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#1

Sune as a single commutator

I think I should post a problem sometime. This, however, will be a cube problem; nevertheless, it's a lot like the others presuming some cube knowledge.

Many cubers know knows that the Sune (RUR'URU2R') can be written as a two commutators ([R, U][U2, R]) or as a conjugated commutator ([R U2; U', R']). But even Johannes didn't know it could be written as a single commutator. In fact, I wasn't even sure until I tried it, and the task turned out to be pretty fun.

So, the problem: Write the Sune as a commutator in the pure form [moves, moves].

(Doesn't have to be pretty unless you want it to be.)

If you've found it or already know it,

And if you think that's too easy: It's well-known that commutators generate all the even permutations. Show that any even permutation can be written as a single commutator, or show that it can't be done.

I think I should post a problem sometime. This, however, will be a cube problem; nevertheless, it's a lot like the others presuming some cube knowledge.

Many cubers know knows that the Sune (RUR'URU2R') can be written as a two commutators ([R, U][U2, R]) or as a conjugated commutator ([R U2; U', R']). But even Johannes didn't know it could be written as a single commutator. In fact, I wasn't even sure until I tried it, and the task turned out to be pretty fun.

So, the problem: Write the Sune as a commutator in the pure form [moves, moves].

(Doesn't have to be pretty unless you want it to be.)

If you've found it or already know it,

*please*use spoiler tags, as seeing a solution even for a glance may be distracting for people who haven't solved it yet.And if you think that's too easy: It's well-known that commutators generate all the even permutations. Show that any even permutation can be written as a single commutator, or show that it can't be done.