Is by any chance the casing part of the puzzle ? As, maybe, when you solve the arrows once, you can slide out a part of the box. Then you would have to unsolve it to slide it some more. And repeat until the casing is fully separated from the arrows. We can see on the thumbnail that the casing if partly sled out. And it seems to interact directly with the arrows.
Nice conjecture, but alas incorrect. The puzzle is the same without casing. The purpose of the casing is to explain the challenge: "remove the casing". That is easier to than "make all the arrows point inward".
Brilliant work, all around. Answer: the exponential growth only determines the ratio between the number of moves needed to solve the puzzle for N dials, and to solve the puzzle for N +1 dials. The base for this is phi for both puzzles, but this says nothing about the number of moves it takes to solve the N=2 puzzle, which fully defines the sequence. The video demonstrates that the number of moves needed to solve the N=2 configuration for each puzzle is different, thus they will have different minimum move counts for any N.
if both are phinary, all that means that adding one piece will asymptotically increase the number of required moves by a factor of phi It doesn't say anything about, for instance, how many moves it takes for the first two elements to be solved. If that already takes like twice as many moves, then the thing overall is gonna take twice as many. Or if, for instance, in one you only need one move of the first thing to allow the second to move, but in the other, you need two, it's like starting the exponential chain in a more advanced state, so if it takes sum_k=1^n Fib(k) moves for one, the other is gonna take sum_k=1^n Fib(k+1) moves instead which, due to exponential growth, is significantly more. I'm not sure either of those are the answer for this particular puzzle, but that's at least some possible reasons
Yeah, that is similar to how a puzzle with two additional arrow pieces takes longer to solve than one without, but both are phinary puzzles. N = c * phi^n The phi^n makes it phinary, but the c makes a difference.
Is by any chance the casing part of the puzzle ?
As, maybe, when you solve the arrows once, you can slide out a part of the box. Then you would have to unsolve it to slide it some more. And repeat until the casing is fully separated from the arrows.
We can see on the thumbnail that the casing if partly sled out. And it seems to interact directly with the arrows.
Nice conjecture, but alas incorrect. The puzzle is the same without casing. The purpose of the casing is to explain the challenge: "remove the casing". That is easier to than "make all the arrows point inward".
I have no clue!😮💨
Brilliant work, all around.
Answer: the exponential growth only determines the ratio between the number of moves needed to solve the puzzle for N dials, and to solve the puzzle for N +1 dials. The base for this is phi for both puzzles, but this says nothing about the number of moves it takes to solve the N=2 puzzle, which fully defines the sequence. The video demonstrates that the number of moves needed to solve the N=2 configuration for each puzzle is different, thus they will have different minimum move counts for any N.
if both are phinary, all that means that adding one piece will asymptotically increase the number of required moves by a factor of phi
It doesn't say anything about, for instance, how many moves it takes for the first two elements to be solved. If that already takes like twice as many moves, then the thing overall is gonna take twice as many.
Or if, for instance, in one you only need one move of the first thing to allow the second to move, but in the other, you need two, it's like starting the exponential chain in a more advanced state, so if it takes sum_k=1^n Fib(k) moves for one, the other is gonna take sum_k=1^n Fib(k+1) moves instead which, due to exponential growth, is significantly more.
I'm not sure either of those are the answer for this particular puzzle, but that's at least some possible reasons
I presume hat you are correct.
Yeah, that is similar to how a puzzle with two additional arrow pieces takes longer to solve than one without, but both are phinary puzzles.
N = c * phi^n
The phi^n makes it phinary, but the c makes a difference.
Why are both puzzle phinary, but one takes many more moves to solve?
Sounds like you used a different mantissa, as of 3:07. Same exponent, but faster growth.
Sorry wrong word. Not mantissa, but base. Slight but significant difference between the two.