Fewest moves

Solve on paper in as few moves as you can: blocks, edge orientation, domino reduction, skeletons and insertions.

Fewest moves (FMC) is the WCA event where you are given a scramble, paper and an hour, and the shortest written solution wins. Speed does not matter, and neither do algorithms you could execute fast: every move counts, so the craft is finding efficient structures, trying many of them, and joining the best into the final solution.

The rules

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You get the scramble and paper, and 60 minutes in total to find and write a solution (WCA Regulations E2a, E2b).
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The result is the number of moves in the Outer Block Turn Metric: a face turn or a wide (outer block) turn counts one, a rotation counts nothing (E2d, 12a5).
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The solution may not exceed 80 moves counted with rotations (the Execution Turn Metric, E2d1), must be one unambiguous sequence in standard 3x3 notation (E2c2, E2c4), and must not be derived from the scramble (E2e).
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A round is a single attempt, the best of two, or the mean of three (9b4a).

How a solution is built

Nobody finds an optimal solution by hand. A strong solution is built in pieces: a good start that solves a lot in few moves, a skeleton that solves everything except a few pieces, then insertions that fix those pieces somewhere inside the skeleton where moves cancel. Write down every promising start rather than committing to the first, and keep a running move count beside each.

Block building and skeletons

The classic approach builds blocks, as Petrus and Heise do: a 2x2x2 block, extended to a 2x2x3, then the first two layers but a pair, solving pieces where they already are rather than in a fixed order. Stop when what is left is a few pieces that a commutator can cycle: that sequence is the skeleton.

What a good skeleton leaves: three corners cycled and everything else solved.

Checked by the engine: 3 corners moved, 0 edges moved, 0 centers moved

R2 B' L D2 [D, R U R'] D2 L' B R2

Insertions

Three leftover corners are solved by a commutator, a short sequence that cycles exactly those corners. Inserted at the end of the skeleton it costs its full length; inserted at the right point inside the skeleton, with the cycle it needs there, it can cancel moves on both sides. Fewest-moves solvers check every point of the skeleton for the insertion that cancels most. The last-layer forms of these cases are the L3C set.

[R U R', D]

A corner commutator: R U R' D R U' R' D' cycles three corners and nothing else. (8 HTM)

Checked by the engine: [R U R', D] → 3 corners moved, 0 edges moved, 0 centers moved

L3C

18 cases · Three last-layer corners cycled, everything else solved: 18 cases.

Edge orientation

Orienting every edge first, as ZZ does, limits the rest of the solve to turns that keep them oriented, which makes blocks easier to see and to finish. A fewest-moves solver checks edge orientation on all three axes (front-back, left-right and up-down) and starts from the cheapest; the EOLine guide explains how to count the bad edges on an axis.

Domino reduction

The approach most top solvers now use reduces the cube in stages. After edge orientation, domino reduction (DR) orients the corners and the remaining edges on a second axis and puts the middle-layer edges in the middle layer: the cube is then solvable with U, D and half turns of the four sides. Half-turn reduction (HTR) goes further, to a cube solvable with half turns only, and the finish solves it from there. Each stage leaves fewer possible states than the last, so each is easier to search by hand.

A domino-reduced cube: every top and bottom sticker shows the top or bottom colour, and the middle layer holds only its own edges.

R2 U F2 D' L2 U2 B2 R2 D

A quarter turn of a side undoes domino reduction.

Checked by the engine: not dr

R2 U F2 D' L2 U2 B2 R2 D R

NISS and premoves

A solution of the scramble's inverse, written backwards, solves the scramble, and a start that is awkward on the normal scramble is often easy on the inverse. NISS (normal-inverse scramble switch) uses this mid-solve: solve part of the cube on the normal scramble, switch to the inverse with those moves as premoves (moves done before the scramble), continue there, and at the end write the inverse part backwards after the normal part. In the daily fewest-moves challenge, moves in brackets are read as inverse moves.

Practice

Do the daily fewest-moves challenge under a real hour now and then, and spend other sessions on one skill at a time: edge orientation on every axis, short starts, insertions. The scramble is the same for everyone that day, so compare solutions afterwards.

Fewest moves: the whole walkthrough