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no longer accurate) some of the cuts in this video are a bit janky, and it's likely some of the video is going to be outdated within the next week.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
12:47 it sucks when good RUclipsrs say “i don’t think talking about X would be very interesting” when it WOULD be very interesting to watch them talk about it
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! ❤❤
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.
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.
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???
Babe wake up more pentomino facts
*Inserted funny comment, not reply why do everyone call replies commenys*
E
@@VeryMonkelol E
@@blitzyboi8055 E
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
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?
12:47 it sucks when good RUclipsrs 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.
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
13:08 the random floating island of octomino 16×16 😭
-raynekitty
1:40 Important!
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
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 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 happened to search for 'pentomino' because I wanted to watch something like your original. Perfect timing! I feel so blessed~♡
by the math gods 🙏
This feels so daunting with all the possible combinations of parameters
6:13 OH MY GOD HE KNOWS BFDI
l i y pentomino
6:14 LIY BFB NO WAY (also, awesome vid!)
Oh hell yeah it’s a series now, I’m definitely subscribing now
haven't even watched the video yet, but i know its a banger
Now I love pentamino, this series is awesome
P.S. Liy
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!
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.
the "snake snake snake snake snake" part was so dumb, i love 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.
6:12 bfdi!
Bro your content is like carykh
King! Your puzzles and speeds got me into a lot of puzzles, keep up the awesome videos!
Get yourself a man who loves you as much as this guy loves pentominoes
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.
The pentominos could make a niche little board game with those orientations
I could watch this for hours without ever getting bored
I wanted this sequel so much :D
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
found 2 4x10 solutions, one using using the V, L and P pentominoes, and the other also using Z,V and P
PENTOMINOES 🗣️🗣️🔥‼️
Omg yesssss hes back
I loved the vihart reference :)
6:14 BFB fan!
8:08 I have gained the knowledge of More Pentomino Pathfinding
yay more pentominoes :D
Yayyy generalized pentominal grid solutions!!
6:14 THE PENTOMINO GUY LIKES OSC!!!! XD
can’t wait for part 3D!
11:00 just use jan Misali's polyomino naming system
Wait, is that Toki Pona?
@@TetrisRules43 lon.
yet again another banger right here
ooohhh 6:14 id that Liy from hit show Battle For Dream Island's FOURth season?
6:13 why is there a Bfdi reference In my pentomeno video
SO MANY REFERENCES TO COOL PEOPLE
6:14 youve got preventing 2753 deaths
here’s an idea for naming the hexominos: use jan misali’s meathod of categorizing (roughly breaks in 8 groups) then name based on letters
legendary video part 2
6:14 LIY!!!!!!!!!!!!!!
6:15 he knows object shows
6:14 🎉🎉
the yellow one at 10:58 could be called the Z-hexomino
I love this
Not even a day and I’m watching this
It would be VERY COOL if you make a sequel: "Hexomino facts"
Oh cool. Said from someone who had watched the first part.
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!
Liy from bfb spotted
we have been spotted
i appreciate the patricia taxxon music :3
6:53 yea they are! Vihart’s great :D !
What about pentominos and hexominos together? What about different board shapes?
she found her next adventure
I wonder what would happen if we took the tightest path through the maze? Like being able to diagonal through tiles?
6:14 BFDI MENTIONED
never thought that he is a bfdi fan
6:50 omg vihart reference!!!!!
That’s what I was thinking too
You sound just like carykh !!!
When will part 2 come
+ I have a challenge - heptomino pathfinding
6:14 HI LIY!!!!
6:14 BFDI MENTIOKNER
6:49 istg this is a reference to something ive seen, i just forgot what it was.. it has to be
I can't wait
BFDI
HUH,BATTLE FOR DREAM ISLAND
6:10
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)
5:19 i’m a math wiz
67+67=134
6:14 deckard uses bfdi!?!?!?
8:02 yes pun
what about tetrominoes? even if its a really short one, please make it, i would find it really interesting!
I cannot find that 3d pentomino video any where...
The optimal path sizes seem very close to the triangle numbers.
6:50 VIHART REFERENCE OH MY GOD
6:14 i've found my next adventure!
yippee, pentominos
this is pretty interesting
6:14 "bye liy" -x, bfb 5
It was bye not hi if i remember correctly
@@huzzah_2763 whoops mb
"HEY! I wanted to say that!" - 4, BFB 5
a vi hart reference? in my recreational mathematics video?? preposterous!!
Found a 9x17 one with a path length of 56!
4:05 why two 65s?
I'd love to watch a loop of 6:50 ^^
From vi hart
And then we do heptominoes, because that will of course be fun and not excruciatingly painful.
6:15 LIY?!??!?!?!
1:03 I can’t find that website
Liy what are you doing here? 6:15 6:14
3:22 damn im in the video lol
This hexominoe
⬜️⬜️⬜️⬜️⬜️
⬜️⬜️⬜️🟥⬜️
⬜️⬜️⬜️🟥⬜️
⬜️🟥🟥🟥⬜️
⬜️⬜️🟥⬜️⬜️
⬜️⬜️⬜️⬜️⬜️
Should be called “THE FLUSHER!!!”
IS THAT LIY FROM BFB AT 6:14
Will there be 4D pentomimoes and/or 3D hexominoes?
What about Heptominos, Octominos and Nonaminos and So On!
6:14 HI LIY
6:13 LIY
6:13 liy jumpscare