Start with the fixed center piece. Look for adjacent inner-center pieces to form a straight line of 5 pieces of the same color.
When you reach the final two edges, you will no longer have "safe" unsolved edges to swap out. You must use specific algorithms to flip pieces into their correct orientations. 4. Phase 5: 7x7 Parity Algorithms
Build & Design
Because the 7x7 has an odd number of layers, it does not suffer from OLL (Orientation) parity like a 4x4 or 6x6 does. However, it does suffer from during the last two edges stage.
Here is the step-by-step roadmap:
Scramble: 3U 2R' 4F 6L 2D' 5B 3U2 2L 4R' 3D ... (100 moves) Solution (169 moves total): 1. 2R U 2R' U' (pair first center block) 2. 4F' 2U 4F 2U' ... 28. 2R U2 2R' (pair edge triplet) 29. 3U 2L' U' 2L 3U' 30. R U R' U' R U2 R' (first layer of 3x3 phase) ... 169. U' R2 D B2 (final PLL)
Number of positions of a 7x7 cube (ignoring parity constraints): [ \frac24 \times 24!^6 \times 32! \times 64!^3 \times 12! \times 8! \times 3^7 \times 2^11(4!)^24 \times 2^32 \times (2^64) \approx 1.95 \times 10^160 ] Thus heuristics are mandatory. 7x7 cube solver
Turn the cube horizontally. Pick a color (e.g., Green) and build its 5x5 center grid using 1x5 bars. Because the top and bottom (White/Yellow) are protected, you can freely rotate the side layers. Repeat this process for the Red and Blue faces. Step 3: The Last Two Centers (L2C)
Performance