Here is my tutorial for how to solve the Skewb Ultimate. There's really only the one formula that you have to remember but orienting it correctly and performing it can be confusing. Hopefully this tutorial helps people solve this easier.

The required formula is:
R' L R L'

Step 1: Place 4 corners in place around the base/bottom center piece and orient them correctly.

Potential Problems: None

Step 2: By swapping the top center piece into the sides get all center pieces into their correct spots.

Potential Problems: If the top piece is at the top before all the other center pieces are in their correct spot - swap it with any of the other center pieces so you can continue. Sometimes you will find yourself solving for the same center pieces that you already solved - don't worry about this just keep at it until it's all done.

Step 3: Solve the remaining corner pieces. Remember to use the formula twice when doing this section.

Problems: If you don't have a scenario where 2 top colours are on the same side, pretend that 1 side is correct (even though it isn't) and perform the formula (twice) on that side then reevaluate the scenario. Keep doing this until you have a scenario where 2 top colors are on the same side.

Step 4: Flip center pieces to complete the Skewb.

Problems: Sometimes you will have only 2 incorrect center pieces (you need 4 incorrect to complete the solve) or perhaps you have 4 incorrect but the 2 correct sides are on opposite sides of the skewb. Just make sure that when you perform the formula (6 times) one of the incorrect sides changes while the other stays the same. This should then generate the scenario you want with 4 incorrect and 2 correct but touching each other.

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