Super Method Step 2 — Last Five Edges

In the second step of the Super Method we will solve all five of the remaining edges on the cube. I will explain how to do this by first orienting the edges (getting them to all face the correct direction) and then by permuting the edges (putting them all in the correct places). As you get better at this step, you can actually learn to permute the edges while orienting them so that it all happens at once. This step is still completely intuitive so I will do an example solve and explain the principles of how to think about it.

	Let's take our edges to be initially in this state. We are first going to orient our edges, meaning make them place the correct direction. We will do this by using the slot between the Red and Yellow faces to strategically take edges in and out of the U layer. We want to put the edges that belong in the top layer into the top layer with the U face color on the U face. Currently we have the Blue-White edge in the slot. We can put it into the top layer with an F' move.
	The Blue-White edge is now in the top layer and oriented correctly. We next want to move a new edge into the open slot using a turn of the U face. A simple U will move the (currently misoriented) Blue-Orange edge into the slot.		We now close the slot with an F.
	We now have the Blue-Orange edge in the slot and can put it into the top layer correctly oriented with an R.		Next we move the Blue-Orange edge out of the slot and a misoriented edge into it. We can move the Yellow-Red edge in with a U'.
	We use an R' to close the slot.		For the equator slice edge (Yellow-Red here), correctly oriented means that when it is in the top layer the front color is on top (meaning Red should be on the Blue side). In that orientation, the edge can be solved using only R and U moves. To put that edge into the top layer with that orientation from here, we use an F'.
	We move the edge we just oriented out of the slot and the remaining misoriented edge into the slot with a U move.		Finally from here we close the slot with an F move.
	We will refer back to this cube state later as the orientation checkpoint. At this point all of our edges are oriented! If you put any edge where it belongs using only R and U moves from this state, you will see that the edge is also facing the correct direction. Don't use F moves as they will break this. We are now limited to R and U face turns. Also, because want to protect our thick-v, if we open the slot on the right we have to then close the slot on the right. So, now to solve our edges we will have to make moves of the form U-by-some-amount then R then U-by-another-amount then R' then U-by-yet-another-amount. We can repeat this formula at will. The strategy for solving our edges is to place them correctly one at a time by this formula. We can start with the edge already in the slot (Blue-Yellow). An R move solves that edge.
	We now want to move a new edge into the slot. We can choose to do a U to put Blue-Red into the slot.		We close the slot with R'.
	We think of Blue-Yellow as placed correctly since we put it in the U layer already. If Blue-Red was solved relative to Blue-Yellow, it would be where Blue-White is right now (the UL position). This is because Red is clockwise of Yellow on the Blue face. To put Blue-Red in that spot, we need it to be on the Right face. So, do a U2.		We place Blue-Red relative to Blue-Yellow using an R (which also opens the slot).
	We need to move an edge we haven't solved yet into the slot. We already solved Blue-Yellow and Blue-Red, so we must choose one of the other two edges in the top layer. Blue-Orange when solved should be opposite Blue-Red. It already is (the Orange sticker is hidden on the L face), so it's solved! U' is our only option left.		Close the slot with an R'.
	We never deliberately placed the Blue-White edge but because we placed all the other edges, its placement is forced to be in the last empty spot. Because we placed all the other edges correctly, it is automatically solved relative to the others! Do a U2 to align the edges overall.		We finished the last 5 edges!

The solution above is how permuting the edges goes 50% of the time. The other 50% of the time, after you have placed the third edge intentionally, instead of the last two edges falling directly into the correct spots they fall automatically into the incorrect spots. I will explain why this happens at the bottom of the page. If this happens, you need to turn the U layer by a quarter turn (either a U or a U', it doesn't matter which) and start permutation over again. Let's do an example. Going back to our orientation checkpoint from before, we could have looked at that cube state and instead of solving everything relative to Blue-Yellow we could have tried to solve everything relative to Blue-Orange. Then, because Blue-Yellow should be clockwise of Blue-Orange, we prepare the alignment of the top layer with a U'.

	We place Blue-Yellow relative to Blue-Orange with an R, opening the slot.		We want to move an unsolved top layer edge into the slot. Blue-Red is available (the Red sticker is hidden on the L face). Move it into position with a U2.
	Close the slot with an R'.		Blue-Red should go opposite Blue-Orange, which means we need to do a U to get it into position to be inserted there.
	R puts Blue-Red in the top layer opposite Blue-Orange.		The only edge we haven't solved yet that can be moved into the slot is Blue-White, so do a U'.
	Close the slot with an R'		Now align the top layer so that the pieces we have already placed are solved by doing a U2.
	Just two edges are unsolved, the Yellow-Red and Blue-White edges are swapped! To fix this, we need to redo edge permutation adjusted by a single turn. So, do a U'.		We now will place the Blue-White piece in the top layer and solve everything relative to it. So, do an R.
	We need to move a new piece into the slot so do a U.		Close the slot with an R'.
	Blue-Yellow is now in the slot and should go opposite Blue-White so do a U to prepare.		Place Blue-Yellow with an R.
	Move a new piece into the slot with a U.		Close the slot with an R'.
	We've placed all but two of the edges deliberately which now that we have adjusted relative to the previous time we did this by a single turn, the last two edges are guaranteed to be solved automatically. Adjust with a U'.		We finished the Last 5 Edges!

Why do the last two edges solve themselves 50% of the time and anti-solve themselves the other 50% of the time? It actually is due to same logic that got us the First Law of the Cube. As explained on that page, it takes 3 swaps to cycle 4 pieces. A single turn of a single side does 3 swaps of Edges and 3 swaps of Corners. It is possible to use repeated 3 swaps to perform only 1 swap overall (by essentially having a pair of swaps in the 3 swaps cancel each other). So, any cube state which is an odd number of edge swaps away from solved also must be an odd number of single turns away from solved. All of the slot-based logic we were doing before always using an even number of turns because you have to get the U layer back to where it started (which means do a multiple of 4 U turns) and you have to close any slot you open (which means do an equal number of R and R' turns). So, that slot based logic will never solve the edges from an odd permutation state. But, a single U or U' turn then brings us to an even permutation state which can be solved by the slot based thinking.

Although in this tutorial I explained how to do edge orientation and then edge permutation, if you practice this step a bunch you will find you can actually do both at the same time by being careful how you are taking pieces in and out of the slot during orientation.