9 minutes in and I just realized this is basically Flow. All of the logic you were applying just suddenly connected once I realized that ..Or rather this is where flow came from, I suppose
Flow adds a constraint of not allowing one to draw out mini-segments. One must map an entire path between numbers for the highest achievement level. This technique would not work well in Flow.
@@scottperry9581 That's a constraint of the app, not a constraint of the puzzle. You can write down a puzzle and solve it. If anything Flow should change to adopt best practises as you see with other puzzle software.
wow i am so impressed watching simon intuit the answer. i find these puzzles so difficult because strict logical deduction is actually not the best approach for solving. well done mate.
This puzzle is like finding gold. Simon is so good at this kind of thing. I am going back to see how this channel to see how it started and this one stands out, even beyond the early killer sudokus.
I used the inefficiency but never really thought about corners logic and how they propagate, and seeing how it's used over and over again, paying more attention to geometry could be really the key. Nice video
Trial and error!?? BIFURCATION BY SIMON!!??? my worldview has collapsed.. only kidding, it's nice to see one of the videos that got me interested in the channel to begin with show up again on the feed. So happy how far you've gotten. Much love from Canada, I hope to become a patron one day when I'm not on welfare. :)
Nikoli released a Numberlink puzzle game on Switch recently and I was stuck on the last unsolved one (#47 in-game) until applying the tricks in this video. Thanks!
I never thought about the corners trick. Now that I realize it, I’ve been doing that for years, but I never took that approach. I have pretty good special skills, so I find a path to connect, usually not bothering to draw segments. Then again, most of my experience with this type of puzzle is with flow, which doesn’t allow you to draw segments.
Numberlink is such an odd puzzle type compared to the other Nikoli puzzle types. Provable deductions don't get you very far most of the time, unless there are some non-obvious deductions known only to elite solvers.
I think a good and easy example would be at 21:35 . He's saying the line on the right can't connect to the 11, because it would be "inefficient". What he means by that is that, if that line were to actually be connected to the 11, then there would be absolutely no reason why it wouldnt connect to the 11 in the cell above it. That way it would connect earlier and more "efficiently" but also leaves the cells on the right of the number empty and with no way to be filled anymore. Since this puzzle was build to try to connect the numbers as straight forwardly (or efficiently) as possible outcomes like that aren't possible.
Ok guys, thank you for the suggestions, but I think I've just didn't get the rules and still don't. Why are 'inefficient' routes against the rules? I think I've missed that somehow and I've seen the start of the video few times already.
@@Bawanni Yes but nowhere in the rules he stated it said a line can't be inefficent. You state it here, but he doesn't. Then he start to eliminate variations because they arn't efficient.
Found this video in my recommendations yesterday. I love these puzzles but I'm sad you can't play them on Nikoli anymore. Anyone know a way to play them? I know there's other similar games but often you can't create partial lines without connecting to one of the ends, and also often the other games are not challenging enough.
That site has an additiona rule: One line can't cover a 2x2 block. Interestingly, that rule is almost equivalent to the 'efficiency' thing which people here complain is 'metagaming'. It even think it's exactly equivalent but I'm not in the mood to prove that mathematically. It certainly leads to the same 'efficiency' logic SImon has explained here.
I think it would be nice to see a little number at each end of a line cnnected to a number with that number. It would be easier than backtracking so long to see to which number a line must connect.
Actually, Numberlink puzzles require very little trial and error most of the time. You just need to find numbers that can quickly and easily reach their pairs while not cutting off the paths for other numbers to get to their pairs.
I have no idea where to find puzzles like this. does anyone know of a book I can buy with difficult numberlink puzzles in it? ive tried small grid like 5x5 or 9x9 but nothing this massive. please someone link a website that offers puzzles like this. i'd like to pay money to do these puzzles as well. I do not care. these puzzles are so much fun but I need something more difficult and challenging, anyone??
If you are still interested try searching for Link-a-pix. It’s a pretty similar game that has a bunch of apps and websites and the puzzle looks like a painting at the end
At the start of the video you say that lines have to be “efficient” or “move naturally”. Not only is this totally unclear/ambiguous, it’s also not an actual rule of Numberlink. If it’s a strategy that follows from the rules, then you haven’t explained why having a ┌┐ curve is impossible. I therefore couldn’t follow your logic at all.
If a solution exists that entails doubling back (e.g. see 20:20) to fill the graph and waste empty space, then obviously a second option exists which instead leaves those spaces empty and simply draws a straight path without any such curves. Conversely, the only valid solution for a given puzzle may require not wasting any space at all. Ergo, if given a choice between a solution that entails doubling back on your own path and a solution which avoids doing so by conserving as much space as possible, one should choose the latter, because the former increases the likelihood your solution fails. And yes, Numberlink puzzles are generally designed to only have one unique, valid solution, meaning doubling back is never required. This is similar to Sudoku: it's not a formal rule of Sudoku that only one unique solution exists, it just makes for a shitty logic puzzle when its not so puzzles are designed to require a single solution by custom. Or more specifically, it's not a "rule" Sudoku _players_ need to follow to play Sudoku but rather a self-imposed rule Sudoku puzzle creators employ to create enjoyable Sudoku puzzles.
HeyItzMeDawg so it's not actually *impossible* that the solution will contain an inefficient line? It's just more likely that it won't, and therefore a reasonable thing to assume?
The assumption is that there is a unique solution. If a line could snake around, there'd be another solution where an adjacent line could take that bend instead. The validity of that assumption depends on the designer/generator of the puzzle.
Please include the rules of new puzzles in the written intro. You said 1. link pairs of numbers and '2 more'. 2. was 'every square has a line through it. I never heard rule 3. You said something a couple minutes later about 'move naturally', but the word 'naturally' is so ambiguous and abused as to be nearly meaningless. Without knowing what the real rules are, I stopped watching after a couple more minutes.
Those are the rules. Fill the entire grid with lines, lines can't cross or overlap with eachother, and each line must link only a single pairs of numbers. That's all there is to it. Everything else he said was part of his own technique in solving the puzzle.
➊ Connect each two cells with the same numbers by a line. Sections The sections of a line run horizontally or vertically between the center points of orthogonally adjacent cells. ➌ Each cell must be visited exactly once by a line. ➍ A single line must not cover an area if size 2x2 or larger. His "Naturally" refers to rule 4.
@@icycloud6823 Yeah, this makes a lot of sense, but there is a slight problem. Most of these are created in a way, that, in fact, all lines moves "naturally". He's using it even though it's not in the rules, because if he finds a solution this way, it is also a solution of the puzzle. BUT he also uses the fact, that all squares are non-empty. If the puzzle would contain inefficient lines, his logic would not actually hold.
@@martonnemeth236 But if there are inefficient lines, that also means there are efficient lines. Which in turn means the puzzle wouldn't have a unique solution. You'd have at least one efficient and one inefficient solution, and very likely multiple inefficient solutions. In general, a good puzzle will have a unique solution, else the logic will get ambiguous.
9 minutes in and I just realized this is basically Flow. All of the logic you were applying just suddenly connected once I realized that
..Or rather this is where flow came from, I suppose
Hi, my name is Ben and I am a Flow addict.
my thoughts exactly, just a larger version of flow
Flow adds a constraint of not allowing one to draw out mini-segments. One must map an entire path between numbers for the highest achievement level. This technique would not work well in Flow.
@@scottperry9581 That's a constraint of the app, not a constraint of the puzzle. You can write down a puzzle and solve it. If anything Flow should change to adopt best practises as you see with other puzzle software.
Flow Free is great. Still getting support after 12 years
wow i am so impressed watching simon intuit the answer. i find these puzzles so difficult because strict logical deduction is actually not the best approach for solving. well done mate.
This puzzle is like finding gold. Simon is so good at this kind of thing. I am going back to see how this channel to see how it started and this one stands out, even beyond the early killer sudokus.
Got recommended it, but I agree.
I used the inefficiency but never really thought about corners logic and how they propagate, and seeing how it's used over and over again, paying more attention to geometry could be really the key. Nice video
Trial and error!?? BIFURCATION BY SIMON!!??? my worldview has collapsed.. only kidding, it's nice to see one of the videos that got me interested in the channel to begin with show up again on the feed. So happy how far you've gotten. Much love from Canada, I hope to become a patron one day when I'm not on welfare. :)
Nikoli released a Numberlink puzzle game on Switch recently and I was stuck on the last unsolved one (#47 in-game) until applying the tricks in this video. Thanks!
Your production quality has improved massively.
Long time fan and I've never seen this puzzle. This was cool.
I never thought about the corners trick. Now that I realize it, I’ve been doing that for years, but I never took that approach. I have pretty good special skills, so I find a path to connect, usually not bothering to draw segments.
Then again, most of my experience with this type of puzzle is with flow, which doesn’t allow you to draw segments.
Very interesting solve. Too bad they closed the site down because it was truly amazing.
Why did Nikoli shut down the ability to play puzzles on their site?
Another Random RUclips Algorithm video, but I'm definitely not disappointed. Nice work on that puzzle.
Reminds me drawing tracks for PCB
On a single layer
Fascinating puzzle, a first for me.
Now I want to play a Masyu, Slitherlink, and Numberlink all in one puzzle. That'd be a lot of fun.
Numberlink is such an odd puzzle type compared to the other Nikoli puzzle types. Provable deductions don't get you very far most of the time, unless there are some non-obvious deductions known only to elite solvers.
what does "efficient" mean? it's the first trick you use and i am already lost
I think a good and easy example would be at 21:35 .
He's saying the line on the right can't connect to the 11, because it would be "inefficient".
What he means by that is that, if that line were to actually be connected to the 11, then there would be absolutely no reason why it wouldnt connect to the 11 in the cell above it.
That way it would connect earlier and more "efficiently" but also leaves the cells on the right of the number empty and with no way to be filled anymore.
Since this puzzle was build to try to connect the numbers as straight forwardly (or efficiently) as possible outcomes like that aren't possible.
Czeckie put another way, in the final solution, lines won’t ever go out of their way JUST to fill the space.
i think 20:23 is the best expample
Ok guys, thank you for the suggestions, but I think I've just didn't get the rules and still don't. Why are 'inefficient' routes against the rules? I think I've missed that somehow and I've seen the start of the video few times already.
@@Bawanni Yes but nowhere in the rules he stated it said a line can't be inefficent. You state it here, but he doesn't. Then he start to eliminate variations because they arn't efficient.
Problems like this is why we have more the single layer circuit baords
Found this video in my recommendations yesterday. I love these puzzles but I'm sad you can't play them on Nikoli anymore. Anyone know a way to play them? I know there's other similar games but often you can't create partial lines without connecting to one of the ends, and also often the other games are not challenging enough.
You can play them at Janko www.janko.at/Raetsel/Arukone-3/index.htm
That site has an additiona rule: One line can't cover a 2x2 block.
Interestingly, that rule is almost equivalent to the 'efficiency' thing which people here complain is 'metagaming'. It even think it's exactly equivalent but I'm not in the mood to prove that mathematically. It certainly leads to the same 'efficiency' logic SImon has explained here.
I think it would be nice to see a little number at each end of a line cnnected to a number with that number. It would be easier than backtracking so long to see to which number a line must connect.
Very difficult to distinguish/follow the lines.... I would need tonuse colours...
Wow this puzzle is HUGE. You're barely more than a couple squares of it!
wait.. what's the website? no link -_-
This was very interesting!
Actually, Numberlink puzzles require very little trial and error most of the time. You just need to find numbers that can quickly and easily reach their pairs while not cutting off the paths for other numbers to get to their pairs.
Can some1 share link to this app for Windows. I cant find it.
I miss this website so much :(
I won't lie, I don't get it. But it's hard to argue with the results
It’s literally just the game flow except without the colours making it easier to tell where you are
I have no idea where to find puzzles like this. does anyone know of a book I can buy with difficult numberlink puzzles in it? ive tried small grid like 5x5 or 9x9 but nothing this massive. please someone link a website that offers puzzles like this. i'd like to pay money to do these puzzles as well. I do not care. these puzzles are so much fun but I need something more difficult and challenging, anyone??
If you are still interested try searching for Link-a-pix. It’s a pretty similar game that has a bunch of apps and websites and the puzzle looks like a painting at the end
where can you play this ?
Nikoli
@@hhaavvvvii no you can't member services shut down you can't do anything on the site nymore
Somebody make one of these that forms a maze that you then have to solve.
how intuitive..
At the start of the video you say that lines have to be “efficient” or “move naturally”. Not only is this totally unclear/ambiguous, it’s also not an actual rule of Numberlink. If it’s a strategy that follows from the rules, then you haven’t explained why having a ┌┐ curve is impossible. I therefore couldn’t follow your logic at all.
If a solution exists that entails doubling back (e.g. see 20:20) to fill the graph and waste empty space, then obviously a second option exists which instead leaves those spaces empty and simply draws a straight path without any such curves. Conversely, the only valid solution for a given puzzle may require not wasting any space at all. Ergo, if given a choice between a solution that entails doubling back on your own path and a solution which avoids doing so by conserving as much space as possible, one should choose the latter, because the former increases the likelihood your solution fails.
And yes, Numberlink puzzles are generally designed to only have one unique, valid solution, meaning doubling back is never required. This is similar to Sudoku: it's not a formal rule of Sudoku that only one unique solution exists, it just makes for a shitty logic puzzle when its not so puzzles are designed to require a single solution by custom. Or more specifically, it's not a "rule" Sudoku _players_ need to follow to play Sudoku but rather a self-imposed rule Sudoku puzzle creators employ to create enjoyable Sudoku puzzles.
HeyItzMeDawg so it's not actually *impossible* that the solution will contain an inefficient line? It's just more likely that it won't, and therefore a reasonable thing to assume?
The assumption is that there is a unique solution. If a line could snake around, there'd be another solution where an adjacent line could take that bend instead. The validity of that assumption depends on the designer/generator of the puzzle.
Flow 2.0
Duzzying
Please include the rules of new puzzles in the written intro. You said 1. link pairs of numbers and '2 more'. 2. was 'every square has a line through it. I never heard rule 3. You said something a couple minutes later about 'move naturally', but the word 'naturally' is so ambiguous and abused as to be nearly meaningless. Without knowing what the real rules are, I stopped watching after a couple more minutes.
Those are the rules. Fill the entire grid with lines, lines can't cross or overlap with eachother, and each line must link only a single pairs of numbers. That's all there is to it. Everything else he said was part of his own technique in solving the puzzle.
It’s flow. The game is flow
➊ Connect each two cells with the same numbers by a line. Sections The sections of a line run horizontally or vertically between the center points of orthogonally adjacent cells. ➌ Each cell must be visited exactly once by a line. ➍ A single line must not cover an area if size 2x2 or larger.
His "Naturally" refers to rule 4.
@@icycloud6823 Yeah, this makes a lot of sense, but there is a slight problem. Most of these are created in a way, that, in fact, all lines moves "naturally". He's using it even though it's not in the rules, because if he finds a solution this way, it is also a solution of the puzzle. BUT he also uses the fact, that all squares are non-empty. If the puzzle would contain inefficient lines, his logic would not actually hold.
@@martonnemeth236 But if there are inefficient lines, that also means there are efficient lines. Which in turn means the puzzle wouldn't have a unique solution. You'd have at least one efficient and one inefficient solution, and very likely multiple inefficient solutions. In general, a good puzzle will have a unique solution, else the logic will get ambiguous.