWorld 6 жыл бұрын
There are 65 solutions with the square piece in the centre, if you disregard rotations and reflections of a solution as being different (or 520 if you count those as being different).
@Oshisaure 6 жыл бұрын
As a Tetris nerd and hobbyist programmer, I tried to play Tetris but with pentominoes. After a bit of practice and tweaking the game to make it more adapted to pentominoes, it turns out you can get the hang of it. Makes me wish we had a new Tetris game but with only pentominoes. -I assume one of the reasons why Alexey Pajitnov downscaled the game to tetrominoes is because the computers in USSR back in the 1980 couldn't possibly handle pentominoes. We're talking 18 pieces of 5 blocks if you keep the mirrored pentominoes as 2 different pieces instead of 7 pieces of 4 blocks. Now that we are able to do this easily,- I think a game based around pentominoes instead of tetrominoes could be a nice tribute to the puzzle that started it all. Edit: I've been told Pajitnov actually did pentoes so I must have misheard/misinterpreted something (my guess is I heard algorithmic complexity when I should have heard gameplay complexity?), my bad on that. My point still stands though.
@aleixalva6073 6 жыл бұрын
Lilla Oshisaure Are you sharing the code somewhere? I'd love to play such game.
@Oshisaure 6 жыл бұрын
Sure, lemme clean off a little bit and I can give it to you after this weekend, I'm not home at the moment and i'll come back on sunday i believe. Tell me again if I forget.
@aleixalva6073 6 жыл бұрын
Lilla Oshisaure awesome! Thanks!
@BlurryHeart15 6 жыл бұрын
I'm not aware of a pure pentominoes game like tetris but then new game Puyo Puyo Tetris has a versus mode where someone can activate a "punishment" on the other player that makes all tetrominoes into pentominoes for a short while.
@Oshisaure 6 жыл бұрын
It doesn't have all of them though. What it does is turn your next 5 pieces into pentominoes by adding a mino to it, but that means that you only get to see 7 pentominoes in the game. So I guess we're getting somewhere. As for unofficial games however, I'm sure there are probably a few out there, each with their own set of rules. I'll try to come up with something behaving similarly to the recent games (kind of like Puyo Puyo Tetris' pentominoes but for all 18 pieces).
@theFado96 6 жыл бұрын
I have the pentomino set too at home and I remember I was able to combine the pieces to compose the word "Golomb" and even arrange them to make (i think) a perfect 3x4x5 solid figure. I had a small book with the many things you could do with them such as writing words and compose 2D and 3D figures.
@CrucialMuzic 6 жыл бұрын
I love Tetris so much, glad to know more about the history of all of this and the origin. Time to go play some tetris now :)
@missrobinhoodie 4 жыл бұрын
I‘d love this for my elementary school! Have you made a video about the soma cube yet?
@Tlelkina 6 жыл бұрын
I just realised the origins of game's name "dominoes".
@Kabooomof 6 жыл бұрын
yeah same here
@poznyakpoznyak 6 жыл бұрын
Actually, it's a kind of backwards etymology. Dominoes are named dominoes because of entirely different reason, but Golomb, apparently, chose to read as do-minoes (two-minoes) so he could generalize the name.
@GriimX 6 жыл бұрын
Mathematicians, always trying to generalize things!
@medexamtoolsdotcom 6 жыл бұрын
But what is the origin of the name "Little Ceasars"?
@Sunomis 6 жыл бұрын
Salad, I guess
@d3athmarines 6 жыл бұрын
I didn't know Count Dooku liked Puzzles.
@RDSk0 6 жыл бұрын
I've been looking forward to this
@vaprin2019 6 жыл бұрын
Great stufff
@theleetstright791 5 жыл бұрын
1:00 4x4...?
@ValkyRiver 4 жыл бұрын
He means 2x2
@FinetalPies 6 жыл бұрын
Alexey's favourite childhood toy was a pentomino puzzle, he tried to use them for his video game but it didn't really work out. Everyone should check out the gaming historians video on the origin of Tetris for a more complete understanding.
@RMoribayashi 6 жыл бұрын
I googled "5 square Tetris" and an online version topped the list. It's damned hard.
@bennylofgren3208 6 жыл бұрын
I got a set like that but in plastic way back in the 70s which I played with a lot. Still got it. And I also have a similar one but with a 6x10 board, without the 2x2 square piece.
@tonywoodhouse6988 6 жыл бұрын
I have a plastic 6x10 set too. I got it in the 50s and I was always playing with it when I was about 10. I only ever found one extra solution to the one they gave you when you bought the set.
@coosoorlog 6 жыл бұрын
I've seen the 6x10 version many times but this square one in this video was completely new to me.
@Siebs293 6 жыл бұрын
Yeah, my high school geometry teacher had the 6x10 and i loved it so i made a 3D printable version.
@PhoenixFire32 6 жыл бұрын
I was obsessed with pentominoes as a kid. So much fun.
@rickgraham8701 6 жыл бұрын
I've known the six coin puzzle forever and at one time figured out all the possible solutions. As for the topic, I'm gonna 3d print that sucker.
@pelerflyp5398 6 жыл бұрын
Its really funny that you did that because I thought of that last week!
@nymalous3428 6 жыл бұрын
I would love to own a copy of that Pentomino Puzzle, and I know a lot of nieces and nephews who would love to play it! These are the kinds of things that help young minds start to grasp mathematics and get excited about it. Thanks for the video!
@japeking1 6 жыл бұрын
For a holiday program we had 30 sets of pentominoes made up. Almost all the kids just gave up looking for solutions and we had to revert to a competition to see who could stack them in the highest tower. Wonder what the maths of that would be?
@tomf3150 6 жыл бұрын
Yeah and tease them with the only 2 possibilities of 3x20.
@tedpaulus 6 жыл бұрын
Any ideas where on Crete to purchase the puzzles? I’m visiting Crete this week for vacation and I’m interested. Cheers.
@OtreblaMaslab 6 жыл бұрын
I remember I had a pentomino game for Windows 3.1 where you had to take turns with the computer at placing the pieces.
@lookoow9775 Жыл бұрын
How a wonderful research for the pentomino and the series of games. When I played Blokus and found L project. I realised they should be a same family (system).
@donkosaurus 6 жыл бұрын
Ive been reading one of alex bellos' books on my way to work
@phaedruscj3330 Жыл бұрын
Thanks for posting this. Now combine solving a puzzle using the 12 pentominoes plus a square 4 piece into an 8 by 8 Latin Square by coloring each of the 5 squares on each pentomino piece.
@kentrel2 6 жыл бұрын
The Talos Principle is a video game that uses these puzzles. It's a brilliant Portal-style game where you collect these pieces as rewards for solving each level. Then you have to solve the puzzle to unlock the next levels. It sticks to Tetris shapes only. I found I could solve even the hardest just by moving them randomly without much planning.
@shubhamsingh3635 6 жыл бұрын
Thank you.
@metleon 6 жыл бұрын
Had a toy of this as a kid. The only difference was they were plastic and came with a book of 2D and 3D patterns that you could make with them.
@mstmar 6 жыл бұрын
I remember we had one of those games as a kid. Every time one of us solved it, we would compare it to other solutions. If it was a new one, we would put a piece of paper over it and rub a pencil over it to keep a record. In the end we had something like 30 solutions, not counting rotations, reflections, and simple swaps (like in the solution given, if you swap the + with the one below it, you get another solution). I doubt we got them all, but still a fun game.
@jamesyeung3286 6 жыл бұрын
Nice
@subhoghosal7 6 жыл бұрын
Is these 13 shapes have any link with partition number. I mean if you have n squares how many different shapes you can combine them.
@aigen-journey 6 жыл бұрын
When I was a kid this puzzle was pretty popular where I grow up. We had a version with 6x10 board, so without the 2x2 square piece. I've kept a notebook with all the unique solutions I was able to find. This was way before I ever heard of tetris.
@gavinorr 5 жыл бұрын
Me too, I am in the process of transcribing the solutions I have already found for the 10 x 6 rectangle (just over 900 so far) into an excel spreadsheet which makes checking whether a "new" solution is actually a duplicate of one already found much quicker and more reliable.
@boscorner 6 жыл бұрын
A vudeo on the self tiling decominos would be great:)
@4ut0m8 6 жыл бұрын
Does this have anything to do with partitions and ferrers diagram? (for calculating # of ways)
@Asher.Yodaah 6 жыл бұрын
I remember playing with these as a kid, although I always made rectangles instead of squares. I remember discovering one of the only two ways to make a 3x20 rectangle.
@viveksoley 6 жыл бұрын
Just had the 'joy of learning' moment..
@robertbrookes2000 4 жыл бұрын
There's a game called Spear's Multipuzzle, which uses all the hexominoes (all the shapes made of six squares). There's a 6 by 10 rectangle to fit ten hexominoes in. Some shapes you get two of, such as a 1x6 straight line. The instructions have 48 combinations telling you which pieces to use and the easy ones show where one or two pieces go. However, on my copy someone wrote in a 49th combination.
@FLS96 3 жыл бұрын
I had a similar game when I was a kid, except it was on a 10x6 grid. It kept me going even after finding so many solutions to it.
@HatterTobias Жыл бұрын
Yeah I have a similar set at home, my set also came with some papers demonstrating the cool shapes you can make with them
@arturoislas4698 4 жыл бұрын
Holy heck I've been trying to find the name of this puzzle for too long, I just randomly remembered trying to complete it when I was younger and was just wildly searching for it.
@umairfaisal8558 3 жыл бұрын
i had this as a childhood but my grandpa lost it. ive been searching for this as well but the one i had had different pieces. i cannot remember all the pieces and cannot find them anywhere either.
@dr.firefetus5119 6 жыл бұрын
NIce vid!
@zh84 6 жыл бұрын
You can also pack the twelve pentominoes, without using the 2x2 block, into a 3x4x5 solid.
@medexamtoolsdotcom 6 жыл бұрын
Blocks are falling down, and you must line them up or die, if they make it to the top, your game is through. The 4 by 1 is rare, so rely, if you dare, but the speed will only rise, so you'd best beware.
@zooblestyx 6 жыл бұрын
There's a two-player game called Cathedral based around these shapes (and some smaller ones) which I can highly recommend.
@GeneralPotatoSalad 6 жыл бұрын
Anyone remember the Flash game Pentrix? Pentomino Tetris with an added settling mechanic? That thing is addictive, I still play it sometimes.
@romanemul1 6 жыл бұрын
so how many possible ways are to finish this puzzle ?
@ondrejbouchala 6 жыл бұрын
16146 without reflections and rotations, or 129168 altogether.
@romanemul1 6 жыл бұрын
Diky
@adhyasuman 6 жыл бұрын
Ondřej Bouchala please elaborate
@carnsoaks1 6 жыл бұрын
he's bs'ing us.
@jaapsch2 6 жыл бұрын
Yes, 16146 is correct. There are many polyomino solving computer programs out there, and any of them should be able to verify this within a few minutes of running time (I just did so with my own). There is probably no way to prove this number other than just trying all possibilities like those programs do.
@TheSentientCloud 6 жыл бұрын
I got bored once and designed and 3D printed a tetrimino soma cube for a project. The entire class was playing with it. I still have it in my closet lol. I need to see if NullpoMino has a full range of pentominoes. I know you can turn on a few pentominoes, but IDK if it has a full range of them.
@TheSentientCloud 6 жыл бұрын
I'm a bit obsessed with block puzzles. Tetris is basically my boyfriend and I love all sorts of "fit these blocks into this shape" puzzles. Tetris is the most satisfying and I spend a few hours a day playing Tetris lol
@NesrocksGamingVideos 6 жыл бұрын
"Dominoes". Mind. Blown.
@PuzzlePals 4 жыл бұрын
I made a similar puzzle 🧩🧩🧩using legos. Thanks for sharing this here.
@shrimatkapoor2200 6 жыл бұрын
Lol snap I went to holiday in Crete as well!
@kdborg 6 жыл бұрын
My father got me into pentominoes. It was a plastic game in a 6 by 10 format and no square piece. He started a book recording the number of solutions he and others found.
@Recon777x 6 жыл бұрын
Wow, I had this puzzle as a kid in the early 80's. It was made of blue plastic pieces, not wood. I'm sure I don't still have all the pieces, but now with this video I can probably recreate it.
@tmfan3888 6 жыл бұрын
can u also talk about the 3d polyominoes? i think it would also be interesting!
@KafshakTashtak 6 жыл бұрын
Also, you can put all those pentominoes into a 6x10 rectangle, with many different possible arrangements.
@mina86 6 жыл бұрын
Can’t wait till fall for Classic Tetris World Championship 2018!
@zywang8910 6 жыл бұрын
if the cubes are allowed to arrange in three dimensional, how many variation there will be?
@murrfeeling 6 жыл бұрын
The carpentry puzzle of the MMO Puzzle Pirates are all pentomino fitting puzzles, if you're into that sort of thing.
@MitchTheRonin 6 жыл бұрын
Is it possible to solve it and having the 2x2 square right in the middle?
@elevown 4 жыл бұрын
Is there only 1 solution? or can they fit in multiple ways?
@mareeludenia9688 6 жыл бұрын
If you just use the pentominoes you can create a series of rectangles, including one that is 3 x 20. (There are two versions of the solution, but one is a rotational Centre of the other.)
@jakewwwjake 6 жыл бұрын
@numberphile I actually made a puzzle very similar to this. Except it has three layers and the pieces may be placed across layers. I wasn’t aware of this puzzle at the time I made it, I just thought of it as a sort of 3D Tetris.
@xaostek 6 жыл бұрын
There is a gameboy game called "Daedalian Opus" that uses pentominoes! It's not a variation of tetris though, it's just the same "fit the pentominoes into the shape" puzzle. I think it was 36 different puzzles, the final level being the 8x8 square.
@lmartinson6963 4 жыл бұрын
There's a game called Pentix, which is just upgraded Tetris with pentominos. It's free on the app store, and I love it.
@lmartinson6963 4 жыл бұрын
Still no Hexis or Heptis, though :(
@starspawn507 6 жыл бұрын
Is there a formula for calculating the number of polyominoes that can be created with a given number of squares?
@slimehound1934 6 жыл бұрын
I have this puzzle (well my square is split into two 1x2 rectangles) and I take pictures of different solutions that I find. I’m on like 4 or 5.
@YingwuUsagiri 6 жыл бұрын
Are there less solutions in the original "chessboard" story? Since a chessboard is alternating colours and the wooden example in this video has only 1 colour.
@mikeCD62 4 жыл бұрын
There are 12 different ways to organize 5 blocks into a shape. A dodecahedron has 12 faces, each with 5 sides. Is there some kind of underlying relationship between 5 and 12 that informs these two connections?
@tropezando 6 жыл бұрын
Not quite the same puzzle, but a game called Blokus uses all configurations of one square up to pentominoes, touching corners to claim space on a grid. It's a great game for both adults and kids and I recommend it for people who like puzzles, strategy, and competition.
@martysears 2 жыл бұрын
i LOVE blokus
@zachm638 6 жыл бұрын
You should check out the boardgame Patchwork. You're trying to fill as much of a 9x9 as possible with these and other sized shapes.
@JackFate76 6 жыл бұрын
Thx great video as usual. Where can I buy this? My mom‘s a Tetris-Addict and likes wooden things.
@Tevildo 6 жыл бұрын
Jack - A Google Shopping search on "pentominoes" will give you quite a few candidates.
@JackFate76 6 жыл бұрын
Tevildo Thank you
@adamhansraj2314 3 жыл бұрын
There's a series of related puzzles. It is possible to arrange all 12 pentominoes into a rectangle of dimensions 3x20, 4x15, 5x12 and 6x10. Can you find them all?
@undeadp0wer390 6 жыл бұрын
The 4x4 in the middle? It looks like a 2x2 to me...
@BradTrapp 6 жыл бұрын
The game boy sound made my day.
@rainieralbertsz4165 6 жыл бұрын
No way! My dad brought that puzle home a week ago and now theres a video about it 😂😂😂
@CalamityInAction 6 жыл бұрын
I remember doing these, but the version I used was with laminated paper.
@LieseFury 6 жыл бұрын
Did you intend to have a tetrimino in the thumbnail?
@olleicua 6 жыл бұрын
oh hey, its the exact cover problem!
@zackszekely6618 3 жыл бұрын
Apparently this puzzle has over 16 thousand different solutions (disregarding rotations and reflections), but I couldn't help but notice that the decision to make the leftover 4 squares into a 2 by 2 tetromino seemed a bit arbitrary. Has anyone ever looked into how the number of solutions is different if the leftover 4 squares are built into a different tetromino?
@KelseyThornton 6 жыл бұрын
I have this, but without the 2 x 2 'interloper'. Together they make a 3 x 4 x 5 cuboid.
@The_Omegaman 6 жыл бұрын
Will those pieces fit on a 6x10 puzzle minus the square?
@martysears 2 жыл бұрын
yes :) 12 x 5 and 20 x 3 also possible
@chonchjohnch 4 жыл бұрын
I remember reading a book when I was a kid where a character was obsessed pentiminoes, I asked my mom to buy me some
@edvogel56 4 жыл бұрын
"Imperial Earth" by Clarke?
@zetadroid 6 жыл бұрын
How many different solutions are there for this puzzle? A friend of mine and I worked out that a similar 3D puzzle had 110 independent ones, so I'm guessing this one must have more than one...
@matthewbusche4547 5 жыл бұрын
There are 16146 rotationally unique solutions to this puzzle. If you constrain the 2x2 tetromino to the center of the solution, then there are 65 unique solutions.
@marvicklentz2857 6 жыл бұрын
Block of 2x2 right? Not 4x4?
@MajenkoTechnologies 6 жыл бұрын
I have that puzzle in my cupboard somewhere. I got it decades ago when I was a wee bairn. It's blue and plastic. I could put it together with my eyes closed.
@ondrejbouchala 6 жыл бұрын
There are actually 16146 ways how to solve it, and I am not counting rotations and mirror images, with them it would be 129168 solutions!
@darren3687 6 жыл бұрын
Ondřej Bouchala can you show me your calculations? Sounds interesting tho
@briandiehl9257 6 жыл бұрын
I don't think that is right
@trickytreyperfected1482 6 жыл бұрын
You couldn't have brought this up a month ago when I randomly started thinking about polyominoes?
@TPRJones 6 жыл бұрын
Hey, it's the carpentry mini-game from Puzzle Pirates!
@suave319 6 жыл бұрын
"LINE PIEEEECE"
@zanti4132 4 жыл бұрын
I am reading in the comments that there are 16,146 solutions to the puzzle. So how many ways are there to fill a rectangle (either 5x4 or 2x10) with the five tetraminoes?
Brother-live_mob
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LED Screen Factory-EagerLED
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