Due to the fact that I had to keep re-editing and re-recording (because people would keep finding new solutions that would make what I said no longer accurate) some of the cuts in this video are a bit janky, and it's likely some of the video is going to be outdated within the next week. Any changes/updates to boards shown in this video will be updated in this message! CHANGELOG: - This was just a mistake, 4x14 should be credited to mister_person - Another mistake I forgot to catch. The 42x42 has a solution of 148, not 147. When I initially recorded that part, 147 was the best solution, being n+105, but it was slightly improved leading to n+106 & 148. I re-recorded the n+106, but forgot to re-record the 148. - The 15x15 shown was the wrong one, the record for that is 96. - 12x12 pentominoes has had a slight tweak (found by drake), swapping the N, Z, and F pentominoes, making the path now 80! - 4x6 and all boards of 4xn and above have had more optimal solutions found. - 11x11 has also had a new improvement up to 68 found by Freddy.
As a math enthusiast (not quite doing/discovering math on my own but still enthralled by it), this is exactly what i was thinking. Like this is basically a subsection of geometry, which is in itself a category of math. They can call themselves not mathematicians all they want but they are literally creating proofs and theorems and algorithms for a basically untouched subject.
@@adryanlucas096 it's a part of optimisation, although approaching it from a game theory angle might be interesting. I'd call the class of problems "path blocking" for the double meaning of "block"
Another mathematician chiming in. What these folks are doing is more pure math than my work! I wonder if by "actual mathematician" they mean someone institutionally trained, who may have a toolkit of high level techniques that might crack open solutions.
@@blobberberry Yeah I think it just has a mystique to it, doing "real maths" and being a "real mathematiciain". For this kind of problem, I think the feeling comes from not "proving" that something is the best solution, which they both do do for certain grids in the previous video, and something that is absolutely not possible in all sorts of area of maths, and there's so many mathematicians who are just hunting slightly better upper and lower bounds on complicated combinatorial problems. But it's easier to recognise coming up with an elegant proof of something as "real maths" than recognising this kind of in-the-trenches exploration, which in truth is the very core of the subject
13x13 was so funny because no one could break 84 for like a week, and then I come back to the server and all of a sudden there’s like 5 new records lmao
I didn’t subscribe on the last video and then I couldn’t find it again so I convinced myself it was just a hallucination. Thanks for making a sequel so I can hallucinate again! ❤❤
12:47 it sucks when good UA-camrs say “i don’t think talking about X would be very interesting” when it WOULD be very interesting to watch them talk about it
It's very cool watching mathematical discoveries happen in real time like this. This is very cool! Also apologies for not responding like I said I would on the last video, tbh I just forgot and then I found this again.
Random polyomino fact I found via computer search: the six free tetromimoes that are possible to make on the surface of a 2x2x2 cube can all be packed onto that surface. In fact, there are four different ways to do so. However, there is only one way to do it that has the O tetromimo go over an edge.
As good news, I’m trying to prove if 9x9 can be improved. I saw the hidden Liy. At 9:56 , I found 2 more 25 solutions, 1 that uses the exact same 3 pieces and another that use the L and Y instead of the P and V. I just found another 25 solution for 4x10, and it uses the L, W and Y. At 13:54, 5x20 was actually tested before and I found 53, which Cloth later found 55.
I think this problem could be interesting if, at the point where you get the final degenerate pattern, you suddenly allowed duplicate pentominoes. The solution space would be much richer to explore!
what's the longest unoccupied path you can construct on a Blokus board, following the game's rules? (4 differently colored sets of all 1-5minos, where any two minos of the same color must be connected by corners only)
Due to the fact that I had to keep re-editing and re-recording (because people would keep finding new solutions that would make what I said no longer accurate) some of the cuts in this video are a bit janky, and it's likely some of the video is going to be outdated within the next week. Any changes/updates to boards shown in this video will be updated in this message!
CHANGELOG:
- This was just a mistake, 4x14 should be credited to mister_person
- Another mistake I forgot to catch. The 42x42 has a solution of 148, not 147. When I initially recorded that part, 147 was the best solution, being n+105, but it was slightly improved leading to n+106 & 148. I re-recorded the n+106, but forgot to re-record the 148.
- The 15x15 shown was the wrong one, the record for that is 96.
- 12x12 pentominoes has had a slight tweak (found by drake), swapping the N, Z, and F pentominoes, making the path now 80!
- 4x6 and all boards of 4xn and above have had more optimal solutions found.
- 11x11 has also had a new improvement up to 68 found by Freddy.
what's the website called
Question, where could I find the discord where these problems are being tested? I want to help (and definitely not force you to make more changes :])
@@11frends39check desc
Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake Snake
12X12 found by who???
As a mathematician I can confirm that you are, in fact, mathematicians and what you are doing is maths
As a math enthusiast (not quite doing/discovering math on my own but still enthralled by it), this is exactly what i was thinking. Like this is basically a subsection of geometry, which is in itself a category of math. They can call themselves not mathematicians all they want but they are literally creating proofs and theorems and algorithms for a basically untouched subject.
What could we name it
@@adryanlucas096 it's a part of optimisation, although approaching it from a game theory angle might be interesting. I'd call the class of problems "path blocking" for the double meaning of "block"
Another mathematician chiming in. What these folks are doing is more pure math than my work!
I wonder if by "actual mathematician" they mean someone institutionally trained, who may have a toolkit of high level techniques that might crack open solutions.
@@blobberberry Yeah I think it just has a mystique to it, doing "real maths" and being a "real mathematiciain".
For this kind of problem, I think the feeling comes from not "proving" that something is the best solution, which they both do do for certain grids in the previous video, and something that is absolutely not possible in all sorts of area of maths, and there's so many mathematicians who are just hunting slightly better upper and lower bounds on complicated combinatorial problems.
But it's easier to recognise coming up with an elegant proof of something as "real maths" than recognising this kind of in-the-trenches exploration, which in truth is the very core of the subject
Babe wake up more pentomino facts
*Inserted funny comment, not reply why do everyone call replies commenys*
E
@@VeryMonkelol E
@@blitzyboi8055 E
13x13 was so funny because no one could break 84 for like a week, and then I come back to the server and all of a sudden there’s like 5 new records lmao
Are you leiz
Btw 6:14
@@Xavier-kp3yy No I’m CringeCat I appeared a few times in this video
@@Cats83747 Whats the server and why can't i find it?
@@Cats83747 Whats the server?
I didn’t subscribe on the last video and then I couldn’t find it again so I convinced myself it was just a hallucination. Thanks for making a sequel so I can hallucinate again! ❤❤
Here's a comment for you to hallucinate as well! :D
I happened to search for 'pentomino' because I wanted to watch something like your original. Perfect timing! I feel so blessed~♡
by the math gods 🙏
12:47 it sucks when good UA-camrs say “i don’t think talking about X would be very interesting” when it WOULD be very interesting to watch them talk about it
EXACTLY!! I hate it when people do so as much as you do
Bro was so happy snaking the path arround 😂
Important! 1:40
It's at 6:50; the other comment is a bot.
13:08 the random floating island of octomino 16×16 😭
-raynekitty
1:40 Important!
This reminds me of that one puzzle game where you're making a game and need to make really long paths so no one can get a refund
Veggie quest?
Indeed @@daepe
i might make a physical board game out of this with magnets
That sounds fucking awesome
@@guruthemaster4516first I’ll have to convince my mom to buy it
First I’ll have to convince my mom to get the supplies
You might just be able to modify blockus slightly
This feels so daunting with all the possible combinations of parameters
6:14 LIY FROM BFB
No escape from the osc and i dont mind
@@yahoo5726 truly no escape
yoylecake
@@WaterOnTheHill-xp3yx i cant escape from geometry dash
Gas gas gas
@@WaterOnTheHill-xp3yxosc is everywhere
6:14 LIY BFB NO WAY (also, awesome vid!)
Oh hell yeah it’s a series now, I’m definitely subscribing now
6:13 OH MY GOD HE KNOWS BFDI
l i y pentomino
haven't even watched the video yet, but i know its a banger
the "snake snake snake snake snake" part was so dumb, i love it
Now I love pentamino, this series is awesome
P.S. Liy
It's very cool watching mathematical discoveries happen in real time like this. This is very cool!
Also apologies for not responding like I said I would on the last video, tbh I just forgot and then I found this again.
King! Your puzzles and speeds got me into a lot of puzzles, keep up the awesome videos!
The pentominos could make a niche little board game with those orientations
Get yourself a man who loves you as much as this guy loves pentominoes
6:12 bfdi!
Bro your content is like carykh
Random polyomino fact I found via computer search: the six free tetromimoes that are possible to make on the surface of a 2x2x2 cube can all be packed onto that surface. In fact, there are four different ways to do so. However, there is only one way to do it that has the O tetromimo go over an edge.
I wanted this sequel so much :D
As good news, I’m trying to prove if 9x9 can be improved.
I saw the hidden Liy.
At 9:56 , I found 2 more 25 solutions, 1 that uses the exact same 3 pieces and another that use the L and Y instead of the P and V.
I just found another 25 solution for 4x10, and it uses the L, W and Y.
At 13:54, 5x20 was actually tested before and I found 53, which Cloth later found 55.
I could watch this for hours without ever getting bored
8:08 I have gained the knowledge of More Pentomino Pathfinding
Yayyy generalized pentominal grid solutions!!
6:51 Viheart reference?
I’m so glad I’m not the only one who thought that
The text that flashes actually says "vihart reference because her videos are cool as hell" so yes!
I loved the vihart reference :)
12:00 YOO THATS MEEE
12:16 ME AGAIN YAYAYAYA (one of ur favourites?!?) {idk if I'm hyped for no reason lol}
😮 11:34
yay more pentominoes :D
can’t wait for part 3D!
6:14 youve got preventing 2753 deaths
PENTOMINOES 🗣️🗣️🔥‼️
It would be VERY COOL if you make a sequel: "Hexomino facts"
SO MANY REFERENCES TO COOL PEOPLE
11:00 just use jan Misali's polyomino naming system
Wait, is that Toki Pona?
@@TetrisRules43 lon.
6:14 BFB fan!
Omg yesssss hes back
yet again another banger right here
i appreciate the patricia taxxon music :3
Not even a day and I’m watching this
found 2 4x10 solutions, one using using the V, L and P pentominoes, and the other also using Z,V and P
Oh cool. Said from someone who had watched the first part.
6:53 yea they are! Vihart’s great :D !
she found her next adventure
6:14 THE PENTOMINO GUY LIKES OSC!!!! XD
6:50 omg vihart reference!!!!!
That’s what I was thinking too
legendary video part 2
Liy what are you doing here? 6:15 6:14
I love this
I wonder what would happen if we took the tightest path through the maze? Like being able to diagonal through tiles?
a vi hart reference? in my recreational mathematics video?? preposterous!!
the 14x14 hexomino is 108 not 107, i own it actually
And then we do heptominoes, because that will of course be fun and not excruciatingly painful.
6:14 LIY!!!!!!!!!!!!!!
What about pentominos and hexominos together? What about different board shapes?
6:14 HI LIY!!!!
BFDI
HUH,BATTLE FOR DREAM ISLAND
6:10
6:50 VIHART REFERENCE OH MY GOD
3:22 damn im in the video lol
This hexominoe
⬜️⬜️⬜️⬜️⬜️
⬜️⬜️⬜️🟥⬜️
⬜️⬜️⬜️🟥⬜️
⬜️🟥🟥🟥⬜️
⬜️⬜️🟥⬜️⬜️
⬜️⬜️⬜️⬜️⬜️
Should be called “THE FLUSHER!!!”
6:14 i've found my next adventure!
the yellow one at 10:58 could be called the Z-hexomino
what about tetrominoes? even if its a really short one, please make it, i would find it really interesting!
6:14 nice
hi pie bye liy!
@@ManiTheObbyist hey! i wanted to say that!
@@rojandyyyyyyyyy well, if you don't like it, just screech me!
Damn, no septiminos? Fine, ill do it myself
19x19 pentominoes looks like an ostrich
Are we going to get hexomino facts at some point?
this is pretty interesting
The optimal path sizes seem very close to the triangle numbers.
6:13 why is there a Bfdi reference In my pentomeno video
Are you gonna stream Minecraft 24\7?
Edit: 2 likes letss gooo
In the nebulous future, yes! Not any time soon, though
@@v.deckardoh,cool.
6:15 he knows object shows
Challenge: Tetromino pathfinding
I can't wait
I think this problem could be interesting if, at the point where you get the final degenerate pattern, you suddenly allowed duplicate pentominoes. The solution space would be much richer to explore!
You sound just like carykh !!!
never thought that he is a bfdi fan
6:14 🎉🎉
cool! question, where is that back ground?
Found a 9x17 one with a path length of 56!
I am more interested in a Tetris-like with pentonimos instead of tetronimos.
yippee, pentominos
6:14 HI LIY
i'd recognize that vihart snaking sound anywhere!
colored blocks arrangements
chess battle advanced
When will part 2 come
+ I have a challenge - heptomino pathfinding
6:13 liy jumpscare
Again, you could publish a collective paper with this. Do it. Publish a paper.
Someone found a path of 80 for 12x12 pentominoes
what's the longest unoccupied path you can construct on a Blokus board, following the game's rules? (4 differently colored sets of all 1-5minos, where any two minos of the same color must be connected by corners only)
6:49 istg this is a reference to something ive seen, i just forgot what it was.. it has to be
imagine how many heptominoes there will be
Liy easter egg
6:14 BFDI MENTIONED
6:14 liy