Orders for puzzles with identical pieces

[Marius0509]

I think the widely accepted definition of the order of a scramble is how many times you need to execute it from the solved state in order for the cube to come back to the solved state. So, I don't think -o and --ordertree should output orders for the supercube unless --distinguishall is mentioned. If doing the lcm of every cycle doesn't work for puzzles with identical pieces, then an alternative approach is doing the lcm of every set's order. For example, I think the scramble "R U' R U R U R U' R' U' R2" should have the order 3 on 4x4 (not 12), just like on the 3x3 cube.

[rokicki]

I'm not so sure this is the "widely-accepted definition", although I see cases where it can be useful. One might consider what twsearch does now as "pure order" and what you are asking for is "impure from solved" but of course there can also be impure from any arbitrary position.

Is this of immediate utility? It would be pretty trivial to add an impure order option.

On Wed, Feb 21, 2024 at 5:21 AM Marius0509 @.***> wrote:

I think the widely accepted definition of the order of a scramble is how many times you need to execute it from the solved state in order for the cube to come back to the solved state. So, I don't think -o and --ordertree should output orders for the supercube unless --distinguishall is mentioned. If doing the lcm of every cycle doesn't work for puzzles with identical pieces, then an alternative approach is doing the lcm of every set's order. For example, I think the scramble "R U' R U R U R U' R' U' R2" should have the order 3 on 4x4 (not 12), just like on the 3x3 cube.

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[Marius0509]

Considering the old version calculated impure orders, I think this should also be a feature in the current version. It also wouldn't remove any existent feature, the pure order can still be obtained using --distinguishall.

[rokicki]

Ahh, you raise a good point. Two, in fact. But I don't like the "default" (no distinguish-all) to calculate "impure" orders as I think that's a special case and dependent on what "solved" position you work from. I considered the old behavior a bug.

I propose adding a "--impure" option that affects this (and possibly other functionality). The implementation will likely calculate the pure order, then check dividing this by the various prime factors to find the "impure" order.

On Thu, Feb 22, 2024 at 9:12 AM Marius0509 @.***> wrote:

Considering the old version calculated impure orders, I think this should also be a feature in the current version. It also wouldn't remove any existent feature, the pure order can still be obtained using --distinguishall.

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[Marius0509]

That sounds like a great idea.