But how hard IS Flow?
448,378
Published 2024-01-15
This video is dedicated to ML for playing the game alongside me and listening to me explaining the research that went into this video. It is also dedicated to GS and JH for always entertaining me in discussing the random puzzles/problems I come up with. Lastly, this video is dedicated to RG for inspiring passion in me and encouraging me to continue my journey of teaching.
I also would like to address a couple of questions that you may come up with while watching the video:
Q: You said that we should consider an arbitrary 3SAT formula, but then proceeded to use a specific 3SAT formula.
A: Good point. Choosing a specific 3SAT formula was solely done for the purpose of visualization. However, the procedure of constructing the graph is generalizable because it works for any 3SAT formula (create vertices for each variable, each clause, etc.)
Q: I'm confused as to what the difference is between P and NP. The "friends subset" question doesn't seem that hard since we used brute force. Didn't we essentially use brute force for the "oldest person" question?
A: Yes! Both are essentially brute force. The difference appears in the amount of "queries" you have to do. For the "oldest person" question, you need to query every person exactly once. So if there are n people, then you need to only make n queries. For the "friends subset" question, I would have to query every group of 8 people. There are (n choose 8) = (16 choose 8) = 12870 such groupings. The second problem requires many more queries and grows at a faster rate.
Finally, I would like to thank Grant (3Blue1Brown) and the team that develops manim for the brilliant tool that is manim.
Music Credits:
'Filaments' by Scott Buckley is under a Creative Commons license Attribution 3.0 Unported (CC BY 3.0)
@ScottBuckley
Music promoted by BreakingCopyright: bit.ly/filaments-song
All Comments (21)
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You know you’ve played a lot when you recognise a lot of the puzzles
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I like how "3blue1brown style math explainers" are just straight-up a genre on youtube now.
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This game indirectly trained me in a way that is quite easy and enjoyable for me to draw PCB tracks when I'm designing
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so interesting how I can look at a puzzle from this game after having not played it in years and my eyes still instantly show me the solution for any board smaller than like, 9x9
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I beat every flow game, including the two flow games that aren’t flow free. It took me like 3 years and was a huge meme with my friends because I beat roughly 100k levels, getting all achievements
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There are at least three questions related to Flow, and the one you tackled is "given a set of endpoints, is there a solution?". There's also "given a set of endpoints and the fact that there is a solution, what is the solution?", which is what players are doing, and "find a way to generate valid Flow maps", for which there's almost certainly better options than "guess endpoints, check if there's a solution".
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Great video but the music makes me feel like I’m watching a documentary about a recent tragedy
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I've played this quite a bit over the years and it's nice to see it intersect with complexity theory. Great video, glad it got recommended.
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I used to play flow free obsessively and its so easy, eventually you can just kinda see where everything goes before even drawing any lines, even at the bigger levels. That being said, introduced it to my mom and was astonished to see just how long it took her to solve even the smaller levels and she's a pretty clever person. So it definitely is just a question of experience
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i was starting to think i was the only one playing flow anymore. good to see theres so many other fans out there!! absolutely my favorite mobile game, i love the balance of “must think about this puzzle” and “pattern recognition skills are all i need” great for occupying your brain without tiring it at all
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Ok so as a Flow veteran, I had literally beaten every puzzle from every flow game (there are actually 4 official versions from big duck games, flow free is just one of them, plus levels locked behind a pay wall) I have to say, that for humans these puzzles are like you said, absolutely not hard. I LOVED this video, it’s mathy and I’m a nerd. still, the mental algorithm for brute forcing these puzzles is not complicated- there are only a handful of tips like the one given in 2:55 that are needed for solving these puzzles. I encourage you to go play the game on the harder levels, 9x9 or higher for a slightly challenging experience, it’s not mentally draining and super rewarding. Great video!
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I love that these 3B1B style videos are trending now. Always learning something new
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The sound effects are without a doubt the best part of flow
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Well, wasn’t expecting a Flow Free essay video to be on my 2024 bingo board. Well-thought out video, by the way.
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I've completed every single level in the original game and difficulty is mostly dependant on if there is a line that is incorrect but looks like it could be correct, and size. Great video
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I remember playing this game when I was very young. Brings back memories.
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Flow free has had a permanent Tetris effect on my brain I’m excited to watch this
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Y'know, I never expected to come across a video going so in-depth about Flow. I always just thought, "Connect dots, win game."
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Such an amazing video from a small channel! I have been playing Flow Free on and off for over 6 years now, people close to me don't seem to know the game but I'm glad there's people out there that still talk about it.
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i was a few packs away from 100%ing the free levels, then i lost my phone.
then i watch this video and decided to install flow on my new phone and it recovered my cloud data.
best day of my life
