NOTE: Amazingly, despite there being a month of time between working on this video, the 3x3x3 and 4x4x4 pentacube pathfinding solutions were both beaten AFTER I rendered this video, but BEFORE I uploaded it. Both were beaten by a single cell, which is pretty wild.
20:00 of course it's always the X pentomino to bring it home, just like in the entire series, what a legend for somehow turning into its letter form and taking over the whole board (also hexomino facts gonna be hype once you figure out all those names)
@@thelollykitty if we're going by single character names they should be single characters on a standard keyboard. thorn isn't on most keyboards unless you're icelandic or actively use thorn for other reasons, so it would be best to just use the standard letters and numbers everyone already has access to
@@Intergalacticprismaticcreature if you go to the spreadsheet in the description and click on the "pentomino cubes/tesseracts" link (third one from the top), that one has every 3d and 4d solution so far, along with a picture of the 3d and 4d pentominoes
i've been on a bit of a bejeweled binge lately so this got me thinking of what a match 3 game would be like if it were in a cube instead of on a flat 2D plane lol
@@Iam1Person i've actually been thinking about it more and it might work better if it were in a 4x4x4 cube and you only had to match 2 gems instead of 3 lol. that'd drastically simplify it i think... i hope...
Actually thr series would end with pentatesseracts, as anything above that would only contain the same penta-things as before, since there's a maximum of four different directions you can take using 5 cells
This is super well done again! I hope that you'll periodically make update videos for some of the coolest new pentomino shenanigans/updated records for the existing ones, as even though I'm definitely not smart enough to figure out these on my own (haha!) I would love to see the community's continued work!
I might tbh! A lot of the stuff from all the videos are outdated now as better solutions have been found, so I think in the distant future I might do another update video once new better solutions stop being found. That would not be for a really long time though, as to give as much time as possible for people to find even better solutions for many of these boards
Actually, for the pentacube pathfinding, those split layer diagrams on the right are quite understandable for me. This is a similar to how Lonpos presents those pyramid puzzles - they have split layer diagrams too. These split layer diagrams work well for 4D too.
Here's a unifying framework for thinking of all these different varieties you have come up with (2d, 3d, torus, cube faces). I think the correct generalization is a graph G as the "space", and subgraphs with 5 vertices as the "pentominoes". The problem can then be posed as, given a connected graph G and a beginning and end vertex x and y, maximize the distance from x to y by removing a sequence of pairwise non-isomorphic k-vertex subgraphs from G. Under this definition the weird corner cases and loopy cases from the cube and torus count as distinct new pentoninos.
I was one of the first 10,000 viewers on this video Also, this series inspired me to make my own google sheet called "ominoes" and share it with my classmates
can't wait for some big mathematicians to discover the series and write a paper with weird symbols in which they prove and generate the paths for n-dimensional n-minos in a n-dimensional grid
Once you come back to polyominoes, you should look into hex-based pentominoes. (For clarity, use hexagonal tiles instead of square tiles to form the pentominoes. (I think there are 18 of those on a 2D plane, but I only tried to figure them out in my head.)
Has anyone been throwing computer search at these problems, or do people feel that to be against the spirit of the community? I'm not sure off the top of my head what sort of algorithm you'd use, something that can optimize with extreme constraint satisfaction in a highly multimodal search space. Maybe a tree search algorithm would work, placing a shape at a time? The branching factor is really high to start but diminishes fast, at least on small boards.
14:45 you can use retextured blocks. So you would only need to retexture once and then just place blocks. Easier keep an index on the corner of the screen with "block youre facing = pentomino" and just highlight what youre looking at.
You should put item frames pn the inside of your minecraft visualizations so you can still see through it but if you add a grey block you will see the walls more easily.
Something i think would be cool (and something i have done myself already) is connecting dominoes so that all the pieces of a number connect (while obeying domino rules). The maximum you can do in 2D is 4. In 3D i managed to do 6.
8:15. Sorry to be a massive nerd but technically it’s called a Euler diagram not a Venn diagram. The reason why is because not all regions are connected. Edit1: also do 4-hypertorus next
NOTE: Amazingly, despite there being a month of time between working on this video, the 3x3x3 and 4x4x4 pentacube pathfinding solutions were both beaten AFTER I rendered this video, but BEFORE I uploaded it. Both were beaten by a single cell, which is pretty wild.
Really funny
lol
Alright I’m making a Blueprint for Hexomino Facts GET UP HERE DECKARD
Try 4 dimenional
@@Joshplays-Games already done up to 3x3x3x3 I think
20:00
of course it's always the X pentomino to bring it home, just like in the entire series, what a legend for somehow turning into its letter form and taking over the whole board (also hexomino facts gonna be hype once you figure out all those names)
⬛️🟨🟨⬛️
🟨🟨🟨🟨
this hexomino should be former english letter thorn, change my mind
@@thelollykitty if we're going by single character names they should be single characters on a standard keyboard. thorn isn't on most keyboards unless you're icelandic or actively use thorn for other reasons, so it would be best to just use the standard letters and numbers everyone already has access to
Instant Carykh feel to the videos (Very good thing) keep up the good work!
5:15 they even got the Carys
Hell yeah my 4³ solution came in even though it was beaten 🔥
I can't wait for 4D pathfinding
ah yes
fun fact: there are exactly 26 4d pentominoes (pentatesseracts), meaning there's exactly one for each letter
the new ones in 4d are O, C, and D
I wanna see!
@@Intergalacticprismaticcreature if you go to the spreadsheet in the description and click on the "pentomino cubes/tesseracts" link (third one from the top), that one has every 3d and 4d solution so far, along with a picture of the 3d and 4d pentominoes
obsessivr compulsive disorder
@@Intergalacticprismaticcreature good luck seeing them
@@alesonbrjk i am 4d creature 👽
Can't wait to pathfind on a 3-torus!
i've been on a bit of a bejeweled binge lately so this got me thinking of what a match 3 game would be like if it were in a cube instead of on a flat 2D plane lol
Much more confusing.
@@Iam1Person i've actually been thinking about it more and it might work better if it were in a 4x4x4 cube and you only had to match 2 gems instead of 3 lol. that'd drastically simplify it i think... i hope...
Well well well
Time for pentatesseracts
Actually thr series would end with pentatesseracts, as anything above that would only contain the same penta-things as before, since there's a maximum of four different directions you can take using 5 cells
What about hexatesseract?
@ sounds very fun indeed
@@diegonalsbut you could orient and rotate them still in higher dimensions. Until some much higher dimension
there would be 1 new one i tihnk being the * pentesseract
2:56 MOM LOOK! IM ON A DECKARD VID!!! :DD
didn't expect to see you here :P
and on 2^8 !
Yoooooo
Yay a young person who doesn’t use emojis
Minecraft path findings are a genre of videos i didn't know i loved ^_^
Thankkkk u soooo muchhhh
This morning i watched all the videos and im so happyyy that u dropped the 4 todayy ❤❤
This is super well done again! I hope that you'll periodically make update videos for some of the coolest new pentomino shenanigans/updated records for the existing ones, as even though I'm definitely not smart enough to figure out these on my own (haha!) I would love to see the community's continued work!
I might tbh! A lot of the stuff from all the videos are outdated now as better solutions have been found, so I think in the distant future I might do another update video once new better solutions stop being found. That would not be for a really long time though, as to give as much time as possible for people to find even better solutions for many of these boards
@@v.deckard narnia
I started beatboxing when he was mentioning the pentacubes for the 6x6x6
19:32 - Yay I'm there
More new cube boards stuff:
5x5x5 has been improved to 55
6x6x6 has been improved to 80
I'm guessing it's the bottom layer with the 6x6x6 because it looked pretty open.
is there somewhere I can find these solutions?
@@blockshift758it already used every piece
What a way to end the pentomino pathfinding series. This had me hooked from the start. Awesome stuff man!
Okayy , so I know what I'll build next on the server with my friends
can't wait for part 5: pentomino pathfinding hexomino edition
Actually, for the pentacube pathfinding, those split layer diagrams on the right are quite understandable for me. This is a similar to how Lonpos presents those pyramid puzzles - they have split layer diagrams too.
These split layer diagrams work well for 4D too.
I love the pentomino series.
It has been so much fun :3
Here's a unifying framework for thinking of all these different varieties you have come up with (2d, 3d, torus, cube faces).
I think the correct generalization is a graph G as the "space", and subgraphs with 5 vertices as the "pentominoes".
The problem can then be posed as, given a connected graph G and a beginning and end vertex x and y, maximize the distance from x to y by removing a sequence of pairwise non-isomorphic k-vertex subgraphs from G.
Under this definition the weird corner cases and loopy cases from the cube and torus count as distinct new pentoninos.
I was one of the first 10,000 viewers on this video
Also, this series inspired me to make my own google sheet called "ominoes" and share it with my classmates
So cool!!! Exited for whatever you do next!
YES!!!!! Wait the series is over NOOOOOOOOOOO!!!!!
It’s sad this series HAS come to an end and im soo saad RECONTINUE IT!!!!!!!!!
Next step:3d hexominos
Later step:4d pentominos
AHHH I WAS SO EXCITED FOR THIS BUT I FORGOT
can't wait for some big mathematicians to discover the series and write a paper with weird symbols in which they prove and generate the paths for n-dimensional n-minos in a n-dimensional grid
actually it would be n-dimensional m-minos in an o-dimensional grid
3:43 very readable text
very
8:16 tpot credits
well now we dream of “5d chess battle advanced with multiverse time travel pentomino pathfinding”
X and I casually being the absolute GODS of symmetry
Once you come back to polyominoes, you should look into hex-based pentominoes. (For clarity, use hexagonal tiles instead of square tiles to form the pentominoes. (I think there are 18 of those on a 2D plane, but I only tried to figure them out in my head.)
10:28 bro sounded like carykh for a moment
small tip: you can use mods to force the player model to "swim" which makes it possible to traverse 1x1 spaces making the larger models unnecessary
6:22 Actually, M has 2 axes of symmetry. You can make it diagonally, slicing between the 2 sticky-outy nubs
First tpot 14, then this? This day can't get any better,
There is one way... For Geometry Dash update 2.207 to release on mobile!
*snap*
So to clarify, this one's going in r/suddenlyBFDI
And time for the 7:00 with object Unicode 1 (NOT 1A) is here
YESSS MORE PENTOMINO CONTENT 💕💕
Q AND R PENTIMENTO HAS RETURNED!!
6:50 the A tetracube actually has a rotational symmetry, going trough a side instead of a corner
18:08 challenge accepted
Never have I been more upset to have aphantasia. Even seeing the cube in real time it's breaking me brain.
I want the larger 3D pathfindings to be big playgrounds ❤
part five: polytominos
using pentominos and tetrominos together to make weirder boards
YAYA, PART 4 IS HERE 🔥🔥🔥🔥
🥵🥵🥵🥵
@NmpPnm lol
Your "venn diagram" of which tetracubes are in each pentacune was actually an euler diagram
Has anyone been throwing computer search at these problems, or do people feel that to be against the spirit of the community? I'm not sure off the top of my head what sort of algorithm you'd use, something that can optimize with extreme constraint satisfaction in a highly multimodal search space. Maybe a tree search algorithm would work, placing a shape at a time? The branching factor is really high to start but diminishes fast, at least on small boards.
Haven’t watched but it’s peak
Don't worry about the diagram, JacknJellify uses a diagram like that in the credits
My next Meet Your Maker base is gonna go crazy
more *mino content wooo
14:45 you can use retextured blocks. So you would only need to retexture once and then just place blocks.
Easier keep an index on the corner of the screen with "block youre facing = pentomino" and just highlight what youre looking at.
Not me reading the title as cube facepainting 💀
i feel like someone could make a maze out of these pentominos, probably in minecraft
You should put item frames pn the inside of your minecraft visualizations so you can still see through it but if you add a grey block you will see the walls more easily.
6:32 MSG THE KING OF FLAVAH
Next - sextominoes, sextacubes, septominoes, septacubes, octominoes, octacubes, nonaminoes, nonacubes, and finally decaminoes and decacubes
19:45
Please call the olive hexomino with a 3x by 5y bounding box "Rutherford B. Hayes' Hexomino" for no reason
cursed tetris
Welp. My yt recommended me this and I'm gawking
Can you release your pentomino image pack?
19:32 im in the video!!!!!
next: 4D pentominoes
This is a good video 👍
Something i think would be cool (and something i have done myself already) is connecting dominoes so that all the pieces of a number connect (while obeying domino rules). The maximum you can do in 2D is 4. In 3D i managed to do 6.
19:24 shouldn't the 1 and 2 be switched in the 5x5x5 pentacube pathfinding net?
Idea: 4D pentominoes
11:00 you could have used wool blocks for a more "uniform" look
the goat
YAAAY
Aight but like 4D pentominoes when
Try Triangle pentomonoes, that instead of squares, you replace them by Triangles.
diapentomino ( diagonal pentominos) pathfinding
Well, guess the next one will be pentatesseracts 😊
Can you make the pentacubes out of glass as well?
can i ask for the list of materials needed for the 6x6x6?
What about pathfinding with only one kind of pentominoes?
When you brought out Minecraft
Me: happy happy happy happy happy happy
On the 5x5x5 they went 18 19 10 21 22
its funny that 6 by 6 by 6 has a path of 77, while the credit says ondra77
wtf Marble Blast music?
Neato! Now what's it like to navigate in 4D?
It's pentominover
inecarfet :)
Is it possible to expand this methodology up to 4d?
people be talking about 4d pathfinding but what i wanna see is hyperbolic geometry pathfinding
how can it be over when we haven't gotten 4d pentominoes :(
Or 5d
3d pentomino pathfinding was already hard enough to visualize as is lol
@@v.deckard 4d chess, 4d minesweeper... and we gave up on this ? 🥺
currently tesseracts that have solutions:
2×2×2×2 - 6
2×2×2×3 - 9
2×2×2×4 - 14
2×2×3×3 - 16
2×2×2×5 - 17
3×3×3×3 - 31
Hmm... I wonder how hard it would be to turn the 6x6x6 pentacube pathfinding into a house.
what about hyperbolic pentominos
Should we do Hypercubes?
I can do the hypercube versions if you want
8:15. Sorry to be a massive nerd but technically it’s called a Euler diagram not a Venn diagram. The reason why is because not all regions are connected.
Edit1: also do 4-hypertorus next
For April fools could you do monomino facts
for some reason i wanna see trianglular pentominoes
9:49 shouldnt the path start from the middle cell, which also increases the length by 1?
rise one cube. go right right one cube. 4 becomes 3 lowering the total path length by 1
8:33 about half of the E pentacube (in the A tetracube group) does not show up.
wait wheres the 4d path making?
PENTOMINOOOOOOOOOOOOOOOES
I wanna do 7x7x7
1 hour ago
What about triominoes
theres only two of them so it wouldnt be too interesting
9:39 pentacube pathfinding in minecraft