First Two Layers (F2L)

For example, in Q1, the corner and the edge have the same color on top, so we reduce to I, which means that the target edge is UF in the position shown. DwR' is therefore the correct opening, U' moves the edge to the target, and R brings back the corner, completing the first step. These solutions should all feel obvious after some practice.

Note that, for R1 and R2, both U'R and DwR' keep both the edge and the target edge on U. We choose the opening that allows for more finger tricks or has less cube rotations.

For K1 and K2, neither opening keeps both the edge and the target edge on U. We group this together with the second group.

Corner and edge on U, corner points up (and K)

We now hold the edge in the first two layers and keep the corner on U. For U and V, the edge is aligned with the first two layers, hidden in the first two layers, and the pair is reduced to I. The alternate algorithms provided for V1 and V2, which are sometimes useful from different angles, do not follow this pattern.

Note the similarity in the first steps of K1 and N2 and of K2 and N1.

The last case, M, can be reduced to I or T. However, the optimal solution (first line) does not follow the two-step pattern. This is one of the few F2L sequences with no intuitive explanation. Sorry.

Corner in place, Edge on U

Corner on U, Edge in place

G and H differ in the first step only in the direction of the second quarter turn U. G is reduced to I, and H is reduced to T. B can be reduced to either and can be used to control the edge orientation of the last layer.

Corner and edge in place

The optimal sequences for all cases here are difficult to understand intuitively. C1 and C2 can be reduced to U2 and N2 by RUR' and RU'R', respectively. The first three moves of the first algorithm for A0 reduces the case to J2. The second can be used for last layer edge control.

Corner or Edge (but not both) in a wrong slot

It happens very often in F2L that none of the standard cases seemingly applies. The following technique allows us to use one of the algorithms above even when a corner or an edge is in the first two layers as long as the other piece in the pair is on top.

This is actually almost the standard case. Since every case among the 41 standard cases that has either a corner or edge in place has the two-step structure discussed earlier, their equivalents with corner or edge in wrong slot can be solved without any additional algorithm. Pretend that the wrong slot containing a corner or an edge is in fact the target slot, and perform step 1 (the italicized part) for the appropriate case. Since this brings the corner-edge pair onto U and in one of the four standard cases, the pair can easily be inserted into the correct slot after adjusting by appropriate numbers of U and Dw.

The following examples demonstrate this. Use the second arrow from the right on the applet to see each solution one move at a time.

Different Angle or Target Slot

Using the technique just described along with the algorithms above for the 41 standard cases, we can solve almost any F2L. The only exception is when none of the four edges and four corners of F2L are on the U layer, in which case an unsolved slot (say at FR) must be brought to the U layer, for example by RUR'. Otherwise, we can solve any every corner-edge pair by bringing the target slot (or the wrong slot containing a corner or an edge) to FR. Repeating this four times, one for each pair, completes the F2L.

Real F2L: In practice, however, bringing the target slot to FR is often a waste of time. To increase speed, we must minimize whole cube turns and maximize finger tricks, which usually involve RU or LU combinations. Both of these can be achieved by learning to use the three target slots other than FR. Although some cases have special algorithms for different target slots, at the start it is enough to learn the algorithms given above for the 41 standard cases from different directions. This can be accomplished in part by understanding how the algorithms work.

We start by reexamining the examples from the preceding section.

Things become slightly more difficult for cases other than the four standard ones.

Empty Slot

When we are solving the first three corner-edge pairs, at least one slot is not yet solved; we call these empty slots (visually, a gray slot in the applet). Algorithms with the usual two-step structure can be simplified significantly using empty slots. The following examples demonstrate this.

Here are some more examples with various empty and target slots.

Here are more applications of empty slots:

Learning to recognize these cases is a skill that requires time to acquire. Once developed, it allows us to choose the easiest corner-edge pair for each of the four slots most of the time.

Mismatched Pair

Also known as "misaligned pair," mismatched pair refers to solving a corner and an edge from two different slots at the same time. We need to pretend that they form a corresponding corner-edge pair and determine the appropriate F2L case. This comes in handy when there are two slots, one with the corner solved and the other with the edge solved.

Although not as common as the other standard techniques, mismatched pair allows us to shorten our solution significantly by solving in one step what would otherwise require two steps.

Looking Ahead and Simple Multislotting

In Getting Fast with an Easy Method and elsewhere, I've repeatedly stressed the importance of looking ahead. By solving slower than at top speed and looking for the next corner-edge pair as you solve one, you eliminate gaps between pairs, making F2L into one seamless motion. While this allows you to always choose the easiest next pair, once the pair is chosen, the techniques covered so far apply just to this one pair

In certain special cases, instead of merely anticipating the next pair, you can use looking ahead as an active tool; in multislotting, the current pair is solved so as to create the next pair, or to at least simplify it. Although true multislotting requires many extra algorithms, a good look-ahead suffices for the simplest types explained here.

To be sure, a good anticipatory look-ahead is already very, very advanced (sub-15 level). Even for very experienced speedcubers, unless they know multislotting algorithms, these (basically) accidental multislotting do not occur very often. But when they do happen, they often lead to extremely fast single solves.

These examples give you a taste of advanced F2L. Hopefully, you're now convinced that F2L is the most intricate step, and that it is the step with the most opportunities for dramatic speed-ups.

Sample F2Ls

As a final note, none of the techniques discussed here deals with cases where there is no corner and no edge on top. Some special cases of this will be addressed in the advanced F2L section; for the rest, we need to spend three moves (for example, RUR') to bring some F2L pieces to the top layer.