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Random Cubing Discussion

Cool new alg for this case
1427917933381

U' F R' F' R F' U2 F U R U R'
I found it when messing around with insertions
 
Consider the following:

Megaminx FMC, but only scrambling notation can be used. (In other words, no rotations allowed; only R++, R--, D++, D--, U and U' are legal moves.)
 
This is probably hard to answer but I thought it was interesting,

What's the shortest algorithm on Square-1 that looks valid but cannot be executed fully on any square 1 state?
 
What's the shortest algorithm on Square-1 that looks valid but cannot be executed fully on any square 1 state?

Found this one (might not be shortest): / (1,1) / (2,2) / (-1,-1) /

If the (2,2) leads to a "sliceable" shape, then it must be moving at least one corner piece across the slice, so if you do a (-1,-1) after that, there'll be at least one corner preventing the slice. If you require that the initial shape is sliceable, then the initial slice is unnecessary.
 
What's the rarest single cubeshape on sq1? By 'single' I mean one side of a cubeshape. I'm guessing this one is the CEECEECEE shape, though i can't be sure.

What's the rarest combined cubeshape? I'm guessing square/square.
 
What's the rarest single cubeshape on sq1? By 'single' I mean one side of a cubeshape. I'm guessing this one is the CEECEECEE shape, though i can't be sure.

What's the rarest combined cubeshape? I'm guessing square/square.

This has some probabilities
 
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