Ultimate challenge

[mrCage]

Hi. Chris inspired me to come up with this variety of forced turn fewest moves challenge. Use this weeks challenge at http://fmc.mustcube.net and find a solution where exactly every second turn is a F turn. Noe tricks that i know will give a trivial solution based on a norm,al solution.

By the way the scramble is this one: D' F D F' L U F L' U2 B' D2 B' U' F' D' L D' F2 B L2 F2 R' L D' U F' B' L' R' F'

Per

 

[Stefan]

Noe tricks that i know will give a trivial solution based on a norm,al solution.

Here's one:

1. Replace every F* turn with (U D L2 R2 U' D') B* (U D L2 R2 U' D').
2. Separate the turns with F B F B F B2 F.

 

[trying-to-speedcube...]

You *could* do your solution with F F2 F between every single move. But that kind of throws off the challenge again.

 

[Stefan]

You *could* do your solution with F F2 F between every single move.

I don't know how something can done "between a single move", plus I think your idea violates the "where exactly every second turn is a F turn" requirement.

 

[Robert-Y]

Ah I think there could be some confusion.

@Per do you mean every second turn is F or do you mean every second turn is either F, F' or F2?

 

[trying-to-speedcube...]

You *could* do your solution with F F2 F between every single move.

I don't know how something can done "between a single move", plus I think your idea violates the "where exactly every second turn is a F turn" requirement.

I'm sorry, I wasn't entirely clear. I meant you could do your normal solution, with F F2 F between every 2 moves. For example, for R U R', you would do R F F2 F U F F2 F R' F F2 F.

Why does it violate the "exactly every second turn is an F turn" requirement? I don't see how this implies other moves may not be F turns.

 

[Tim Reynolds]

Why does it violate the "exactly every second turn is an F turn" requirement? I don't see how this implies other moves may not be F turns.

The word exactly used like that usually means something like if-and-only-if; that is, the moves that are F turns are exactly those that are every second turn.

Put another way: consider the algorithm F F F F F F F F. Is every second turn an F turn? Definitely. Is exactly every second turn an F turn? No, that is not an exact description of which turns are F turns; rather, every single turn is an F turn.

 

[trying-to-speedcube...]

Sorry, I didn't understand what it actually had to imply.

I am NOT going to try this challenge anyway

Maybe I can get a 2x2x2 block? Maybe 2x2x3, but that's where I'll give up :/

 

[mrCage]

Noe tricks that i know will give a trivial solution based on a norm,al solution.

Here's one:

1. Replace every F* turn with (U D L2 R2 U' D') B* (U D L2 R2 U' D').
2. Separate the turns with F B F B F B2 F.

Ok ok!! Smartass I need to sharpen my formulation of the challenge.

Take the scramble of my first message in this thread and solve it with a sequence where exactly every second turn is exactly F and not F' or F2. Furthermore, the solution cannot also contain any subsequence that is an identity sequence - like for example F B F B F B2 F. Try to spoil this one Stefan:rolleyes:

Per

 

[trying-to-speedcube...]

2x2 Block: B F R' F U F U' F D F D F B' F L2 F U' F U F U' F U F U2 F D' F

Per, what exactly is an identity sequence? A sequence which can simplify or a sequence which does nothing to the cube? For example F B' F, is that forbidden?

 

[mrCage]

2x2 Block: B F R' F U F U' F D F D F B' F L2 F U' F U F U' F U F U2 F D' F

Per, what exactly is an identity sequence? A sequence which can simplify or a sequence which does nothing to the cube? For example F B' F, is that forbidden?

Yes, a sequence that does nothing to the cube (except possibly rotate centers ... )

Per

 

[Herbert Kociemba]

Why should it be possible at all to find such a solution?

 

[TMOY]

Well, here's my solution:
U' F B F L' F B F B2 F L F B F R': corner orientation
F B F L2 F B F R2 F B2 F U2: corner separation and xLL combined, 2 edges already solved
F B2 F L F B' F B2 F D': 3rd and 4th edge
F B2 F D F B2 F U2 F B2 F D: 5h edge
F D' F B2 F B' F R: 6th edge
F D2 F B F B F L F B2 F B2 F B2 F B F U2 F B2 F D F B F D2: 7th and 8th edge
F L F B2 F B" F D' F B2 F R2 F B2 F D F B2 F B2 F B2 F B F L': middle layer orientation
F B2 F D2 F U2 F B' F B2 F L2 F: middle layer permutation

 

[trying-to-speedcube...]

Wow, Francois, that's incredible... did you come up with all those algs yourself?

 

[TMOY]

Well, with CF it's really not very difficult once you master some little tricks for putting the F and B layers in the position you want

 

[trying-to-speedcube...]

I found a shorter 2x2x2 block, in ULB, so it also gives nicer continuation because the F layer is free.

U F U F B' F R F U F R F B' F U2 F B F R' F B

I haven't found a nice continuation yet though...

 

[mrCage]

Why should it be possible at all to find such a solution?

I think TMOY has clearly shown that it is possible. A hidden part of the challenge was to alternatively prove it's impossible:rolleyes:

Per

 

[calekewbs]

are cube turns legal?

 

[Stefan]

the solution cannot also contain any subsequence that is an identity sequence

This is impossible in most cases. You probably mean substring, not subsequence.

http://en.wikipedia.org/wiki/Subsequence#Substring_vs._subsequence

 

[mrCage]

the solution cannot also contain any subsequence that is an identity sequence

This is impossible in most cases. You probably mean substring, not subsequence.

http://en.wikipedia.org/wiki/Subsequence#Substring_vs._subsequence

Hairsplitter, nitpicker !! Is it ok if i call it a subsequence of turns?? This should be the same as a substring defining a subsequence .... You know semantics right??

Per