It's very important to tile a plane with pentominoes and not tetrominoes. Tiling a plane with tetrominoes causes the plane to disappear, but you get the highest score possible in tetris.
Fun fact, Tetris was originally supposed to be Pentris and it was based on pentomino, but Soviet computers scientists realized their hardware specification they chose for the project doesn't have enough of memory to handle pentomino pieces, so they downscaled to tetromino pieces and created Tetris.
Tetris was actually inspired by a puzzle its creator owned, which involved fitting pentaminos into a box. He figured that pentaminos were too complicated, and switched them out for tetraminos. guy saw pentaminos and was like “its got too much… 1 thing its exactly 1 thing too much
One very important pentomino fact that you forgot is the parity of the pieces. If you imagine putting each piece on top of a chessboard, where the cells cover up the black and white squares, you’ll find that all but 1 pentomino has a 3-2 parity, where it covers 3 black, 2 white, or 3 white 2 black. The only piece with a different parity is the X, which has a 4-1 parity. This means that if you place an X somewhere, you’ll need to place 3 non-X pentominos to get back to covering an equal amount of white and black squares, or just by placing one additional X pentomino.
tetronimoes actually get used all the time in geometry teachings. wonder what could have possibly caused such a specific interest in so many mathematicians... it's a mystery.
@@maeve-wav I had the GBA game for that, and I really wish they did more with the idea. As a kid I really liked fitting the shapes together in different ways. Because of the die unfolding theme you specifically get the 11 cube net hexominos, rather than the set of 35 total hexominos, but it still ends up being a wide variety. I don't remember much about the game other than the dice, so I couldn't say whether it was actually fun as a game, haha.
P-pentomino is the only one that has a perimeter of 10, while all the others have 12. My fourth grade teacher claimed that they all had a perimeter of 12 and asked students to try and prove her wrong. None of them tried the P shape and concluded she was right, but I discovered it later. I was too shy at that age to argue against a whole class so I’ve spent my whole life without vindication.
My favorite type of youtube video is one that is just listing off facts partaining to a particular math subject. My favorite part of math is simply just how much you can do just by playing around and having fun with interesting constructions. And then... what's that? A Patricia Taxxon background song?? My favorite musical artist?? This is a perfect video.
Blokus is a fun board game, where you are given 1 of each pentomino, tetromino, triomino, domino, and monomino, and try to place as many as you can while only expanding via corners, and you can't touch edges. It's impossible to fit them all, so you have to compete with other players for space.
Guys, I have an ideia for a video game. So we make a 2D box and let random pentominos fall slowly till they reach the bottom, the player can move the piece left and right, and spin the pentomino. Once a line is filled the game give points and clear the line leaving the space where the pentominos above fall. The game is over when there's no more free space. The game will be called Petris
As someone who (casually) plays Pentris, this is a fun analysis! Pentominos are definitely a lot more complex and interesting than their 4 tiled counterparts, and it really spices up the amount of thought you have to put in (especially during the faster phases when you have to make split second moves with awkward shaped pieces). Highest score I've ever gotten has only been a bit over a couple thousand points, so this could definitely be improved with a good bit of theory.
I hope I'm not too late for this, I've found a way to get an upper bound for a given nxn grid and a given number of pieces. Basically, each square on the best path is flanked by 2 walls, these walls might not be directly adjacent, but surrounding each square there will be 1 exit square, 1 entry square, and 2 other squares that either have a wall, or are an an empty path towards a wall. If the paths were not empty (ie they contained a cell that was part of the maximal path) then the path would simply choose to go towards the current cell via this empty path, meaning the maximal path is not maximal. If that made sense, the next step is to see that each piece provides exactly 12 blocks of adjacency, when you account for multiplicities (ie the L block gives 1 square in the elbow with a multiplicity 2 adjacency). Also, there is free adjacency provided by the exterior wall, equal to n * 4. So the basic adjacency score is 12 * b + n * 4, where b is the number of blocks. So the max path length is less than (12 * b + n*4)/2 However we can adjust the adjacency score to make it more accurate. First, notice that when pieces touch each other to form a connected wall, they lose one adjacency (unless they touch on their corners). This means that each non-corner touching gives a -2 to adjacency score. Also, we should assume that there is a square on the outside rim, so that is another -1. Also Also, the last sections of the path require 3 adjacent walls, instead of 2. So that takes 1 more adjacency score. We are left with an equation that looks like: (12 * b + n*4 - 2 * (b-c) - 1 - 1 )/2. where c is how many corner connections are between the blocks. Note that c
not surprising, considering each X is a water block with cane on each side! the fact that this tiles the plane exactly with no gaps corresponds with the fact that this is the maximum amount of cane that can exist in that space for that amount of water, which is of course true since each water block cannot possibly connect to more than 4 sand/dirt blocks! neat!
And now you know that a trivial game design choice created a scenario that due to the underlying and often ignored structure of mathematics has exactly one solution. Isn't that crazy? The plane can be tiled so many ways by so many monotiles, but due to the inherent geometry of a grid and this gameplay restriction there's exactly one way to build such a farm, and everyone must eventually stumble upon it. If the shape was any different there could be infinite farm designs, but this one provides no room for personal choice without sacrificing efficiency.
So lucky to find this video. Throughly intersting for its entire runtime with nice editing and good sound quality. Reminds me of Kuvina Saydaki, but higher energy. Subscribed in a heartbeat.
thank you very much!! kuvina was one of the inspirations for this video- I'm a massive fan of their sorting algorithm explaining video so I'm happy to be compared to them lmao
wait wtf this only has 500 views?? this video was great it feels like the type of video that should have like a million or something!! Keep up the great work !!
That pentomino game sounds like something that would be on an old school website and have a leaderboard on it where the people with the highest scores are shown.
17:47 For board sizes n=42 and above, as soon as you’ve found the perfect solution for one board you’ve found the perfect solution for all of them because the game becomes a matter of “hiding” the two ends of the path. The optimal solution will just keep growing a bigger empty middle section the higher n gets. Why 42? Because 41 is the sum of the lengths of the “long sides” of every pentomino, the longest length a shape built from one of each can reach. 42 makes it impossible to block off the middle area.
@@jakobr_ basically, once the grid has doubled, the longest distancethe line can travel is no longer the adjacent corner, but instead the opposite diagonal. Because of this, its meaningless to make the stacked line anymore, and instead it's best to make dense mazes in either one corner or opposite corners
@@YeaCloth I don’t understand why the longest distance wouldn’t be to the opposite corner (or inside structures near opposite corners) from sizes 42-84
Huh, that pentomino path packing puzzle is pretty interesting, wouldn't be surprised if you could get it into a recreational maths journal with a bit of write up.
The mathematical properties of these objects are actually surprisingly interesting, thank you for sharing all these fun facts! They remind me of symmetry groups, especially at the start of this video of course. What i mean by groups is that field of math with algebraic symetries or whatever it's called, like the ever-mysterious monster-group (which is like mathematical cosmic horror imho, the smaller groups tend to be more comprehensible to mere 3d mortals 😅).
I quite enjoyed this. The letter names you gave are in the Wikipedia article. I like the alternative naming they give by John Conway which uses the consecutive letters O through Z, though assigning O to the long straight pentomino is a bit dodgy. Other than that, my main math objection is the use of "regular symmetry" which is better known as "reflectional symmetry". Not that I know much, I'm an engineer.
Got excited to see a pentomino video on my feed out of nowhere! Gave me a bit of a throwback to a book series from Blue Balliet that got me interested in them. A character in that series used them for all sorts of things, a couple of which were mentioned here (I think rectangles of pentominoes were brought up a few times) and a few more unconventional things. Actually, OP, as an artist you might enjoy those books, as they're art-themed mysteries and treat the pentominoes as halfway a math object and halfway an art object, kind of like you did here.
i feel like this was one of the most pointless videos ive ever watched and simultaneously one of the most insightful and interesting and one of my personal favorites
When I was a kid, we did a Halloween school project where we had to make mixed media presentations on a mystery book. I found a book called Finding Vermeer about kids solving an art theft, and one of the kids was obsessed with pentominos, using them as a metaphor for conceots throughout the book. I made a fake newspaper clipping decorated with cardboard pentomimos, and ever since then I've been thinking about pentominos (and also Johannes Vermeer lol) at every possibly relevant time. I feel seen
This is a great video, with one exception: it's so annoying that there's a lot of text that only pops up for a split second (you have to pause or go frame-by-frame to read it)
Not only are there several of those games already, but technically it would be called Pentis since the R in Tetris is from the "Tetra" part of the name.
@@mateuszszulecki5206 Yeah but without the R that T is holding back all the dyslexic mistakes a reader could make all by itself. I don't think T has it in him, do you?
For a while in high school i was obsessed with fitting pentominoes (specifically including their mirrors too) into large rectangles. After succeeding a couple times, I eventually tried the same with hexominoes and heptonimoes but to no avail, they’re so much harder to work with the further you increase cell count
i am watching because i have refreshed my recommendation list over 10 times today but this is always at the top so i will watch in the hopes youtube will finally recommend something else.
I'm pretty sure the reason that grouping kept appearing was because of the underlying graph structure, ILNVUWZ are all lines, and FTY all have a central square with two branches of length 1 and one of length 2
interesting stuff, I'm pretty familliar with pentominoes since I play a lot of tetris variants with them, but it really surprised me to see some of these connections that I've sort of understood intuitvely layed out like this. You're proposed puzzle is also really damn interesting, played around a bit myself but it's a lot more initmidating than it first seems, do wish to see someone take a brute force computer though, if only for the satisfaction of knowing.
important detail on the tetrominoes is that you often see them referred to as being 7, JZ TOILS, but J and Z are mirrors of L and S which are only distinct if mirroring isn't allowed but rotation is (as in the video game Tetris, which is where most people first encounter this subject)
Fascinating video! I really liked this format of just sharing what you have discovered about a specific topic. Pentominoes are incredibly interesting, and this scratched that itch I've had for a few years now.
I spent a year or so playing with pentominos after reading about them in a novel. I can't remember which one, it was so long ago, but it was an integral part of the plot.
where? this arrangement doesn't work, if that's what you're thinking of vv o=path ==wall _=empty o o o o o o _ o = = = = o _ o = o o = o _ o = o = = o _ o = o o o o _ o o = = = = = _ o o o o o o
It's so nice when you just hear someone talk about their interests with no ulterior "trendy" motive. It must be weird for one of your videos to suddenly blow up.
I can’t believe that you called the R-pentomino the “F-pentomino”… (wait… Conway calls an R-pentomino) Anyway, starting from the R-pentomino, one can do an RF28B to a B-heptomino, then BFx59H to a Herschel, then HL95P into a pi-heptomino (releasing a glider), then PF35W into a wing, then WFx46H into a Herschel again, and finally HRx65R back into an R-pentomino (releasing another glider)
@@dmcdouga07 I guess I’m a member of the ConwayLife community, and everyone there calls it the “R-pentomino” since that’s what Conway calls it In fact, Conway called the I, L, F, and N pentominos “O”, “Q”, “R”, and “S”, so that the pentominos would be OPQRSTUVWXYZ
Personally it looks more like a lowercase f to me, doesn't really look like an R at least in the font of YT comments, so the label of " F-pentomino" makes more sense to me. Also I haven't ever played conway's game of life but I have heard of it and know a game inspired by it called "Cell Machine" (yes that Cell Machine that was made by Sam Hogan)
the visual explanations/infographics are perfect and you did a great job with them. i also cannot imagine being able to say all of the things you said without needing like 46 takes for each so thats also impressive.
I've done surprisingly similar research on four celled shapes but where diagonal adjacentcies are permitted. I found this information to be really interesting and I don't know why I never thought of looking at this. I once made a computer tile game using the shapes that was very interesting.
Fun video. Would be cool to see more on higher polyominoes. You might also find the 11 different nets of cubes to be interesting, since they're a subset of the hexominoes.
Your channel is very underrated! This was a great, well-edited video that I found very interesting and well-written. You deserve at least a couple thousand subs. I'm gonna help get you closer :)
It's very important to tile a plane with pentominoes and not tetrominoes.
Tiling a plane with tetrominoes causes the plane to disappear, but you get the highest score possible in tetris.
take your like and get out
.
Do not fill a box with pentominoes
Fun fact, Tetris was originally supposed to be Pentris and it was based on pentomino, but Soviet computers scientists realized their hardware specification they chose for the project doesn't have enough of memory to handle pentomino pieces, so they downscaled to tetromino pieces and created Tetris.
@@minskghoul what? I'm scared now
in my head it went like: 'this is a square; also known as a monomino..." which I'm laughing at just thinking about it.
Do doo, da do do.
A monomino, more commonly known as a mahjong tile or a Scrabble piece.
The O monomino
The "." mononino@@newcantinacrispychickentac7754
@@ArcheoLumiereThank you, that was my immediate thought upon seeing this comment
the not-allowed pentomino at 0:16 is a conway's game of life glider! it would move diagonally up and to the left if it advanced
Now that you said it I cannot unsee it
God I love nerds like you
THE GLIDER HAS BEEN OUTLAWED
a wild glider has been spotted!
thats such a niche thing to know and I hate that I instantly knew what you were talking about
i like how you alternate between "zed" and "zee"
oh the woes of being a Canadian
@@v.deckard I can’t believe that you called the R-pentomino the “F-pentomino”…
@@ValkyRiverunacceptable
@@VivianAttler You’re clearly not someone from the ConwayLife community…
@@VivianAttler you are lemongrab’s 3rd cousin (twice removed)
"it's not all that important" *introduces a mathematical research question*
guy saw tetris and was like "its missing something... 1 thing its missing exactly 1 thing
Specifically speaking, exactly 1 thing per piece
Tetris was actually inspired by a puzzle its creator owned, which involved fitting pentaminos into a box. He figured that pentaminos were too complicated, and switched them out for tetraminos.
guy saw pentaminos and was like “its got too much… 1 thing its exactly 1 thing too much
@@FizzyChalice So it went from Pentaminoes, to Tetraminoes in Tetris, then back to Pentaminoes in Pentris? Interesting
katamino has been around longer than tetris . look it up
@@FizzyChaliceTETROMINOES AND PENTROMINOS. NOT TETRA AND PENTA, TETRO AND PENTRO.
I’ve just always called the P pentomino “Utah”
As a Canadian who doesn't know he shape of each individual US state, I assume Utah looks like a P
@@djangel3108it’s more like a lowercase b
@@djangel3108
¤¤
¤¤¤
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@@djangel3108It looks like the P pentominobut not a P
As a Utahn I approve
You could say that the P pentomino contains LOTS of tetrominoes
Omg your a genius XD
Lmao I thought of that too
Oh crap you are right
P can fit the T, J, Z and O tetriminos
NO
@@AerianTelevisionThat isn’t what he meant…
One very important pentomino fact that you forgot is the parity of the pieces. If you imagine putting each piece on top of a chessboard, where the cells cover up the black and white squares, you’ll find that all but 1 pentomino has a 3-2 parity, where it covers 3 black, 2 white, or 3 white 2 black. The only piece with a different parity is the X, which has a 4-1 parity.
This means that if you place an X somewhere, you’ll need to place 3 non-X pentominos to get back to covering an equal amount of white and black squares, or just by placing one additional X pentomino.
New floor tiling just dropped!
Holy hell
how do you even know this
this feels like an entire untapped branch of mathematics and i’m all for it
tetronimoes actually get used all the time in geometry teachings. wonder what could have possibly caused such a specific interest in so many mathematicians... it's a mystery.
heavily tapped, but still very tappable, plenty more to research
Yu-Gi-Oh Dungeon Dice does some stuff with hexominos-you unfold a die into different shapes depending on where you want to go
@@maeve-wav I had the GBA game for that, and I really wish they did more with the idea. As a kid I really liked fitting the shapes together in different ways. Because of the die unfolding theme you specifically get the 11 cube net hexominos, rather than the set of 35 total hexominos, but it still ends up being a wide variety. I don't remember much about the game other than the dice, so I couldn't say whether it was actually fun as a game, haha.
P-pentomino is the only one that has a perimeter of 10, while all the others have 12. My fourth grade teacher claimed that they all had a perimeter of 12 and asked students to try and prove her wrong. None of them tried the P shape and concluded she was right, but I discovered it later. I was too shy at that age to argue against a whole class so I’ve spent my whole life without vindication.
Very interesting
I will tell her 🫡
@@VivianAttler 🫡
16:27 some pentominos? (Changes position) PERRY THE PENTOMINOS!?!?
Hilarious
Glad I'm not the only one who noticed that haha. Pattern recognition go brr
My favorite type of youtube video is one that is just listing off facts partaining to a particular math subject. My favorite part of math is simply just how much you can do just by playing around and having fun with interesting constructions. And then... what's that? A Patricia Taxxon background song?? My favorite musical artist?? This is a perfect video.
Blokus is a fun board game, where you are given 1 of each pentomino, tetromino, triomino, domino, and monomino, and try to place as many as you can while only expanding via corners, and you can't touch edges. It's impossible to fit them all, so you have to compete with other players for space.
Such a fun, simple game!
Can confirm, used to play it fairly often with family when I lived at my father's place.
It is a very fun game! I play it with my family on weekends sometimes
Ah yes, the domino.
I'm going to try and create a program for your pentomino game! I'll report back to explain how it goes.
good luck
Good luck
Good_er_ luck
Waiting response
Good luck
Guys, I have an ideia for a video game. So we make a 2D box and let random pentominos fall slowly till they reach the bottom, the player can move the piece left and right, and spin the pentomino. Once a line is filled the game give points and clear the line leaving the space where the pentominos above fall. The game is over when there's no more free space. The game will be called Petris
Tetris with Pentominoes has been implemented and it's really really really hard. Tiling pentominoes is so much harder than tiling tetrominoes.
its called tetris because theyre tetrominos. as in tetr-is. so naturally, the pentomino game should be called penis.
It's Petris, not tetris. They're completely unrelated and unique
@@megapussi PENTRIS, NOT PEE
As someone who (casually) plays Pentris, this is a fun analysis! Pentominos are definitely a lot more complex and interesting than their 4 tiled counterparts, and it really spices up the amount of thought you have to put in (especially during the faster phases when you have to make split second moves with awkward shaped pieces). Highest score I've ever gotten has only been a bit over a couple thousand points, so this could definitely be improved with a good bit of theory.
Yo aren't you the channel(besides me) that comments on all those Matt Rose videos?
@@BinglesP I comment on a lot of videos yeah but for some reason people know me from Matt Rose (probably because I watched him way before he blew up)
I hope I'm not too late for this, I've found a way to get an upper bound for a given nxn grid and a given number of pieces. Basically, each square on the best path is flanked by 2 walls, these walls might not be directly adjacent, but surrounding each square there will be 1 exit square, 1 entry square, and 2 other squares that either have a wall, or are an an empty path towards a wall. If the paths were not empty (ie they contained a cell that was part of the maximal path) then the path would simply choose to go towards the current cell via this empty path, meaning the maximal path is not maximal.
If that made sense, the next step is to see that each piece provides exactly 12 blocks of adjacency, when you account for multiplicities (ie the L block gives 1 square in the elbow with a multiplicity 2 adjacency). Also, there is free adjacency provided by the exterior wall, equal to n * 4. So the basic adjacency score is 12 * b + n * 4, where b is the number of blocks. So the max path length is less than (12 * b + n*4)/2
However we can adjust the adjacency score to make it more accurate. First, notice that when pieces touch each other to form a connected wall, they lose one adjacency (unless they touch on their corners). This means that each non-corner touching gives a -2 to adjacency score. Also, we should assume that there is a square on the outside rim, so that is another -1. Also Also, the last sections of the path require 3 adjacent walls, instead of 2. So that takes 1 more adjacency score. We are left with an equation that looks like: (12 * b + n*4 - 2 * (b-c) - 1 - 1 )/2. where c is how many corner connections are between the blocks. Note that c
😮
🤓👆
@@nicholasstanton9575 wtf man
The P Pentomino has "LOTS" Of Tetronimos in it.
The X pentomino tiling is exactly how I build my sugarcane farms in Minecraft!
Same!
I'd imagine Pentominos working well for Minecraft building in general
not surprising, considering each X is a water block with cane on each side! the fact that this tiles the plane exactly with no gaps corresponds with the fact that this is the maximum amount of cane that can exist in that space for that amount of water, which is of course true since each water block cannot possibly connect to more than 4 sand/dirt blocks! neat!
And now you know that a trivial game design choice created a scenario that due to the underlying and often ignored structure of mathematics has exactly one solution. Isn't that crazy? The plane can be tiled so many ways by so many monotiles, but due to the inherent geometry of a grid and this gameplay restriction there's exactly one way to build such a farm, and everyone must eventually stumble upon it. If the shape was any different there could be infinite farm designs, but this one provides no room for personal choice without sacrificing efficiency.
No!
THE X PENTOMINO TILING CAN’T
So lucky to find this video. Throughly intersting for its entire runtime with nice editing and good sound quality. Reminds me of Kuvina Saydaki, but higher energy. Subscribed in a heartbeat.
thank you very much!! kuvina was one of the inspirations for this video- I'm a massive fan of their sorting algorithm explaining video so I'm happy to be compared to them lmao
7:00 this makes me want to make a factory game where you merge ominos
Yes omg that’s so good what
wait wtf this only has 500 views?? this video was great it feels like the type of video that should have like a million or something!! Keep up the great work !!
my thoughts as well
Not anymore
fr
Yay, the video's up to 10k views - but I bet it'll get way more than that lol
-Paintspot Infez
Wasabi!
its 83k now
That pentomino game sounds like something that would be on an old school website and have a leaderboard on it where the people with the highest scores are shown.
By the end of this video, I really felt like this group of shapes were my old friends. I knew so much about them.
0:39 Canadian spotted
What I was thinking
😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂😅😂
the work done to reach the conclusion you did at 3:06 did not go unnoticed by me!
17:47 For board sizes n=42 and above, as soon as you’ve found the perfect solution for one board you’ve found the perfect solution for all of them because the game becomes a matter of “hiding” the two ends of the path. The optimal solution will just keep growing a bigger empty middle section the higher n gets. Why 42? Because 41 is the sum of the lengths of the “long sides” of every pentomino, the longest length a shape built from one of each can reach. 42 makes it impossible to block off the middle area.
this was looked in to, and that play only works from 42x42 up to around 84x84, when it's no longer the longest distance
@@YeaCloth I’m curious to know what happens when the size is doubled that makes the strategy change
@@jakobr_ basically, once the grid has doubled, the longest distancethe line can travel is no longer the adjacent corner, but instead the opposite diagonal. Because of this, its meaningless to make the stacked line anymore, and instead it's best to make dense mazes in either one corner or opposite corners
@@YeaCloth I don’t understand why the longest distance wouldn’t be to the opposite corner (or inside structures near opposite corners) from sizes 42-84
Your strategy only works for 16 board sizes, at 58x58, it is more optimal to create a line that leads directly to a corner, unlike 42x42.
I love watching people gush about special interests.
Same!!!
me too
very swag pfp :3
@@sweetmesaJS Thanks! I'm not really sure what yours is but it's cool!
hey you're that one celeste person
Huh, that pentomino path packing puzzle is pretty interesting, wouldn't be surprised if you could get it into a recreational maths journal with a bit of write up.
For some reason my friend group has colloquially named the F pentomino the 'Seahorse'
The mathematical properties of these objects are actually surprisingly interesting, thank you for sharing all these fun facts!
They remind me of symmetry groups, especially at the start of this video of course. What i mean by groups is that field of math with algebraic symetries or whatever it's called, like the ever-mysterious monster-group (which is like mathematical cosmic horror imho, the smaller groups tend to be more comprehensible to mere 3d mortals 😅).
in chemistry we also use symmetry groups because they are related to the ways in which materials interact with light
this channel gives off carykh vibes
agreed
Yeah
even the voice is similar!
Definitely!
CARY MENTIONED 🎉🎉🎉🎉
this is exactly what i need as source material for my Sokoban x Game Of Life mashup
I quite enjoyed this. The letter names you gave are in the Wikipedia article. I like the alternative naming they give by John Conway which uses the consecutive letters O through Z, though assigning O to the long straight pentomino is a bit dodgy. Other than that, my main math objection is the use of "regular symmetry" which is better known as "reflectional symmetry". Not that I know much, I'm an engineer.
Got excited to see a pentomino video on my feed out of nowhere! Gave me a bit of a throwback to a book series from Blue Balliet that got me interested in them. A character in that series used them for all sorts of things, a couple of which were mentioned here (I think rectangles of pentominoes were brought up a few times) and a few more unconventional things. Actually, OP, as an artist you might enjoy those books, as they're art-themed mysteries and treat the pentominoes as halfway a math object and halfway an art object, kind of like you did here.
seeing the x pentomino be such an anomaly gives me insurmountable amounts of joy
The very video that got me into a rabbit hole about pentominoes and eventually let me make my own game:
link?
@@YeaCloth still making it so none yet
i feel like this was one of the most pointless videos ive ever watched and simultaneously one of the most insightful and interesting and one of my personal favorites
When I was a kid, we did a Halloween school project where we had to make mixed media presentations on a mystery book. I found a book called Finding Vermeer about kids solving an art theft, and one of the kids was obsessed with pentominos, using them as a metaphor for conceots throughout the book. I made a fake newspaper clipping decorated with cardboard pentomimos, and ever since then I've been thinking about pentominos (and also Johannes Vermeer lol) at every possibly relevant time. I feel seen
This feels like a Wikipedia page if it was audio, but it’s very relaxing to listen to
This is a great video, with one exception: it's so annoying that there's a lot of text that only pops up for a split second (you have to pause or go frame-by-frame to read it)
Now we need pentris for pentominoes to match tetris for tetrominoes
Not only are there several of those games already, but technically it would be called Pentis since the R in Tetris is from the "Tetra" part of the name.
Someone made Pentatris in an app called SilentWorks Game Creator. You're welcome
@@mateuszszulecki5206 Yeah but without the R that T is holding back all the dyslexic mistakes a reader could make all by itself.
I don't think T has it in him, do you?
7:15 L, O, T and S. That spells Lots!
Professor Layton-ass video (I mean this in an entirely positive way I love hearing people talk about their interests)
This video reminds me of a puzzle
At 1.30 this rather abstract video got insanely interesting for any minecraft builder
Immediately subscribed, I saw someone else mention carykh and I got those vibes as well. I hope you’re going places, this was a great video
5:23 Ah, so that’s why it’s called Tetris. I feel stupid now
1:32 that is glowstone
4:12 For all you stardew valley fans out there
❤
Don't think I didn't see that "AMONGUS" for exactly 1 frame.
Now I'm curious if a proportional amogus shape can be made using only the ominos from every n-omino set
Among Us didn’t die, it became a part of us
For a while in high school i was obsessed with fitting pentominoes (specifically including their mirrors too) into large rectangles. After succeeding a couple times, I eventually tried the same with hexominoes and heptonimoes but to no avail, they’re so much harder to work with the further you increase cell count
you made me emotionally attached to groups of 5 cells
(the W and X ones are my favourite :) )
P and X are my favourites
Those are my favorites, too! W is also very good.
Good luck playing pentris…
i am watching because i have refreshed my recommendation list over 10 times today but this is always at the top so i will watch in the hopes youtube will finally recommend something else.
I'm pretty sure the reason that grouping kept appearing was because of the underlying graph structure, ILNVUWZ are all lines, and FTY all have a central square with two branches of length 1 and one of length 2
I had this as puzzle as kid and loved the idea of those shapes and what can be done with them.
I was never so GLUED to the monitor ever before, totally enchanting, i love pentominoes and the video about them
Lol those two specific frames within 11:34
interesting stuff, I'm pretty familliar with pentominoes since I play a lot of tetris variants with them, but it really surprised me to see some of these connections that I've sort of understood intuitvely layed out like this. You're proposed puzzle is also really damn interesting, played around a bit myself but it's a lot more initmidating than it first seems, do wish to see someone take a brute force computer though, if only for the satisfaction of knowing.
Fun fact: there’s a board game called Cathedral that uses many of these shapes as playing pieces.
11:34 among us :D
mogus
ogus
Gus
Us
S
important detail on the tetrominoes is that you often see them referred to as being 7, JZ TOILS, but J and Z are mirrors of L and S which are only distinct if mirroring isn't allowed but rotation is (as in the video game Tetris, which is where most people first encounter this subject)
this is such a great video for how little recognizment you get, expect to see me on your next video :D
Fascinating video! I really liked this format of just sharing what you have discovered about a specific topic. Pentominoes are incredibly interesting, and this scratched that itch I've had for a few years now.
0:16 is that the conway ship?
yooo thank you for hosting your survivor speeds back when you did, glad to see this blew up!
5:31 TETRIS
I spent a year or so playing with pentominos after reading about them in a novel. I can't remember which one, it was so long ago, but it was an integral part of the plot.
15:40 a properly placed U-pentomimo creates a 30-path
where? this arrangement doesn't work, if that's what you're thinking of vv o=path ==wall _=empty
o o o o o o _
o = = = = o _
o = o o = o _
o = o = = o _
o = o o o o _
o o = = = = =
_ o o o o o o
The path could cut around the U, making this solution invalid
@@saintbrownthetrojan It would be 28
It's so nice when you just hear someone talk about their interests with no ulterior "trendy" motive. It must be weird for one of your videos to suddenly blow up.
I can’t believe that you called the R-pentomino the “F-pentomino”… (wait… Conway calls an R-pentomino)
Anyway, starting from the R-pentomino, one can do an RF28B to a B-heptomino, then BFx59H to a Herschel, then HL95P into a pi-heptomino (releasing a glider), then PF35W into a wing, then WFx46H into a Herschel again, and finally HRx65R back into an R-pentomino (releasing another glider)
I've only heard it been called F before
@@dmcdouga07 I guess I’m a member of the ConwayLife community, and everyone there calls it the “R-pentomino” since that’s what Conway calls it
In fact, Conway called the I, L, F, and N pentominos “O”, “Q”, “R”, and “S”, so that the pentominos would be OPQRSTUVWXYZ
Personally it looks more like a lowercase f to me, doesn't really look like an R at least in the font of YT comments, so the label of " F-pentomino" makes more sense to me.
Also I haven't ever played conway's game of life but I have heard of it and know a game inspired by it called "Cell Machine" (yes that Cell Machine that was made by Sam Hogan)
a a a I love this video! Its premise, the time you put into it for the game, everything!
my autism brought me here
so did op's i think
anytime the subject of pentominoes comes up i immediately think of the carpentry minigame from puzzle pirates
The pentomino game you came up with already kinda exists. It's called veggie quest and it's a really good puzzle game, highly recommend
dude i don't know how you came up with this idea for a video but it's so cool, i never expected 18 minutes of *pentominoes* could be so engaging
Ngl the U and P pentominoes are bottoms
never looking at graph paper the same
we've found the final boss of autism
nah that would probably be Yenji Jem
the visual explanations/infographics are perfect and you did a great job with them. i also cannot imagine being able to say all of the things you said without needing like 46 takes for each so thats also impressive.
meow :3
I get a feeling Oshisaure will be interested in this too.
Well-constructed and nicely presented.
i think N is my favorite pentomino, it just flows like a river. thx for the awesome facts, these are some iconic shapes to me
I've done surprisingly similar research on four celled shapes but where diagonal adjacentcies are permitted. I found this information to be really interesting and I don't know why I never thought of looking at this. I once made a computer tile game using the shapes that was very interesting.
Thank you for creating this video, it was fun to watch you share your passion, and I learned a few things too!
Fun video. Would be cool to see more on higher polyominoes. You might also find the 11 different nets of cubes to be interesting, since they're a subset of the hexominoes.
The P Pentomino in particular is so much more interesting than I thought it was.
I watched this while recovering from an overdose, thank you
I absolutely love hyperfixating on certain topics most people would not be interested in. All these facts are so cool!!
The infinite planes were all optical illusion... They looked like they were moving lol
these tiling make my brain feel good
0:48 "eh, sucks for them" got me dying 💀
This is probably one of the most niche videos I have watched on TH-cam, and I am all here for it. Great video!
Take a shot everytime he says a word ending in '-omino'
The puzzle you created is fascinating!
I have somehow grown attached to these little bundle of squares.
so THAT'S where Ex from Puyo Puyo Tetris is from
Oh my god this is exactly the type of thing I like
Your channel is very underrated! This was a great, well-edited video that I found very interesting and well-written. You deserve at least a couple thousand subs. I'm gonna help get you closer :)
I love Tetris. Wait, this would be Pentris.