4×4 Edge Pairing

Each edge of the puzzle has two corners at its ends, with two edge pieces between them. The two edge pieces are called wings. For example, along the top front of your 4×4, there is a left wing and a right wing. As another example, feel the right front of your 4×4. It has an upper wing and lower wing.

This article explains methods for pairing those wings without disrupting the six centers. For help solving the six centers, see 4×4 Overview, Reduction, and Centers.

Single Edge Pairing

In summary, pair two wings by moving them into the left front and right front edges. Pair them with a turn that temporarily splits the centers. Move the edge pair to the upper layer, then restore the centers. Here’s how to do that.

Find two wings with the same two tactile markings. They could be anywhere on your puzzle. Call them the two target wings.

Turn only the outer layers so that one target wing is the lower wing of the left front edge. Turning only outer layers will not disturb solved centers.

Next, turn only the outer layers so that the other target wing is the upper wing of the right front edge, taking care to not dislocate the first target wing.

Verify by touch that the two target wings occupy the lower wing position of the left front edge and the upper wing position of the right front edge. They should both have matching markings.

To pair those two wings and move the edge pair to the top front edge, perform this algorithm.

Dw R U R′ Dw′

Dw turns the bottom two layers together.

The first Dw splits four of the six centers, leaving the top and bottom centers intact. It also pairs the two wings. The next three turns move the edge pair to the upper layer so that the centers can be restored without breaking it. The final Dw′ restores the centers.

After the algorithm, verify by touch that the two wings are adjacent to each other in the left and right wings of the top front edge. The edge pair is in the top front.

Use the single edge pairing method with the Reduction Method to gain familiarity with your puzzle. Pay particular attention to how Dw splits the centers but pairs the two wings, and how Dw′ restores the centers.

Triple Edge Pairing

To reduce your solve time, pair multiple edges simultaneously. You can pair three sets of wings with a single Dw turn, and pair three more with a subsequent Dw′.

The Single Edge Pairing method works by loading one wing into the lower wing of the left front edge and another wing into the upper wing of the right front edge. But the cube contains two more vertical edges (left back and right back). By loading additional wings into the left back and right back edges, a single Dw turn will pair three edges.

Start exactly as in the Single Edge Pairing method, loading a wing into the lower wing of the left front edge and its matching wing into the upper wing of the right front edge.

Rotate the entire puzzle in Y. The wing that occupies the upper wing of the old right front edge should now occupy the upper wing of the left front edge.

Feel the wing just below it, in the lower wing of the left front edge. Find the matching wing, which could be anywhere else on the puzzle. Turn only the outer layers so that this matching wing is the upper wing of the right front edge.

Perform another Y rotation. Identify the wing in the lower wing of the left front edge, and turn only outer layers to move its matching wing into the upper wing of the right front edge.

Check your work by rotating the entire puzzle in Y. For three of the four side faces, the lower wing of the left vertical edge should match the upper wing of the right vertical edge.

At this point, perform a Dw turn.

Again, check your work. Three of the four vertical edges should now contain edge pairs. The fourth vertical edge will usually contain unmatched wings, which will be the starting point for the next step.

Because the Dw turn split the centers, we must restore them. Before we do, load three more pairs of matching wings in the opposite arrangement., such that a Dw′ will pair them. To do this, use the following steps.

Rotate the cube in Y until the vertical edge with unmatched wings is the right front edge. Identify the markings on the lower wing of the front-right edge. Find the matching wing anywhere on the puzzle. Turning only the outer layers, move that matching wing into the upper wing of the left front edge.

Rotate the puzzle in Y′ and repeat until three pairs of matching wings have been positioned.

Check your work by rotating the entire puzzle in Y′. For three of the four side faces, the lower wing of the right vertical edge should match the upper wing of the left vertical edge.

Perform a Dw′ turn.

Again, check your work. The centers should be restored. Three of the four vertical edges should now contain edge pairs, and another three edge pairs should be somewhere in the top or bottom layers.

Depending on the remaining unpaired wings, triple edge pairing may be impractical. In such cases, be careful to restore your centers, then pair using the Single or Double Edge Pairing method.

Double Edge Pairing

Commonly, matching wings of two edge pairs are mixed across two edges. For example, you might have two mismatched wings in the left front edge and their two corresponding wings in the right front edge.

These matching wings can be paired with a simple algorithm. However, the markings of the two upper wings of the left front and right front must match. Same for the markings of the two lower wings. If this is not the case, invert the two wings of the right front edge with this algorithm.

R U R′ F R′ F′ R

With two matching wings in the upper wing positions and two more in the lower wing positions, pair both edges with the following algorithm.

Dw R U R′ F R′ F′ R Dw′

That is, perform a Dw, then the algorithm to invert the two wings of the right front edge, then a Dw′.

Verify by touch that the left front and right front contain edge pairs.

Final Thoughts on Edge Pairing

In an ideal arrangement, it’s possible to pair three edges while splitting centers, pair three more while restoring the centers, then repeat to pair a total of twelve. This is rarely the case in practice. Eventually, you’ll encounter two sets of matching wings distributed across two edges, or three sets of matching wings distributed across three edges. Both scenarios can make Triple Edge Pairing impractical. If you encounter such a situation while pairing your final group of edges, and your centers are split, a straightforward approach is to restore the centers, then finish using Double Edge Pairing.