@@wiggelpuppy5474 It looks like the point is to turn all the arrows to face the other direction. I think the *real* point of this one is to create a puzzle that needs O( N^ϕ ) steps to solve. Most of his other puzzles look a lot more fun.
Is there something special about phi that lends itself well to mechanical puzzles? Maybe the recursive nature of the sequence? Have you found any examples of non integer puzzles other than phi?
@@Elitekross That's an interesting thought. For binary puzzles you have to undo then redo what you previously did, so the recurrence is A(n) = 2*A(n-1). But if there is a shortcut in the puzzle, then you could get A(n) = A(n-1) + A(n-2), which leads to a phinary puzzle. Similarly, a ternary puzzle A(n) = 3*A(n-1) could potentially have a shortcut that leads to A(n) = 2*A(n-1) + A(n-2), which is Pells sequence and converges to the Silver ratio.
This makes me wonder, is it possible to make a sequential puzzle like this where each piece requires a different state above it, like a 3 bit Grey code? First piece requires 000, second 001, third 011, fourth 010 etc?
That would be fairly easy to design, but cumbersome, as each piece would be different. It would be less fun to solve, as one would need to keep track of the logic for each individual piece.
Integer, I presume you mean. It is meant as a limit. Try the Fibonacci sequence as an example...? Wikipedia has a page on "Golden ratio base" that mentions the colloquial name phinary and that has a lot of background.
What are the step counts for puzzles of size 1-10? ? I'm also curious about how the math works for the "bordering 3 upper neighbors" property, why does it yield a base of phi?
This looks like a fascinating puzzle that I would definitely enjoy interacting with. I think the puzzle would be further enhanced if it came along with an explanatory pamphlet regarding the theory and the strategy.
It comes with a brief pamphlet, namely the description with this video. Other than that: it is a puzzle. Part of the solving fun is getting to understand its operation.
@@OskarPuzzle I completely agree with you, but I’m always looking for ways to get other people involved in puzzling and sometimes if something is a little too opaque regarding its mechanism, people lose interest. Also, from my point of view, the more theoretical information that can be presented in an accessible manner, helps to engage the puzzler and fuel their interest and appreciation for the mechanism.
Here is an article on exponential puzzles in general: arxiv.org/abs/2411.19291. Hopefully, the authors want to look into phinary puzzles as well some time.
Never change that intro. These are really fun puzzles.
they don't look fun to me, are you trying to separate them from the base? what's the point? what's the solve?
@@wiggelpuppy5474 It looks like the point is to turn all the arrows to face the other direction. I think the *real* point of this one is to create a puzzle that needs O( N^ϕ ) steps to solve. Most of his other puzzles look a lot more fun.
@@wiggelpuppy5474 They are fun to me too. What solve do you mean?
@ I just don’t know how I “win”. Most puzzles have a solution. I don’t see what I’m supposed to do.
@@wiggelpuppy5474 I guess bringing the scrambled arrows in the same orientation.
Is there something special about phi that lends itself well to mechanical puzzles? Maybe the recursive nature of the sequence? Have you found any examples of non integer puzzles other than phi?
I would assume the other metallic ratios silver, copper, etc) would be possible at the very least
@@Elitekross That's an interesting thought. For binary puzzles you have to undo then redo what you previously did, so the recurrence is A(n) = 2*A(n-1). But if there is a shortcut in the puzzle, then you could get A(n) = A(n-1) + A(n-2), which leads to a phinary puzzle. Similarly, a ternary puzzle A(n) = 3*A(n-1) could potentially have a shortcut that leads to A(n) = 2*A(n-1) + A(n-2), which is Pells sequence and converges to the Silver ratio.
This makes me wonder, is it possible to make a sequential puzzle like this where each piece requires a different state above it, like a 3 bit Grey code? First piece requires 000, second 001, third 011, fourth 010 etc?
That would be fairly easy to design, but cumbersome, as each piece would be different. It would be less fun to solve, as one would need to keep track of the logic for each individual piece.
Hello. If the number of moves increases with a phinary ratio, how can the number of moves be a décimal number ?
Integer, I presume you mean. It is meant as a limit. Try the Fibonacci sequence as an example...? Wikipedia has a page on "Golden ratio base" that mentions the colloquial name phinary and that has a lot of background.
@landsgevaer is correct. It is meant as a limit, for large numbers of rotors. Indeed like the Fibonacci sequence.
Not sure how to make 1.6 moves. Probably just by turning the arrows more or less
What are the step counts for puzzles of size 1-10? ? I'm also curious about how the math works for the "bordering 3 upper neighbors" property, why does it yield a base of phi?
It almost looks like a heeled shoe. A possible design could have the goal to get the scrambled surface of a shoe right.
Did phinary puzzles already exist before 2024?
How did you post 3 months in advance???
@@marklanchvar This puzzle was designed August 2024.
Would the Towers of Hanoi be one?
@@SupermarketSweep777 Not "phinary"
@@SupermarketSweep777In Towers of Hanoi, N discs require (2^N) - 1 moves: it's binary.
This looks like a fascinating puzzle that I would definitely enjoy interacting with. I think the puzzle would be further enhanced if it came along with an explanatory pamphlet regarding the theory and the strategy.
It comes with a brief pamphlet, namely the description with this video. Other than that: it is a puzzle. Part of the solving fun is getting to understand its operation.
@@OskarPuzzle I completely agree with you, but I’m always looking for ways to get other people involved in puzzling and sometimes if something is a little too opaque regarding its mechanism, people lose interest. Also, from my point of view, the more theoretical information that can be presented in an accessible manner, helps to engage the puzzler and fuel their interest and appreciation for the mechanism.
Here is an article on exponential puzzles in general: arxiv.org/abs/2411.19291. Hopefully, the authors want to look into phinary puzzles as well some time.
@@OskarPuzzlethank you!
did you?
Cool video, giving me Vsauce vibes!
My brain is on fire